0 00:00:02,520 --> 00:00:07,680 Jorge Pullin: Our speaker today is Francesco xeni who will speak about high performance spin for new marks. 1 00:00:09,750 --> 00:00:10,170 Francesco Gozzini: Okay. 2 00:00:10,380 --> 00:00:25,620 Francesco Gozzini: Thanks and thanks for the invitation to give this talk for the series so today i'm going to present very recent results in Spain for metrics using the new code that I have written during last year. 3 00:00:26,760 --> 00:00:31,830 Francesco Gozzini: i'd like to mention that many results, based on previous work done here in Mercedes. 4 00:00:35,370 --> 00:00:55,140 Francesco Gozzini: In Georgia, some sarnoff frantically and other people see morning theater and also activity, working with me in interpreting your results from the code and they will, I am also collaborating with Carlos Francisco and her students in the first applications of my code. 5 00:00:56,430 --> 00:01:10,800 Francesco Gozzini: So I would like to start with some motivations for doing medical work, so if you leave that choosing America competitions can benefit understanding and advanced and of the field. 6 00:01:12,540 --> 00:01:22,440 Francesco Gozzini: This is because your metrics, for example, uses different approximations or an approximation so tool and can also suggest the new directions and techniques. 7 00:01:24,210 --> 00:01:29,940 Francesco Gozzini: In this story, I will present you a new IT performance code for competition integration API URL. 8 00:01:31,710 --> 00:01:34,050 Francesco Gozzini: In that will show you the very first applications. 9 00:01:35,280 --> 00:01:45,570 Francesco Gozzini: I think that, apart from the interesting results about the API model this work is also interesting because it provides new powerful and easy to use tools. 10 00:01:46,050 --> 00:01:47,040 For the Community. 11 00:01:49,050 --> 00:02:02,400 Francesco Gozzini: Let me start with the very quick introduction to spin forms and to the API model, just to set the notation because I assume that most of you are already familiar with this concept. 12 00:02:03,300 --> 00:02:12,120 Francesco Gozzini: So in covariance take your G we work with graphs and triangulation made by forcing business the trader and other geometrical objects. 13 00:02:13,080 --> 00:02:30,720 Francesco Gozzini: The theory defines quantum transition amateurs between the states of geometry, and they are that are defined on the strangulations is being formed represents a transitional period between us be natural graphs and given a gauge group G we call her the same form. 14 00:02:31,860 --> 00:02:37,740 Francesco Gozzini: We representation of G on the faces, while we color the edges with minors. 15 00:02:38,790 --> 00:02:53,280 Francesco Gozzini: There is a clear geometrical interpretation for the nation's so the very basics of this been phone corresponds before simplex in nz corresponds with a stranger and the face corresponds to the triangle. 16 00:02:54,780 --> 00:03:05,100 Francesco Gozzini: We are interested in his influence, because they are a way of implementing the fine man, but integral for gravity the integral becomes what is called the state some. 17 00:03:06,210 --> 00:03:12,990 Francesco Gozzini: Is the state some and the partition function is the some overall bike degrees of freedom of this beam from. 18 00:03:15,900 --> 00:03:27,720 Francesco Gozzini: The most promisingly more than for the position of GR in was painful formalism is called a prl fk model and we call it the API model for sure. 19 00:03:28,860 --> 00:03:39,240 Francesco Gozzini: The fundamental block of the model is the vertex on p2p we need some representation, the theory of the Lawrence group to define the model. 20 00:03:40,500 --> 00:03:51,630 Francesco Gozzini: So the unitary reducible representation of the principal serious office in to see our liability by very unknown they're all in the same integer number K. 21 00:03:53,760 --> 00:04:04,980 Francesco Gozzini: We can write a basis for these use for the presentation if we single out of the generators ln K of the St Theresa group officer to see. 22 00:04:06,240 --> 00:04:06,840 Francesco Gozzini: and 23 00:04:08,010 --> 00:04:23,070 Francesco Gozzini: We can write to the basis using these generators, the most important ingredient of the pyramid model is the so called way mapper in this is a projection of so true you're upset to Western to see REPS. 24 00:04:24,420 --> 00:04:39,840 Francesco Gozzini: era, you write the mapping as an injection of the beginner mattresses office who choose to be clear mattresses Office and to see where their mattresses are a basis for the space of square impeccable functions on. 25 00:04:43,830 --> 00:05:07,230 Francesco Gozzini: Okay, we can now define what is the vertex amplitude so we take a spin from vertex and then we sphere on eaten we get to graph if they're sick, the sphere with the vertex on the boundary on this graph where we have the same boundary is the space as the inverse base of the quantum realm. 26 00:05:09,270 --> 00:05:20,400 Francesco Gozzini: And there are many possible representation for the vertex samples, but the one that is most relevant here is the one we spend some intern trainers and this is the formula. 27 00:05:21,420 --> 00:05:38,730 Francesco Gozzini: In this formula, you see the contraction of entertainers from the boundary with a group or aging integral over so to see, and there is wanting to go out for the Chair of the of the Center of the vortex minus one one is to be. 28 00:05:40,950 --> 00:05:42,810 Francesco Gozzini: removed from the integration. 29 00:05:44,550 --> 00:05:53,700 Francesco Gozzini: OK, so the purpose of this talk is to get the numbers out of this formula so for doing these one is some. 30 00:05:54,990 --> 00:05:57,570 Francesco Gozzini: formula can be implemented on the computer. 31 00:05:58,860 --> 00:06:02,100 Francesco Gozzini: way to proceed, was put forward by bit theology. 32 00:06:03,180 --> 00:06:09,270 Francesco Gozzini: We can split the previous formula is converting some over what I call the shells. 33 00:06:10,560 --> 00:06:22,650 Francesco Gozzini: of objects that are more easy to compute they're easier to compute on the computer, that is, the 15 symbols and what has been called the booster coefficients that seat along the edge is. 34 00:06:24,750 --> 00:06:38,970 Francesco Gozzini: The convergence some comes from speaking, the product of infineon dimensional europe's into an infinite some overview plus being lovers the species here with it could be classmates. 35 00:06:40,020 --> 00:06:49,020 Francesco Gozzini: And I call a Shell homogeneous cut off on these vehicles planes So if you put a cut off here, this is what a caution. 36 00:06:52,590 --> 00:07:01,230 Francesco Gozzini: In this picture, you can see, the next steps of the splitting so the non compact integrals these boxes. 37 00:07:02,460 --> 00:07:13,140 Francesco Gozzini: are isolated into the symbols, with the loop system, these are called a booster coefficients while this transfer on the writer, I hope you can see my pointer. 38 00:07:14,370 --> 00:07:15,960 Francesco Gozzini: The strength on the right. 39 00:07:18,810 --> 00:07:22,110 Francesco Gozzini: format, the 15 JC most of the for the left. 40 00:07:24,300 --> 00:07:28,320 Francesco Gozzini: This is the complete formula, and you can see that. 41 00:07:29,460 --> 00:07:36,240 Francesco Gozzini: It is defined as the infield limiting in this parameter delta as that I call the number of shares. 42 00:07:39,000 --> 00:07:47,460 Francesco Gozzini: Of course we get the access to the in disneyfied limited but numerically one is to stop at some point, so I will have to talk much. 43 00:07:48,120 --> 00:08:05,250 Francesco Gozzini: about this parameter in the forum in his life, you can see here are the other ingredients for the rooster coefficients are the symbols before and the 15 G symbol, these are defined more precisely in. 44 00:08:06,360 --> 00:08:31,530 Francesco Gozzini: This slide so the 15 Jason what is the usual one for from BF theory, it is a contraction in this expansion is a contraction of 560 scene was while in the booster coefficients you can see the compact integrations of for the these more matrix elements. 45 00:08:32,910 --> 00:08:44,940 Francesco Gozzini: Of the audience group, needless to say, these objects are computationally expensive and one is to do an enormous amount of combinations of of speakers been our best to compete. 46 00:08:46,560 --> 00:08:46,890 For. 47 00:08:49,860 --> 00:08:52,530 Francesco Gozzini: The American challenges more completely. 48 00:08:53,220 --> 00:09:08,610 Abhay Vasant Ashtekar: Before you go to the numerical challenges, can I just ask conceptual questions if you go back to slides that we helpful Thank you know what one before yeah yeah so so the what you call shells are now they carry label which is row and cakes that right. 49 00:09:10,620 --> 00:09:18,300 Francesco Gozzini: In the shares are cut off on these beans so. 50 00:09:19,530 --> 00:09:30,780 Francesco Gozzini: If you put the parameter, that is to zero, you have zero shells with equals zero shells if you put the parameter that test one I call it, why shell. 51 00:09:32,940 --> 00:09:47,310 Francesco Gozzini: And these these vehicles peace and they're these coefficients here and the 15 Jason working they enter, of course, in these more mattresses, and this is. 52 00:09:48,270 --> 00:09:50,940 Abhay Vasant Ashtekar: Right, but you, in passing, you just mentioned that if you. 53 00:09:52,320 --> 00:10:00,600 Abhay Vasant Ashtekar: calculate the real object which is we're taking the limit that are you saying that limit is infinite I didn't understand you said something which is quick to understand. 54 00:10:02,280 --> 00:10:04,470 Francesco Gozzini: yeah yeah yes so. 55 00:10:06,330 --> 00:10:11,520 Francesco Gozzini: The Fulani to show the full P amp between these limits. 56 00:10:12,180 --> 00:10:20,760 Francesco Gozzini: And yes, comes from the fact that when you eat you see in this box when you split the infinite dimensional product of. 57 00:10:22,950 --> 00:10:24,810 Francesco Gozzini: These elements of essence to see. 58 00:10:25,860 --> 00:10:31,050 Francesco Gozzini: Then, that the disarm is in fact infinite because. 59 00:10:31,890 --> 00:10:34,080 Carlo Rovelli: I can, I can I can I just interject maybe they said. 60 00:10:36,420 --> 00:10:37,320 Carlo Rovelli: Well you're just. 61 00:10:37,440 --> 00:10:41,130 Carlo Rovelli: saying is that this infinite number of terms is not saying he's not saying that. 62 00:10:42,540 --> 00:10:46,500 Abhay Vasant Ashtekar: Right, but do you do good exactly that was my. 63 00:10:47,790 --> 00:10:51,480 Abhay Vasant Ashtekar: But are used, but are you saying it is gorgeous and in spite of the treatment. 64 00:10:53,550 --> 00:11:01,500 Francesco Gozzini: He is converting because the Sam the dap lumpy to is well defined when it is well defined, of course, so. 65 00:11:02,520 --> 00:11:05,700 Abhay Vasant Ashtekar: But I mean it's a submission, this is a fact. 66 00:11:06,810 --> 00:11:12,480 Francesco Gozzini: it's a fact is a it's a different way of writing the writing. 67 00:11:13,230 --> 00:11:19,830 Abhay Vasant Ashtekar: But when they're all kinds of divergences in between, is it oh you're saying that you're keeping the number of words is fixes. 68 00:11:22,620 --> 00:11:23,040 Carlo Rovelli: that's here. 69 00:11:23,970 --> 00:11:26,280 Carlo Rovelli: Sorry, this is a single vertex. 70 00:11:26,430 --> 00:11:28,590 Abhay Vasant Ashtekar: single what exactly is fixed up. 71 00:11:28,890 --> 00:11:33,180 Carlo Rovelli: Oh good feelings that this is fine, it yeah yeah. 72 00:11:33,390 --> 00:11:35,130 Abhay Vasant Ashtekar: It single what exactly what I didn't get. 73 00:11:35,520 --> 00:11:35,820 Francesco Gozzini: Thank you. 74 00:11:36,120 --> 00:11:37,110 Abhay Vasant Ashtekar: Thank you know that's fine. 75 00:11:37,410 --> 00:11:41,820 Francesco Gozzini: I will talk about divergent series, but these are different topics. 76 00:11:42,210 --> 00:11:48,060 Carlo Rovelli: there's not yet the some over the the gay, which is a Bible, do you think about that. 77 00:11:50,580 --> 00:11:50,910 Thank you. 78 00:11:52,020 --> 00:11:54,480 Francesco Gozzini: Okay, thanks for the clarifying question. 79 00:11:59,400 --> 00:12:01,620 Francesco Gozzini: So doing medical challenges. 80 00:12:03,270 --> 00:12:06,210 Francesco Gozzini: For computing a single vertex amplitude. 81 00:12:08,340 --> 00:12:19,500 Francesco Gozzini: One has to start by fixing a boundary state and the number of shares, because as a as a save that and we have to pick a finite number of shares the final cut off. 82 00:12:20,970 --> 00:12:39,450 Francesco Gozzini: And then one is to computers, they asked us to to symbols and all the booster coefficients for all the spin combinations of these shares, then one has to multiply and some over all these share so very well developed well as others. 83 00:12:40,560 --> 00:12:47,790 Francesco Gozzini: And then there is a contraction with the boundary states in in the end, of course, we have to study the convergence in these. 84 00:12:49,080 --> 00:12:50,670 Francesco Gozzini: shape parameter because. 85 00:12:52,230 --> 00:12:52,920 We know that. 86 00:12:55,170 --> 00:12:56,670 Francesco Gozzini: drew me to this limit. 87 00:12:58,170 --> 00:12:59,790 Francesco Gozzini: To the number of shares going to. 88 00:12:59,790 --> 00:13:00,810 Abhay Vasant Ashtekar: infinity but, of course. 89 00:13:00,810 --> 00:13:01,530 Francesco Gozzini: One wants to. 90 00:13:02,790 --> 00:13:09,810 Francesco Gozzini: To get good convergence with a low number of shares to compute things quickly. 91 00:13:10,890 --> 00:13:21,480 Francesco Gozzini: And this is just for a single vertex for many vertices, these are the steps so one or two, though the speed from graph and write down all the submission over barking terminus and like faces. 92 00:13:22,050 --> 00:13:41,490 Francesco Gozzini: In here the is a by was thinking, there are possible divergences, because the Samsung over the bike faces can be infinity so there, one has to put some cut offs and. 93 00:13:42,540 --> 00:13:50,550 Francesco Gozzini: and continue with that after that we have to compute the single worst examples for all the combination of biking determinism faces. 94 00:13:51,000 --> 00:14:04,290 Francesco Gozzini: Then multiply and Sam over all these combinations contract with the boundary states, it is supposed to be finite and then we have to study the convergence in all the cutoff parameters that we impose the interesting. 95 00:14:06,150 --> 00:14:10,680 Francesco Gozzini: So disease disease, like a daunting task, but it can be done. 96 00:14:11,760 --> 00:14:13,710 Francesco Gozzini: And this is what. 97 00:14:15,210 --> 00:14:25,890 Francesco Gozzini: has been done here in Mercedes, since a few years with the sm to see form library, so this is a library written in the C language in. 98 00:14:28,260 --> 00:14:31,410 Francesco Gozzini: The library specifically to perform these competitions. 99 00:14:32,730 --> 00:14:37,410 Francesco Gozzini: It includes the computation of laurentian imperial lampeter in bfm. 100 00:14:39,510 --> 00:14:42,300 Francesco Gozzini: queries disco efficient, and it was wonderful it is. 101 00:14:44,070 --> 00:14:44,790 Francesco Gozzini: For. 102 00:14:46,050 --> 00:15:02,910 Francesco Gozzini: Low parameters so low speeds and low number of shares young people are competing competing in seconds on the laptop and from the previous formula of the speaking, we can give a rough estimate of the scaling of the time needed if we increase it. 103 00:15:04,050 --> 00:15:10,530 Francesco Gozzini: If we increase the average boundary spin and the number of shares in the vertex, so there is. 104 00:15:11,070 --> 00:15:19,260 Francesco Gozzini: This power law where a Jay is the average boundaries beam, and that is is the number of shares and you see, that is. 105 00:15:20,070 --> 00:15:35,370 Francesco Gozzini: Power load to the fourth power in the spoon in the six power in the number of shares these are plots from the original paper, and you can see that, indeed, the system eight matches pretty well that the data. 106 00:15:37,500 --> 00:15:48,870 Francesco Gozzini: These library has been used them already to get some interesting results, the first one has been a test of the semi classical awesome topics of the vertex. 107 00:15:49,800 --> 00:16:06,060 Francesco Gozzini: The task is the following so one constructs up dnr fluoridation for simplex and then wants to compute the amputee medically then wireless case the boundaries beans in the parameter Lambda, that is, the. 108 00:16:07,230 --> 00:16:25,680 Francesco Gozzini: The parameter this case, the boundaries piece, and then one can compare with the analytical formula that I every year for the Euclidean for simplest case and also for the relation, for simplest we're not a bleed the frequency of distillations depends on the barbarian is the parameter. 109 00:16:28,170 --> 00:16:43,110 Francesco Gozzini: I can show you the applause from the previous works, so the plot of the left and show the shows the Euclidean mckay's and you can see the normal metrics matches pretty well the analytical formula. 110 00:16:45,990 --> 00:16:57,630 Francesco Gozzini: Even at lowes beans and we've very low number of shares, while, on the right, you can see, the location case, and here the picture is not so nice. 111 00:16:58,020 --> 00:17:07,170 Francesco Gozzini: Because due to the particular boundary configuration one is to go to very high speeds for their underneath there's the same topics. 112 00:17:07,980 --> 00:17:25,980 Francesco Gozzini: and apparently one also has to use more than just one or two shares, so you can see that these competition match the order of magnitude and the scaling but not the destination someday to west. 113 00:17:27,480 --> 00:17:28,500 Francesco Gozzini: Another results. 114 00:17:29,490 --> 00:17:33,870 Abhay Vasant Ashtekar: Sorry, good too, but do you understand that the difference why there is a difference, I mean. 115 00:17:34,920 --> 00:17:45,960 Abhay Vasant Ashtekar: Theoretically, we know that one is a compact group and others and non contact group, but do you sort of can you pinpoint in the you know what what is that is that computer has problems with it so conversions on. 116 00:17:48,450 --> 00:17:49,020 Abhay Vasant Ashtekar: guess. 117 00:17:50,880 --> 00:18:03,150 Francesco Gozzini: yeah, we know that the 30s for the Euclidean case works, also for the gift theory so for the 15 Jason was so you can compute the graph on the left, after. 118 00:18:03,930 --> 00:18:23,670 Francesco Gozzini: The just in a BF theory and it works really well, and this is basically the case because if you stay at the very low number of shares things work out nicely in the Euclidean case and also there is a technical fact because the. 119 00:18:25,320 --> 00:18:31,230 Francesco Gozzini: The boundary space for the Euclidean case, our own genius so they are all equal and. 120 00:18:32,130 --> 00:18:41,430 Francesco Gozzini: If you said, the parameter Lambda to 40 you are looking at the screen software there and just when, but in the morning junkies. 121 00:18:42,630 --> 00:18:51,270 Francesco Gozzini: The configuration that was founded by my colleagues here in marcell has the boundaries piece five and two. 122 00:18:52,080 --> 00:19:01,560 Francesco Gozzini: Interesting numbers and if you scale Lambda you, for example, if you put Lambda, then you already have Spencer for their 15 and. 123 00:19:02,370 --> 00:19:17,700 Francesco Gozzini: 20 So you see that you already in Lambda 10 in the picture on the right, you are at the at the far right most points in the picture of the left, so this is a technical reason for. 124 00:19:18,180 --> 00:19:19,950 Carlo Rovelli: Can I can I get a comment here. 125 00:19:20,190 --> 00:19:23,460 Carlo Rovelli: Is my just because I think many people. 126 00:19:24,510 --> 00:19:33,540 Carlo Rovelli: don't know this terminology because it's pretty exciting game so here up then endurance and do not mean that. 127 00:19:34,290 --> 00:19:49,590 Carlo Rovelli: The PM team in their entirety there's other one is the vessel for their their section to see where it will affect this is always to go into theory it's always the same formula it's always the same, as I said, to see will be the closest thing there. 128 00:19:51,480 --> 00:20:05,340 Carlo Rovelli: But the previous results and elliptical that show that this month example to do there is generic can suppress that unless the boundary configuration sacrifice and conditions. 129 00:20:05,910 --> 00:20:16,800 Carlo Rovelli: And these conditions are of possible case, so the verdict is not to press the two possible case either, and this is the what is called the length and, if you think that this is. 130 00:20:17,490 --> 00:20:30,510 Carlo Rovelli: A fortune glitzy merkin costly space that would be betrayed are needed for the goal, but also in another case, so the length and theory vertex is not suppressed, that if. 131 00:20:32,130 --> 00:20:38,520 Carlo Rovelli: The boundary has a property that it can be immersed in a up in four dimensional space. 132 00:20:40,380 --> 00:20:47,100 Carlo Rovelli: simple example is to imagine the transition from nothing to a full sphere full scale and we must. 133 00:20:49,710 --> 00:20:54,390 Carlo Rovelli: Be so careful not confused, this will be presenting lengthy. 134 00:20:56,070 --> 00:20:58,500 Abhay Vasant Ashtekar: But, at the very good so you're saying that everywhere, the. 135 00:21:00,180 --> 00:21:02,190 Abhay Vasant Ashtekar: representation refrigeration to see. 136 00:21:02,520 --> 00:21:05,160 Abhay Vasant Ashtekar: Right it's just only the boundary yeah. 137 00:21:05,280 --> 00:21:12,630 Carlo Rovelli: Alright, so that is the classification of possible baldo data that you won't see that there are lots of places. 138 00:21:15,000 --> 00:21:15,540 Carlo Rovelli: Yes. 139 00:21:17,070 --> 00:21:26,340 Abhay Vasant Ashtekar: But, but what happens if we just consider I mean look at the ones which are which are possibly suppressed then do get convergence and everything other boundary data. 140 00:21:30,360 --> 00:21:34,140 Francesco Gozzini: So, if we take the duration theory is we are doing this. 141 00:21:34,470 --> 00:21:37,590 Abhay Vasant Ashtekar: Now, but now there's not a lot in general included right because you're talking about. 142 00:21:37,920 --> 00:21:39,750 Abhay Vasant Ashtekar: lorenzen Euclidean as Carver explained. 143 00:21:39,750 --> 00:21:46,950 Abhay Vasant Ashtekar: refers to the boundary data how whether it can be embedded the boundary data I can get a better price, but now i'm just considering. 144 00:21:47,760 --> 00:21:56,400 Abhay Vasant Ashtekar: Generic boundary data which maybe you cannot embed a nuclear in order, I mean I just generate boundaries, without this requirement not not any specific Barbara date. 145 00:21:57,030 --> 00:22:06,210 Abhay Vasant Ashtekar: In which case, Carlos is that the amplitude is suppressed yeah yes, you would see this film, you should be able to calculate it and see that is suppressed can do that. 146 00:22:06,600 --> 00:22:07,050 yeah sure. 147 00:22:08,430 --> 00:22:09,000 Abhay Vasant Ashtekar: So this is. 148 00:22:09,540 --> 00:22:10,920 Francesco Gozzini: This is presenting the paper. 149 00:22:12,000 --> 00:22:20,940 Abhay Vasant Ashtekar: That I referenced in recording or so the statement is that there is a large class of these large class of. 150 00:22:21,780 --> 00:22:34,110 Abhay Vasant Ashtekar: Initial data outer boundary data for which everything works, the new medically, but you are more interested in the ones in which entities are suppressed and therefore you're focusing on that, but is that is that a correct statement. 151 00:22:34,770 --> 00:22:48,480 Francesco Gozzini: Yes, and we are next word for virtually all possible boundary data, but we are interested in very particularly particular boundary data that represents Euclidean or duration for some species, yes. 152 00:22:49,590 --> 00:22:56,340 Abhay Vasant Ashtekar: But the question was about convergence right, I mean in the in this case there is you're showing that the difference in the two cases right. 153 00:22:57,540 --> 00:23:03,960 Abhay Vasant Ashtekar: So that will disappear if I just use a generic boundary data without looking at specific ones. 154 00:23:04,140 --> 00:23:06,330 Carlo Rovelli: That came with the scenes. 155 00:23:07,980 --> 00:23:11,550 Carlo Rovelli: screens the the amplitude is exponential. 156 00:23:12,480 --> 00:23:13,500 Abhay Vasant Ashtekar: And, but we'll see is that. 157 00:23:13,530 --> 00:23:15,870 Abhay Vasant Ashtekar: Once he is that in the new relics that these exposures. 158 00:23:15,900 --> 00:23:16,620 Francesco Gozzini: are present, yes. 159 00:23:16,890 --> 00:23:20,460 Abhay Vasant Ashtekar: Yes, okay good Thank you so much okay thanks. 160 00:23:21,600 --> 00:23:22,350 and 161 00:23:25,230 --> 00:23:34,350 Francesco Gozzini: Okay, so we were at the point where we see that in the the plot on the left is not completed. 162 00:23:35,460 --> 00:23:41,250 Francesco Gozzini: In the end, they one wants to go to higher values of Lambda in high gear number of ships. 163 00:23:44,640 --> 00:23:51,270 Francesco Gozzini: So I was starting roughly two okay to introduce or saw what they call the flatness problem. 164 00:23:52,380 --> 00:24:01,590 Francesco Gozzini: So there is a pretty extensive literature to on this music problem, and here I don't want to discuss it in detail, but I just want to give you the simplest argument. 165 00:24:02,040 --> 00:24:13,980 Francesco Gozzini: Lead into that because I am interested in the matrix so briefly the problem comes from the fact that that classical in the area reggie action is linear in the areas. 166 00:24:15,630 --> 00:24:30,450 Francesco Gozzini: and see serious or dynamical variables in our speed for more this if one bar is so we respect to them, and whether they act as a regular login as multiply yes and force the other terms in the action the to be zero. 167 00:24:31,860 --> 00:24:35,280 Francesco Gozzini: That is the force the Defense dangles to be zero. 168 00:24:36,510 --> 00:24:56,670 Francesco Gozzini: And this is the essence of the problem, so that, apparently, if one performs this variation between I usually one find only the flat solution and the contributions to the party integral are only given by Philip geometries. 169 00:24:57,810 --> 00:25:04,860 Francesco Gozzini: Of course, there are many caveats and subtleties in this argument in Indeed, this is the reason why the problem is to not settle. 170 00:25:06,060 --> 00:25:23,040 Francesco Gozzini: But indeed there is a simple simple way of proving that the statement is false and that is, it is enough to find the contact Center so medically we can try to do that, so we can construct the speed from with internal faces. 171 00:25:24,750 --> 00:25:33,180 Francesco Gozzini: And we can pause boundary data that correspond both to flatter in the Court configurations. 172 00:25:34,320 --> 00:25:42,600 Francesco Gozzini: And then, that we can try to see if indeed the contributions to the State sam's are suppressed in the case of non zero deficient fingers. 173 00:25:43,680 --> 00:25:50,100 Francesco Gozzini: So we the the last year in the case of the BF vertex and. 174 00:25:51,660 --> 00:26:14,580 Francesco Gozzini: In the plots you can see that our algorithm found a southern point in both of the flat in court case here i'm plotting so we have been from with wine internal face that there's this been excellent, and we can compute the amplitude the varying X and then we. 175 00:26:16,080 --> 00:26:18,600 Francesco Gozzini: We find that in the integral. 176 00:26:22,140 --> 00:26:34,470 Francesco Gozzini: Contributing geometry would show is southern point in these plots in the the received, but both in the flat case and in the court case, so this is a first indication that. 177 00:26:35,670 --> 00:26:43,380 Francesco Gozzini: The acid into curvature constraints of the flatness program are not seeing this case. 178 00:26:43,920 --> 00:26:44,310 Abhay Vasant Ashtekar: i'm sorry. 179 00:26:45,600 --> 00:26:54,060 Abhay Vasant Ashtekar: Maybe the terminology, but very safe bfd I thought in BF theory, everything is flat so maybe you're using the word in some other way. 180 00:26:56,580 --> 00:26:59,010 Francesco Gozzini: yeah, this is a delicate point so. 181 00:27:02,430 --> 00:27:05,130 Francesco Gozzini: Indeed, in classical BF theory. 182 00:27:07,140 --> 00:27:08,100 The. 183 00:27:09,270 --> 00:27:10,560 Francesco Gozzini: The connection, that is. 184 00:27:12,660 --> 00:27:21,030 Francesco Gozzini: The dynamic variable of the theory has only flat solution, as we see when we do the variation of the of the classical theory. 185 00:27:22,800 --> 00:27:29,040 Francesco Gozzini: But still, one can I can do the quantum theory and can try to to construct. 186 00:27:30,450 --> 00:27:37,140 Francesco Gozzini: boundary data that corresponds to geometries that non that have different angles. 187 00:27:38,340 --> 00:27:43,260 Francesco Gozzini: On the internal triangle, the eternal zero in this is what we're looking at. 188 00:27:44,910 --> 00:27:52,950 Abhay Vasant Ashtekar: So you're saying that says boundary data appear insider points, therefore, that should be kind of a classical solutions with i'm confused. 189 00:27:54,780 --> 00:27:59,730 Francesco Gozzini: A yeah, this is a bit confusing if we if we consider a BF theory. 190 00:28:02,490 --> 00:28:03,870 Francesco Gozzini: But the point is that. 191 00:28:07,860 --> 00:28:18,030 Francesco Gozzini: We are not looking at the delivery to the connection when we do gift theory, so we are not, of course, we are not seeing that in this plot. 192 00:28:20,940 --> 00:28:22,800 Abhay Vasant Ashtekar: Maybe we can come back and i'm still confused. 193 00:28:24,420 --> 00:28:26,730 Francesco Gozzini: Okay okay we'll try to be more clear. 194 00:28:27,960 --> 00:28:28,290 lead. 195 00:28:30,630 --> 00:28:31,740 Francesco Gozzini: him. 196 00:28:33,540 --> 00:28:43,680 Francesco Gozzini: So these plots were produced with the BF vertex but one would like to produce them or so, with the full API vertex. 197 00:28:45,900 --> 00:29:00,510 Francesco Gozzini: OK, and now we came after these unnecessary preliminary remarks to the main point of the senior, so I would like to present to you a completely new version of the library that they have rewritten from scratch. 198 00:29:02,070 --> 00:29:07,560 Francesco Gozzini: The name is nice to see from next because there's still many DSM meters come from the previous version. 199 00:29:09,180 --> 00:29:15,540 Francesco Gozzini: The new library use a sufficient data structures and multiple parallel position, I used to achieve maximum perform. 200 00:29:16,830 --> 00:29:22,740 Francesco Gozzini: So the library is written, you see, but it provides an interface in the language Julia. 201 00:29:23,970 --> 00:29:27,570 Francesco Gozzini: So essentially analysis, there is a fuel injector activity. 202 00:29:32,070 --> 00:29:39,450 Francesco Gozzini: You can see an example of using the library we're just in a few lines you can complete the API lumpy tools for. 203 00:29:41,010 --> 00:29:44,460 Francesco Gozzini: A single vertex with many different values of the sharepoint. 204 00:29:46,530 --> 00:30:01,920 Francesco Gozzini: As for the performance ISA here I you're on a simple test on my laptop comparing the old version with the previous with with the new version and in the Plus, you can see the results and notice that a timescale is located. 205 00:30:03,120 --> 00:30:21,660 Francesco Gozzini: So the more boundaries increases the more efficient to the new cody's in this table I put the row increasing performance is for a few cases so on my laptop, we can see an increase of performances up to 10,000 times, for example in in these few points. 206 00:30:23,580 --> 00:30:32,100 Francesco Gozzini: I don't want I don't want to spend too much time talking about technical details, because in the end we wanted to physics and not informatics. 207 00:30:32,760 --> 00:30:46,980 Francesco Gozzini: But I would just try to mention if you keep on instead of the code so important improvement comes from using efficient data structures, these are multi dimensional array and they call them in source. 208 00:30:48,840 --> 00:31:09,360 Francesco Gozzini: multiplying matrices is one of the Miss most basic tasks, since the dawn of informatics so you can imagine that this is a task that really can squeezing the highest performers possible out of the cpu and indeed there are optimize the code for doing that in there, called the ass. 209 00:31:10,560 --> 00:31:23,760 Francesco Gozzini: In the key results if that is possible to write the API real estate some as a series of matrix operations in this way a vertex can be represented as a tensor in the five intertwined or indices. 210 00:31:25,170 --> 00:31:32,340 Francesco Gozzini: I use this notation here in the States some, there is the contraction of these vertex dangers. 211 00:31:34,620 --> 00:31:50,220 Francesco Gozzini: In other substantial improvement comes also from the new code for computing booster coefficients I have completed or if you had written the arbitrary procedure with us, and I have implemented a vastly more efficient and precise me to the American integration. 212 00:31:51,270 --> 00:32:03,090 Francesco Gozzini: which also provides our estimates also the booster coefficients can be packed into 10 source and then the vertex everything can be computed content in bunches and bunches of these things or. 213 00:32:06,660 --> 00:32:13,590 Francesco Gozzini: Importantly, the vertex Sam sorry easily parallelizable or are embarrassingly parallel and. 214 00:32:16,110 --> 00:32:28,830 Francesco Gozzini: So the code can divide their visitors been sick or many nodes and then each know divides them across all available cpus so that using for a simple 1000 cpus effectively reduces the time by a factor 1000. 215 00:32:30,540 --> 00:32:36,870 Francesco Gozzini: notice that 1000 cpu which is just a very modest number in the domain of high performance computing. 216 00:32:38,220 --> 00:32:39,240 Francesco Gozzini: And not only that. 217 00:32:40,320 --> 00:32:53,160 Francesco Gozzini: In recent years, the use of gpu brought a huge increase in performance and the new code can use gpus and so since the vertex is represented under the hood as a matrix. 218 00:32:53,790 --> 00:33:07,320 Francesco Gozzini: We can compete compete with many vertices by feeding them to the gpus and they are extremely efficient in multiplying matrices so in the Plaza I show the results of two very simple tests. 219 00:33:08,400 --> 00:33:18,750 Francesco Gozzini: In which you can see again a possible gain of thousand times in performances here in the, for example, constructing the vertex with the fine accrued interest rates. 220 00:33:20,700 --> 00:33:21,210 Francesco Gozzini: Okay. 221 00:33:22,260 --> 00:33:40,260 Francesco Gozzini: After this technically marcia it's time to show some application of the Code, these are the very first application that I have worked with in the last month, we are still collecting data, improving the plots and integrating them, so this is really work in progress, the first application. 222 00:33:41,340 --> 00:34:00,540 Francesco Gozzini: Is the vertex us in politics, which was lifting competing previous work, as I have shown you in the previous blossom the Canadian case work pretty well, but the intervention K was was not conclusive in narnia very low values of monta hi sorry and. 223 00:34:01,920 --> 00:34:09,840 Francesco Gozzini: We, the previous work for each day, only no values of Lambda in low value of the number of shares. 224 00:34:13,980 --> 00:34:16,800 Francesco Gozzini: Within the new code, we can study. 225 00:34:17,850 --> 00:34:24,750 Francesco Gozzini: We can reach very large values of Lambda in many shares from we can study many interesting phenomena, for example. 226 00:34:25,290 --> 00:34:41,760 Francesco Gozzini: We can start a conversation the show parameter, we can study the convergence very the barbarian is the parameter here we can see them set of us in particular solution that one was not present in the previous block and we can study the quantum corrections to the same topics. 227 00:34:43,380 --> 00:34:50,190 Francesco Gozzini: So here is a lot of the new coda with the Burberry me the parameters set to 0.3. 228 00:34:51,360 --> 00:34:58,710 Francesco Gozzini: So the blue line shows the analytic value of the same topics and. 229 00:34:59,910 --> 00:35:10,800 Francesco Gozzini: The points the show the cases the computer that time and zero shares to share and fortunes but I remember you that if we increase the number of shares, we are supposed to to. 230 00:35:11,790 --> 00:35:22,080 Francesco Gozzini: measure the full appear and model and increasing the value of Lambda we are supposed to me as a simplistic form, indeed, we see that in the blotter. 231 00:35:24,120 --> 00:35:24,720 Francesco Gozzini: So. 232 00:35:25,830 --> 00:35:43,440 Francesco Gozzini: We can see that increasing the number of shares from zero to four we gather the REACH, the correct value of the same topics, but then, when we increase Lambda even for shares to start to fall short of this in politics, so it appears that. 233 00:35:44,460 --> 00:35:50,370 Francesco Gozzini: The more we increase Lambda the more shares, we need, and the more the computation experience. 234 00:35:51,390 --> 00:35:58,680 Francesco Gozzini: springs are pretty large in the speaker on indeed for the last point, the boundaries piece are afforded to hundreds. 235 00:36:02,340 --> 00:36:13,560 Francesco Gozzini: notice also that from Spain, about the 15 the red point and click points is start to diverge and this signal that the. 236 00:36:14,880 --> 00:36:15,630 Francesco Gozzini: Two shells. 237 00:36:16,740 --> 00:36:24,540 Francesco Gozzini: Here at 15 are start not to be enough to get conversions to the true value of the API. 238 00:36:26,130 --> 00:36:29,760 Francesco Gozzini: Is plot required about three days and 300 cpu usage. 239 00:36:30,870 --> 00:36:39,660 Francesco Gozzini: Out of which one day to get the points the Lambda for tea and around eight hours, just to get the last point before. 240 00:36:42,210 --> 00:36:47,280 Francesco Gozzini: We move now to the case of gamma 2.0 which is not so nice. 241 00:36:48,720 --> 00:36:49,320 Francesco Gozzini: So. 242 00:36:50,370 --> 00:36:55,350 Francesco Gozzini: Now we see that for shares are not enough to get the. 243 00:36:57,330 --> 00:36:59,250 To get to the value of the same topics. 244 00:37:01,080 --> 00:37:02,250 Francesco Gozzini: We can see that. 245 00:37:03,300 --> 00:37:19,440 Francesco Gozzini: For Lambda is lowest end the core two shares in it for shares of stock to be there, as already here we can see fluctuations, so the convergence is not reached the end is substantially before the case with gamma zero point. 246 00:37:21,060 --> 00:37:38,880 Francesco Gozzini: But what is nice is that we can clearly see them set of oscillations so we don't see you solutions in the case of zero shares and two shares, but we see that we for shares in the the the curse starts was he late, and so it gets to a minimum and then he starts to go up again. 247 00:37:41,310 --> 00:37:55,500 Francesco Gozzini: It is not not targeted to increase the number of shares to get for simple to six so in the next week, so we launched the computation at six shares the cluster that you have access to in marcy. 248 00:37:56,580 --> 00:38:05,220 Francesco Gozzini: And this will run in a few days are using about 1000 views so I estimate to finish the competition with you guys. 249 00:38:06,990 --> 00:38:14,910 Francesco Gozzini: So this is a like the new results for the rotation, as some topics and I moved to the flatness problem. 250 00:38:17,790 --> 00:38:26,310 Francesco Gozzini: So, as I mentioned, it is possible to computing lyrically the amplitude of speed for with internal faces and then look for southern points. 251 00:38:27,780 --> 00:38:41,220 Francesco Gozzini: In this particular case, we can define a spoonful within three vertices and one internal face and this corresponds to free foreseen pieces that are blue there on an internal triangle and the geometries picture here. 252 00:38:42,540 --> 00:38:52,980 Francesco Gozzini: One then can construct the flood geometry, that is not deficit tango on the tenor triangle in the curb geometry with non zero digits and. 253 00:38:55,830 --> 00:39:04,440 Francesco Gozzini: Then one can extract the boundaries piece iniquitous data collectors and can compute the MP3 numerically as a function of the bikes phoenix. 254 00:39:05,370 --> 00:39:14,430 Francesco Gozzini: Then, now we developed an eye going to search for southern pointy next to his other pointed correspond to dominant not suppress contribution this is some pretty integral. 255 00:39:15,750 --> 00:39:20,700 Francesco Gozzini: It is also possible to compute the, for example, the simple biker sellable. 256 00:39:21,780 --> 00:39:23,820 Francesco Gozzini: The average lifespan. 257 00:39:25,230 --> 00:39:38,520 Francesco Gozzini: Is an average X, with the new code so with the video library, we did the computation with the athletics now with the new code, I was able to be a computation using the API there. 258 00:39:40,890 --> 00:39:48,900 Francesco Gozzini: And so we can see the flat cases, so if we impose that flat boundary data. 259 00:39:50,550 --> 00:39:53,400 Francesco Gozzini: These blocks shows the ronnie some. 260 00:39:54,750 --> 00:40:03,180 Francesco Gozzini: were a jumper signals an interval of slowly changing phase in this pollination of the action so. 261 00:40:04,740 --> 00:40:14,940 Francesco Gozzini: These jumper corresponds to a certain point, and indeed if we feel that the data to announce. 262 00:40:16,350 --> 00:40:27,270 Francesco Gozzini: The southern point, we can see the speaker and we see that the pk is precisely at the position of the blue line that corresponds to the value of. 263 00:40:29,340 --> 00:40:30,540 Francesco Gozzini: Of the geometrical. 264 00:40:31,980 --> 00:40:36,090 Francesco Gozzini: Body carrier, so the meaning of this plot is that. 265 00:40:37,620 --> 00:40:40,350 Francesco Gozzini: We have a flat geometry in. 266 00:40:42,240 --> 00:40:47,790 Francesco Gozzini: For the space and these as particular. 267 00:40:48,930 --> 00:41:05,130 Francesco Gozzini: value of the DEMO area and the simulation with the quantum the quantum version matches pretty well the value of the geometry, this is for the flat case, but then, if we impose. 268 00:41:06,000 --> 00:41:19,410 Francesco Gozzini: If we constructed geometry that has a non zero FT tango then we see the same so we can run again the simulation and we can look again for southern points, of course, now the geometry. 269 00:41:21,150 --> 00:41:34,290 Francesco Gozzini: is different, so you can see that the position of the bar is different because the value of the geometrical vicarious different but indeed there, we can see that the subtle point is there. 270 00:41:38,010 --> 00:41:38,760 Francesco Gozzini: So. 271 00:41:40,980 --> 00:41:41,340 Francesco Gozzini: These. 272 00:41:42,390 --> 00:41:56,580 Francesco Gozzini: These looks like a context sample for the for the flatness problem because, indeed, we see that these core geometries have southern points, at least in this case with the free vertices. 273 00:41:57,600 --> 00:42:02,310 Francesco Gozzini: And Euclidean boundary the sound, is it six. 274 00:42:05,640 --> 00:42:08,100 Abhay Vasant Ashtekar: Which is, what are the trends in the boundary data, the two. 275 00:42:08,100 --> 00:42:10,740 Abhay Vasant Ashtekar: cases the flat case and the non flat case. 276 00:42:14,220 --> 00:42:20,370 Francesco Gozzini: In the flat case and these perfectly flat triangulation so in in for the. 277 00:42:20,550 --> 00:42:22,680 Abhay Vasant Ashtekar: For the master data you're talking about boundaries right. 278 00:42:24,030 --> 00:42:25,470 Francesco Gozzini: A yes so. 279 00:42:29,520 --> 00:42:29,940 Francesco Gozzini: So that. 280 00:42:32,370 --> 00:42:38,040 Francesco Gozzini: We can we can define the triangulation in in flat space. 281 00:42:39,090 --> 00:42:44,490 Francesco Gozzini: Okay, so we take free for simplicity and We grew them, we can do them at in. 282 00:42:45,840 --> 00:42:49,770 Francesco Gozzini: If we set certain values of the areas. 283 00:42:51,510 --> 00:43:06,210 Francesco Gozzini: At the boundary, then we can construct these geometry made by free for synthesis and this group, with a particular value of the of the bar area, so in the internal fix in the flat case, then we can try. 284 00:43:07,410 --> 00:43:11,790 Francesco Gozzini: Not to embed this fish for simplicity, seeing flat space, but. 285 00:43:12,870 --> 00:43:15,720 Francesco Gozzini: To construct them in a way that deficit thing. 286 00:43:18,420 --> 00:43:32,850 Abhay Vasant Ashtekar: No, but i'm really interested in calculating this part interior right, so you give me boundary data, and I will say that well the part of the button to go with this boundary data is dominated by flats for geometry. 287 00:43:33,540 --> 00:43:40,590 Abhay Vasant Ashtekar: And then you give me some other boundary data and then you will say it's not dominated by flat job, which was dominated by culture metric. 288 00:43:41,070 --> 00:43:42,300 Abhay Vasant Ashtekar: Is that what is happening. 289 00:43:42,480 --> 00:43:46,530 Abhay Vasant Ashtekar: Or are you using the same boundary data and finding to sunset side at once. 290 00:43:47,460 --> 00:43:51,840 Francesco Gozzini: No, the boundary data in the case of reinforce our disputes. 291 00:43:55,500 --> 00:43:57,600 Carlo Rovelli: Yes, this is what was happening. 292 00:43:59,070 --> 00:44:00,270 Abhay Vasant Ashtekar: Namely the outage at a. 293 00:44:00,300 --> 00:44:01,410 Carlo Rovelli: Different time they did. 294 00:44:03,600 --> 00:44:06,720 Abhay Vasant Ashtekar: That because I did not do what was happening, thank you very much yeah. 295 00:44:06,840 --> 00:44:09,030 Carlo Rovelli: The different boundary data yeah. 296 00:44:09,120 --> 00:44:09,840 Abhay Vasant Ashtekar: Different budget. 297 00:44:10,110 --> 00:44:10,620 Abhay Vasant Ashtekar: So that's. 298 00:44:12,780 --> 00:44:17,340 Abhay Vasant Ashtekar: The devil is dominated by white space, but the other boundary data for, which is why. 299 00:44:17,790 --> 00:44:18,900 Abhay Vasant Ashtekar: Thank you so much good. 300 00:44:19,770 --> 00:44:24,210 Carlo Rovelli: job of saying how we construct guess how he gets this is about. 301 00:44:24,390 --> 00:44:25,800 Abhay Vasant Ashtekar: Right exactly that but. 302 00:44:29,850 --> 00:44:32,370 Abhay Vasant Ashtekar: That, thank you very much, both of you okay things. 303 00:44:34,140 --> 00:44:46,530 Muxin Han: Are question, so I don't think this is a counter example for for the flatness so so flatness or happens only happens when you're signing over the box, but, but this part you it's like you don't come over. 304 00:44:46,890 --> 00:44:47,730 Carlo Rovelli: yeah yeah yeah. 305 00:44:48,450 --> 00:44:49,860 Muxin Han: Not a counter example. 306 00:44:51,420 --> 00:44:53,520 Carlo Rovelli: machine he standing over an internal. 307 00:44:55,020 --> 00:44:55,440 Carlo Rovelli: J. 308 00:44:56,910 --> 00:45:03,240 Muxin Han: Yes, it's it's some momentum about the the horizontal axis is the box in. 309 00:45:05,370 --> 00:45:05,820 Francesco Gozzini: So. 310 00:45:05,910 --> 00:45:09,630 Simone: In this planet storming just brought in the distribution. 311 00:45:10,260 --> 00:45:11,490 Simone: Of the internal spins. 312 00:45:11,580 --> 00:45:12,270 Simone: Right sorry. 313 00:45:12,540 --> 00:45:14,910 Muxin Han: Not so it's not a counterexample. 314 00:45:17,700 --> 00:45:18,780 Jonathan Engle: sushi. 315 00:45:19,080 --> 00:45:39,630 Francesco Gozzini: I say that this is a counter example because I see a certain point, and this is the some indeed because I am summing the over the bath I am something or the vast field, so the value here, for example, is the sun from X X zero to X and the value year so is the final value of. 316 00:45:39,930 --> 00:45:44,520 Muxin Han: Okay, I think the left, the Left Party for something over I think it looks. 317 00:45:44,670 --> 00:45:46,230 Francesco Gozzini: Like a normalized, of course. 318 00:45:48,240 --> 00:45:49,050 Right okay. 319 00:45:50,250 --> 00:45:54,120 Muxin Han: Okay, thanks, thank you, thank. 320 00:45:55,800 --> 00:46:00,990 Carlo Rovelli: You want to see in Thailand in terms of boundary data. 321 00:46:02,910 --> 00:46:11,400 Carlo Rovelli: The fact that there is, there is a subtle point implies that if you put a waste bucket. 322 00:46:14,040 --> 00:46:14,880 Carlo Rovelli: Central. 323 00:46:16,350 --> 00:46:17,340 Muxin Han: Okay okay I. 324 00:46:17,580 --> 00:46:17,970 Get. 325 00:46:20,220 --> 00:46:20,400 Seth K Asante: It. 326 00:46:21,540 --> 00:46:23,220 Francesco Gozzini: Okay, I continue. 327 00:46:25,740 --> 00:46:29,790 Francesco Gozzini: Sorry, are there any other question, yes. 328 00:46:29,850 --> 00:46:35,130 Seth K Asante: Yes, I had a question up front of previous go like on the Left sorry okay. 329 00:46:36,180 --> 00:46:40,200 Seth K Asante: The Left plot what the why exits pressure sounds. 330 00:46:41,940 --> 00:46:42,810 Seth K Asante: Wang what's it. 331 00:46:42,870 --> 00:46:45,450 Francesco Gozzini: what's the liberal into adding y the. 332 00:46:45,540 --> 00:46:51,810 Francesco Gozzini: y axis is the value of the employee to the party, it is just normalize to define value archaeopteryx. 333 00:46:54,150 --> 00:46:54,480 Francesco Gozzini: Okay. 334 00:46:55,950 --> 00:47:06,120 Muxin Han: Sorry, so so actually and even even that you find I mean from the right product even you man that you, there is a like a peek at the spin. 335 00:47:06,600 --> 00:47:16,410 Muxin Han: So I also don't think it's a counter example of the flatness because we by us and politics of have seen form with respect to this being. 336 00:47:17,190 --> 00:47:24,300 Muxin Han: One can already predict that there is a peek at at the box in corresponding to the geometrical oxygen because. 337 00:47:24,690 --> 00:47:36,600 Muxin Han: We know that in case that the box mean it's not too much geometrical than me to explore exponentially suppress and in case the box in years geometrical and it's not surprised it's ambiguous not exponentially. 338 00:47:37,230 --> 00:47:37,860 Muxin Han: So i'm. 339 00:47:37,980 --> 00:47:41,010 Muxin Han: From the US and politics, we know that there definitely is a. 340 00:47:41,250 --> 00:47:44,220 Carlo Rovelli: People she's not it's not the, this is the. 341 00:47:44,670 --> 00:47:52,050 Carlo Rovelli: Defining learning something, this is not a peek in the amplitude and the y axis, there will be empty to do they know that. 342 00:47:54,030 --> 00:48:02,520 Carlo Rovelli: it's a it's a sum of all the terms up to that particular exit so it's really a. 343 00:48:06,540 --> 00:48:10,170 Carlo Rovelli: it's really it's really a the. 344 00:48:11,790 --> 00:48:16,470 Carlo Rovelli: End of those related is oscillation is fascinating less. 345 00:48:18,030 --> 00:48:21,210 Carlo Rovelli: Less past so so so so something that. 346 00:48:22,470 --> 00:48:31,170 Carlo Rovelli: So on the on the y on the X axis is asynchronous horrible Internet speed on the y axis, that is the sum of all those after that value. 347 00:48:32,010 --> 00:48:32,910 Muxin Han: Right right. 348 00:48:33,000 --> 00:48:33,270 Muxin Han: and 349 00:48:33,330 --> 00:48:35,100 Carlo Rovelli: and actually the we cancel. 350 00:48:36,240 --> 00:48:36,570 Carlo Rovelli: Tony. 351 00:48:37,290 --> 00:48:55,710 Muxin Han: Yes, yes, yes that's right but, but I think the Left plot is actually implied by the right cloth right and the right plot, because you have a peek at the boxing and then it implies that laughs applause give you some spin up to certain certain level, then you got this kind of jump. 352 00:48:56,850 --> 00:48:57,150 Right. 353 00:48:58,230 --> 00:49:00,600 Francesco Gozzini: To the right plot is. 354 00:49:01,680 --> 00:49:04,950 Muxin Han: is basically implying the Left plot. 355 00:49:06,090 --> 00:49:12,240 Francesco Gozzini: Indeed, I think, is the contrary, because the right bra is is just the Left plot. 356 00:49:13,680 --> 00:49:24,450 Francesco Gozzini: I mean it's the same is two different ways of showing the same thing in the same thing is that there is that there's slowly very phase here, so it just. 357 00:49:24,510 --> 00:49:41,760 Muxin Han: But because what I mean is that, because you have a peek at at certain spin than when you're summing overspend before you act before you signing up to this point you got us more value and then, once you go after go greater than this. 358 00:49:44,070 --> 00:49:44,940 Francesco Gozzini: Because it does. 359 00:49:45,090 --> 00:49:51,420 Francesco Gozzini: He speak is not there is no meaning in the sense that it is just a way of. 360 00:49:53,040 --> 00:50:06,240 Francesco Gozzini: of showing that there is a southern point but the information is here so here, it is an artifact I can show it in another way, if you want, so the speakers know is no meaning so it's just a way of showing that. 361 00:50:07,230 --> 00:50:11,490 Carlo Rovelli: This is an assumption of xp embedded itself is an oscillating thing. 362 00:50:12,810 --> 00:50:18,990 Carlo Rovelli: So if you just walk walk to the amplitude the function of the a lot of up and down and not big at all. 363 00:50:20,040 --> 00:50:23,760 Carlo Rovelli: At some point the ups and down frequencies slows down. 364 00:50:25,530 --> 00:50:35,040 Carlo Rovelli: So your fascination there is no association association again, so this is a way of capturing window solution is less. 365 00:50:38,430 --> 00:50:38,670 Francesco Gozzini: let's. 366 00:50:38,940 --> 00:50:39,180 See. 367 00:50:41,100 --> 00:50:42,570 Muxin Han: Yes, but I I. 368 00:50:42,870 --> 00:50:47,070 Muxin Han: Just think that i'm, this is not not really a counter example of. 369 00:50:48,090 --> 00:50:51,990 Muxin Han: Of the flatness it's it's just a. 370 00:50:53,190 --> 00:50:56,760 Muxin Han: At least for from the right plot from the right plot. 371 00:50:58,230 --> 00:51:02,310 Muxin Han: It is just like usual which we know what we know from the US and politics. 372 00:51:05,220 --> 00:51:06,600 Francesco Gozzini: Okay, I think that. 373 00:51:06,870 --> 00:51:07,560 Carlo Rovelli: It is in. 374 00:51:09,600 --> 00:51:15,240 Muxin Han: Because I mean from the US and politics, we know that at the fox being there is a bump. 375 00:51:16,980 --> 00:51:19,140 Francesco Gozzini: But this man is not. 376 00:51:20,340 --> 00:51:23,670 Francesco Gozzini: This is not a bump in the amplitude this bump is just. 377 00:51:24,810 --> 00:51:29,100 Francesco Gozzini: A way of showing that there is a southern point it has it has nothing to. 378 00:51:29,190 --> 00:51:30,120 Muxin Han: Other one is. 379 00:51:30,180 --> 00:51:41,250 Muxin Han: Like a setup one of its life cycle point I didn't I i'm not worried, it is no point in the in the sense of in in which sense and but. 380 00:51:41,790 --> 00:51:43,260 Francesco Gozzini: What I can see, of course. 381 00:51:43,260 --> 00:51:50,430 Muxin Han: Is a pig it's like a bank of the in the space of scenes that's what I can see. 382 00:51:51,720 --> 00:51:57,750 Muxin Han: And and and this part one can predict, we found from the automatic. 383 00:51:59,760 --> 00:52:01,980 Francesco Gozzini: Okay, maybe the picture is a bit misleading. 384 00:52:03,810 --> 00:52:10,170 Francesco Gozzini: And of course the from remix we don't ever we just have indications that there is some. 385 00:52:10,920 --> 00:52:13,860 Simone: speeches are misleading I think these pictures are really good because. 386 00:52:13,860 --> 00:52:14,790 Muxin Han: They know I don't think a. 387 00:52:14,820 --> 00:52:15,420 Simone: True. 388 00:52:15,510 --> 00:52:17,400 Simone: picture we just did you see highly. 389 00:52:17,400 --> 00:52:29,730 Simone: oscillating dependent functions and then it's hard for the eye to see where the stationary point is the speeches were a really intelligent way really clever way my opinion. 390 00:52:30,390 --> 00:52:34,260 Simone: To make that the presence of the subtle point more visible. 391 00:52:35,910 --> 00:52:50,340 Muxin Han: I don't think it's misleading I just I just say that i'm, at least for the right direction, it is, it can be predicted from the US is not it's not surprising and it's not a counterexample. 392 00:52:50,670 --> 00:52:52,110 Nice good question Latin. 393 00:52:53,670 --> 00:52:55,500 Muxin Han: War, maybe, maybe we can discuss later. 394 00:52:55,710 --> 00:52:57,630 Francesco Gozzini: yeah I think I think we can discuss it. 395 00:53:00,030 --> 00:53:02,640 Jonathan Engle: Further question on that this is Jonathan. 396 00:53:03,780 --> 00:53:12,450 Jonathan Engle: i'm so it's true that the pot on the left, of course, it shows that the the the some increases once you hit the. 397 00:53:12,900 --> 00:53:19,710 Jonathan Engle: class of the classical value, so there is a definitely a contribution from there, but the thing about the the the. 398 00:53:20,280 --> 00:53:23,490 Jonathan Engle: flatness problem or the accidental curvature constraint, it has to do with. 399 00:53:24,210 --> 00:53:35,520 Jonathan Engle: Saying that the amplitude that the full sun is exponentially suppressed as Lambda goes to infinity so it's really more about the behavior of the full amplitude as as Lambda increases. 400 00:53:35,910 --> 00:53:44,670 Jonathan Engle: And here all you're really showing is that for a fixed Lambda the amplitude increases once you pass that critical point, which of course is going to happen so. 401 00:53:45,330 --> 00:53:51,000 Jonathan Engle: Maybe maybe I agree with new ship machine that it's not a counterexample unless you look at the dependence on Lambda but I guess. 402 00:53:51,390 --> 00:53:52,530 Simone: Maybe john. 403 00:53:52,860 --> 00:54:06,030 Simone: john john maybe maybe you could explain to us how they appear to be exponentially suppressed, the since eating tigran has a critical point, maybe they could clarify the confusion, how can that mathematically happen. 404 00:54:07,470 --> 00:54:11,910 Simone: You are doing an integral of a function that has a point at which the gradient vanishes. 405 00:54:13,050 --> 00:54:15,870 Simone: So why is there no exponentially suppress, how can that happen. 406 00:54:17,550 --> 00:54:18,630 Muxin Han: Actually, complex. 407 00:54:19,290 --> 00:54:23,250 Jonathan Engle: Yet you have a discreet some it's a discreet some and the you have. 408 00:54:23,640 --> 00:54:27,390 Simone: To evaluate which these happens it's a real it's not a complex. 409 00:54:28,860 --> 00:54:29,340 Jonathan Engle: Really. 410 00:54:31,260 --> 00:54:41,460 Jonathan Engle: Of course it's a it's a real value that's been but the song is a sum over in the amplitude for each value of the spin and that that amplitude is complex and there's destructive interference between the phases. 411 00:54:43,110 --> 00:54:43,410 Carlo Rovelli: These. 412 00:54:43,800 --> 00:54:47,520 Simone: Are the pneumatic shows that this doesn't happen, the reason to these new medical interpreting. 413 00:54:48,960 --> 00:54:49,320 This is. 414 00:54:50,970 --> 00:54:51,480 Simone: But anyway. 415 00:54:52,680 --> 00:54:56,220 Carlo Rovelli: that's not happened, I see but. 416 00:54:58,980 --> 00:55:08,040 Simone: But Okay, maybe, maybe anyways it's not a matter of politics is just we are seeing something, then the question is how to properly interpret it. 417 00:55:08,460 --> 00:55:17,430 Simone: And this is not necessarily in contradiction with some of the analytical arguments that you guys have done, and if it is not, it will be interesting to understand why. 418 00:55:18,300 --> 00:55:29,400 Simone: And I think this has already been pointed out before I think my PA throw that there is maybe what's going on here is a different different notions of anonymous or playing a role here. 419 00:55:30,810 --> 00:55:31,290 Simone: But at least. 420 00:55:31,620 --> 00:55:37,710 Simone: let's agree that these numerical method it's useful to highlight certain properties of the integral and. 421 00:55:38,730 --> 00:55:50,730 Simone: How to then push these properties of the integral under the sun man, if you wanted to properties of the sun and to the flatness problem that may be, can be further discussed or at least seen so far as. 422 00:55:51,960 --> 00:55:54,270 Simone: Maybe maybe we can agree on that. 423 00:55:54,570 --> 00:55:57,900 Jonathan Engle: Yes, no I agree it's a very clever method, yes and. 424 00:55:57,990 --> 00:56:11,310 Carlo Rovelli: I did the same it's the same results so not not technically the same but it's the same general results, how and bianca having right, this is similar similar thing happening so. 425 00:56:12,570 --> 00:56:24,960 Carlo Rovelli: It might be exactly I see that I don't see the conflict, I mean I and also why why you say there's only you think, since all converging and it's possible that if you go. 426 00:56:27,360 --> 00:56:29,580 Carlo Rovelli: with lung the higher and higher and higher. 427 00:56:30,960 --> 00:56:37,140 Carlo Rovelli: that's what happened in Michigan in bianca and how calculations right that you do. 428 00:56:38,370 --> 00:56:39,150 Carlo Rovelli: suppress. 429 00:56:41,760 --> 00:56:43,980 Carlo Rovelli: The contribution of. 430 00:56:45,120 --> 00:56:55,290 Carlo Rovelli: Norfolk geometries but that's not the point I mean that's what machine has been saying over right, I mean just to take the tree them it's wonderful to infinity. 431 00:56:56,040 --> 00:57:01,890 Carlo Rovelli: You might get in trouble, but don't take the trigger limit and that's not the right way, they can rename it that's what. 432 00:57:02,190 --> 00:57:09,060 Carlo Rovelli: i've heard machine saying since ever except that the way machine was saying was really confused with it's complicated to be. 433 00:57:09,480 --> 00:57:27,840 Carlo Rovelli: And it seeing now is right, because it's actually coming out from the new metrics you see the long flat geometry is appearing at some final love that so it's all there, maybe the, this is the theory, so the theory to our low flat solutions. 434 00:57:29,970 --> 00:57:38,130 Carlo Rovelli: The way to think about the classical limits, namely is not just the people they are the parameters if it's a big big on the definitive is that exactly the same machine. 435 00:57:39,000 --> 00:57:43,950 Muxin Han: yeah that's exactly yeah exactly i'm sorry i'm sorry I confuse that you had before. 436 00:57:52,050 --> 00:57:52,470 Muxin Han: and 437 00:57:54,240 --> 00:58:07,770 Muxin Han: What I have learned before, but what mine is that confirming my point before or because if it's not clear that the result we have is i'm toward my earlier result. 438 00:58:08,850 --> 00:58:10,080 Muxin Han: or not I don't know. 439 00:58:10,230 --> 00:58:12,870 Carlo Rovelli: I think it is, I think that they. 440 00:58:13,080 --> 00:58:13,350 say. 441 00:58:14,790 --> 00:58:15,630 Carlo Rovelli: to you. 442 00:58:16,500 --> 00:58:25,590 Abhay Vasant Ashtekar: Is this a backache I mean this is really going on between very, very expensive this for finite mortals, can I just like maybe the other people like me here. 443 00:58:25,890 --> 00:58:26,490 Carlo Rovelli: There is. 444 00:58:26,580 --> 00:58:28,350 Abhay Vasant Ashtekar: Someone is the situation as follows. 445 00:58:28,800 --> 00:58:43,920 Abhay Vasant Ashtekar: That he that there is a pattern here, which is like what Carlos ambition and and bianca in the hallway say, namely that maybe there is some intermediate value of Lambda for which. 446 00:58:44,760 --> 00:59:02,370 Abhay Vasant Ashtekar: One rock obtain quote unquote physical correct answer, and this is an indication in that direction, however, wishing and Jonathan and so on are saying that therefore it is interesting, but on the other hand, this is not approve that there is in fact a sadder point. 447 00:59:02,640 --> 00:59:03,270 Carlo Rovelli: At which. 448 00:59:03,720 --> 00:59:06,420 Abhay Vasant Ashtekar: There is a there is a. 449 00:59:07,590 --> 00:59:10,530 Abhay Vasant Ashtekar: Normal five geometry that's what I understood so maybe. 450 00:59:10,800 --> 00:59:13,890 Abhay Vasant Ashtekar: Somebody can correct me a bit briefly, maybe, without going to technicalities. 451 00:59:14,670 --> 00:59:17,490 Carlo Rovelli: Was I think that, without bianca. 452 00:59:18,810 --> 00:59:20,580 Carlo Rovelli: bianca how's it going it's much simpler. 453 00:59:22,740 --> 00:59:24,300 Abhay Vasant Ashtekar: yeah is it much simpler example my. 454 00:59:25,350 --> 00:59:34,050 Carlo Rovelli: model in which much farther than than what Francesco company account because because anything credence. 455 00:59:35,220 --> 00:59:35,550 Abhay Vasant Ashtekar: yeah. 456 00:59:36,180 --> 00:59:39,450 Abhay Vasant Ashtekar: But it's pretty pretty Euclidean in the usual sense of the word. 457 00:59:41,280 --> 00:59:41,580 Carlo Rovelli: Nothing. 458 00:59:43,800 --> 00:59:51,210 Carlo Rovelli: But there one sees that the theory has a regime that correspond to the classical language. 459 00:59:53,190 --> 01:00:00,900 Carlo Rovelli: And they have a number of parameters to play with right Oh, everything is there and, of course, possibly need this, so let us. 460 01:00:01,830 --> 01:00:16,530 Carlo Rovelli: know those you know easily fix all the other parameters and just be glad that that's what I understand it just they take the speed super large by no longer pick up without doing anything to her this, then you get in trouble. 461 01:00:17,670 --> 01:00:19,620 Carlo Rovelli: So you don't see the glass of the limit anymore. 462 01:00:20,910 --> 01:00:34,650 Carlo Rovelli: So when some time ago I and other people were saying look the rightly meat of the theory is just to be a very large speed as well, and this, by the way, is what machine has been saying for the last hour the. 463 01:00:35,700 --> 01:00:37,140 Carlo Rovelli: fact like like that. 464 01:00:37,170 --> 01:00:39,990 Abhay Vasant Ashtekar: So it's up to here i'm completely on the same wavelength, but it's the. 465 01:00:39,990 --> 01:00:41,100 Carlo Rovelli: Next statement. 466 01:00:41,490 --> 01:00:47,400 Carlo Rovelli: The next point the way I understand it, is that this field is a part of this progress until I find. 467 01:00:48,510 --> 01:00:49,170 Carlo Rovelli: A physics. 468 01:00:50,310 --> 01:01:00,090 Carlo Rovelli: Careful because if you take the lead nicely you don't get the right classical limits that we know, I mean I can take. 469 01:01:00,990 --> 01:01:05,010 Carlo Rovelli: Right is it bigger or anything like they just get a three part people. 470 01:01:07,980 --> 01:01:09,780 Carlo Rovelli: Or how many health and. 471 01:01:10,800 --> 01:01:22,230 Abhay Vasant Ashtekar: that's fine I did I don't want to go into and how was that work was just an indication and I brought it up only because Carlo proctor, but if we just focus on what is being saved here, it seems to me that. 472 01:01:23,340 --> 01:01:31,290 Abhay Vasant Ashtekar: The disagreement is on whether this is an interesting indication that something is that that there is possibly a. 473 01:01:33,690 --> 01:01:35,040 Abhay Vasant Ashtekar: Non trivial. 474 01:01:36,330 --> 01:01:38,550 Abhay Vasant Ashtekar: Point of stupid to sleep as descent right. 475 01:01:39,660 --> 01:01:47,430 Abhay Vasant Ashtekar: So semi classical approximation is good, are in fact the shows that that, in fact, is a non flat. 476 01:01:49,980 --> 01:02:00,810 Abhay Vasant Ashtekar: geometry, which is the which is include, which is actually giving you the path of steep as design and nothing I understood it, Jonathan and mission, saying that this was not prove it. 477 01:02:01,590 --> 01:02:09,060 Abhay Vasant Ashtekar: some indication that they're agreeing with it, and I think is everybody agreed with this, because I thought the money was kind of inching towards this conclusion also. 478 01:02:09,120 --> 01:02:18,930 Simone: Right, and I think it's true that john's question should be answered in a more precise way and so maybe Francesco can tell us. 479 01:02:19,410 --> 01:02:34,890 Simone: Whether if he shows if he plots both the real part and the imaginary plot of dysfunction whether they have whether they show a critical point of the same value of the spin or not, because I think he's my go towards answering one of those questions. 480 01:02:35,100 --> 01:02:37,050 I guess, thank you for the interference. 481 01:02:39,570 --> 01:02:43,950 Abhay Vasant Ashtekar: yeah these are very helpful for those of us who are not experts Thank you so to. 482 01:02:44,130 --> 01:02:49,680 Francesco Gozzini: reply to simoni yet the plots are exactly the same if you put the imaginary part. 483 01:02:51,150 --> 01:02:51,570 So. 484 01:02:53,430 --> 01:03:02,640 Jonathan Engle: I just wanted to say one more thing, so I think I agree with you, all this is very, this is a very nice result and then in the in the non triviality of it is, is that before we were doing numeric. 485 01:03:03,060 --> 01:03:16,140 Jonathan Engle: All we had was the same topic limit as Lambda goes to infinity and that's exactly what the problem was and now we're actually able to numerically investigate these intermediate values of the spin and we see that the theory is perfectly fine, so I think the very nice result. 486 01:03:17,580 --> 01:03:23,820 Francesco Gozzini: Thanks Jonathan so to be clear, of course, we are not buying the numeric the metrics. 487 01:03:25,380 --> 01:03:34,920 Francesco Gozzini: without thinking about it, so we would like to understand what's going on here and politically, this is, these are the indications that we have we have. 488 01:03:36,030 --> 01:03:38,100 Francesco Gozzini: Something more to understand. 489 01:03:39,510 --> 01:03:41,250 Carlo Rovelli: I see how can I can I ask. 490 01:03:43,710 --> 01:03:44,940 Hal Haggard: yeah go ahead Carla i'm here. 491 01:03:45,420 --> 01:03:48,810 Carlo Rovelli: Can I ask you what I was hoping, you would say something. 492 01:03:49,140 --> 01:04:03,420 Hal Haggard: yeah thanks I in fact Carlos summary was was fair, I agree with the way he framed it we we see also that you get a semi classical limit but it's not a naive large spin limit. 493 01:04:03,930 --> 01:04:13,650 Hal Haggard: And it's very clear in our models and we can both reproduce motions old estimates as a very in a very simple scaling argument. 494 01:04:14,100 --> 01:04:31,680 Hal Haggard: And we can go beyond those estimates and and do numeric for both triangulation is like the one Francesco is presenting here and ones with an inner edge and maybe the most important thing for me to say here is that it's not just bianca and I, but the sun. 495 01:04:31,710 --> 01:04:37,590 Hal Haggard: is also on this call and young postdoc and a wonderful person and he did a huge body of the numeric. 496 01:04:37,620 --> 01:04:40,410 Hal Haggard: So I wanted to make sure his name got mentioned. 497 01:04:47,100 --> 01:04:48,780 Hal Haggard: The money you're unmuted and we can hear you. 498 01:04:53,580 --> 01:05:01,140 Francesco Gozzini: Okay, thanks everybody for all the comments, is a very interesting discussion, and I see that. 499 01:05:02,310 --> 01:05:05,520 Francesco Gozzini: There are many interesting means. 500 01:05:07,200 --> 01:05:10,860 Francesco Gozzini: If everybody agree, let me just continue. 501 01:05:12,060 --> 01:05:15,900 Hongguang Liu: To ask a single question which type of data are you using. 502 01:05:17,340 --> 01:05:21,660 Hongguang Liu: you're using Euclidean under data organization bounder did. 503 01:05:22,290 --> 01:05:23,190 Francesco Gozzini: They are Euclidean. 504 01:05:24,120 --> 01:05:26,130 Hongguang Liu: Okay, that is a luxury car. 505 01:05:27,180 --> 01:05:27,690 Francesco Gozzini: Yes. 506 01:05:27,750 --> 01:05:30,390 Hongguang Liu: Okay, so okay. 507 01:05:31,320 --> 01:05:36,690 Francesco Gozzini: So I have more plots on these delta free so. 508 01:05:38,490 --> 01:05:41,820 Francesco Gozzini: So here, for example, in the spirit of. 509 01:05:42,960 --> 01:05:55,650 Francesco Gozzini: Harlem gang bianca in set are doing yeah I i've arrived, the, for example, the boundaries between and then I completed the average box been in the need is another indication that. 510 01:05:56,880 --> 01:06:02,730 Francesco Gozzini: The semi classical limited in both flood ks and the curve Kazan. 511 01:06:04,680 --> 01:06:06,330 Francesco Gozzini: agrees with. 512 01:06:07,440 --> 01:06:16,020 Francesco Gozzini: With the medical computation So you can see the flat case the points are the average by speaking in the agree pretty well with the. 513 01:06:16,470 --> 01:06:30,540 Francesco Gozzini: geometrical venue, this is the current case and you see some larger fluctuations, but indeed the qualitative behavior is the same they plotted also the imaginary part of the operator in. 514 01:06:32,190 --> 01:06:35,880 Francesco Gozzini: This is a very long number, and this is probably due to just numerically. 515 01:06:36,990 --> 01:06:50,670 Francesco Gozzini: As far as I understand, and also try to verify it fixed it fixed the Lambda I tried to verify the very near the parameter exactly as Alan Yang can set. 516 01:06:51,810 --> 01:07:07,020 Francesco Gozzini: And you can see, various video stream factor that the efficient manner, does not depend on the Burberry means parameter in this is good, if we want to interpret the results. 517 01:07:08,250 --> 01:07:09,210 Francesco Gozzini: semi classical. 518 01:07:10,710 --> 01:07:29,220 Francesco Gozzini: battle, there is not to complete agreement with the geometrical value and indeed in the corner cases the displacement is larger and again a plotter the imaginary part to show you that the This is very small, and this is just probably due to medical error. 519 01:07:31,260 --> 01:07:46,680 Francesco Gozzini: As the last application, I wish to the case of infrared the divergence ISM is innovative case of application is working progress we picked up off rezone, which is one of the students have Francisco and. 520 01:07:47,640 --> 01:07:58,920 Francesco Gozzini: Here we are studying infrared divergences of the API model in the literature is quite scars about this topic and not to be there are there are the words of our Lord yellow in 2014. 521 01:07:59,580 --> 01:08:17,430 Francesco Gozzini: who found look at it with lower bound for the mail or norovirus infinity graph and also, there is the work from Pietro by 2018 the study for different graphs and provided the power law upper bounds. 522 01:08:19,200 --> 01:08:31,890 Francesco Gozzini: This is the monograph and it is the object of our study, it is a contraction of diversity server for internal ages if there's a six internal dynamical faces, which form sort of. 523 01:08:33,750 --> 01:08:38,970 Francesco Gozzini: And the amplitude should be divergent that because the internal physicists form a bubble. 524 01:08:39,690 --> 01:08:46,260 Francesco Gozzini: In that our Internet speeds that are unconstrained the so that the sounds are not cut by 3am learning is, in this case. 525 01:08:46,980 --> 01:09:02,010 Francesco Gozzini: We know in the theories that such bubbles are divergent because we can increase the performance, the analysis and nice way to divert some factor, but the picture is less clear for a PR la with basically the only normal resolved by. 526 01:09:03,870 --> 01:09:05,940 Francesco Gozzini: And this is the formula. 527 01:09:07,860 --> 01:09:13,650 Francesco Gozzini: With the new coil we can compute these divergent series, so we fix or your genius cut off of an Internet speeds. 528 01:09:14,130 --> 01:09:27,660 Francesco Gozzini: And we look at the amplitude as the cutoff increases, which is very bad very low boundaries piece in the case, one in this case, one alpha boundaries piece and zero man very intertwined and. 529 01:09:29,520 --> 01:09:38,910 Francesco Gozzini: We do these because they're an enormous number of amateurs to compute because six Internet freezes means that number of amplitude scrolls is the gap of to the six power. 530 01:09:39,660 --> 01:09:46,170 Francesco Gozzini: So I show you the plots of these men an amputated computer, we were very musical Stan set to 0.1. 531 01:09:46,590 --> 01:09:54,570 Francesco Gozzini: So we completed after two shares and you can see that there is a substantial difference in the amphitheater says you increase the number of shares. 532 01:09:55,440 --> 01:10:05,730 Francesco Gozzini: Of course, it is hard to tell if, in a way, these correspond to convert into corpse or not from the matrix I have tried to plot the forward differences. 533 01:10:06,240 --> 01:10:18,000 Francesco Gozzini: On the right, that is the difference between consecutive tariffs on the feet series, and they compare them to the value of the natural log everything, so we are basically looking at the derivative that one over X. 534 01:10:19,800 --> 01:10:32,280 Francesco Gozzini: So it appears in this bloody the serious are some logarithmic in the behavior at to kjellson the purple line is not qualitatively different from the one is the Russians. 535 01:10:34,440 --> 01:10:37,980 Francesco Gozzini: We have also some plots of around the barbarian music parameter. 536 01:10:39,270 --> 01:10:46,320 Francesco Gozzini: handle this last plot is interesting because it shows that the convergence and I call this convergence, even in a priori the. 537 01:10:48,120 --> 01:10:56,580 Francesco Gozzini: amplitude are divergent but you see these convert this towards the last day at the I guess cut off normalized one. 538 01:10:57,600 --> 01:11:01,470 Francesco Gozzini: is much better with the low value some very nice. 539 01:11:04,200 --> 01:11:12,150 Francesco Gozzini: And this is another manifestation of the same phenomena that appeared in the US in 30s were higher values of the primary means the parameter require the more shares. 540 01:11:12,870 --> 01:11:21,390 Francesco Gozzini: At the same value of the boundary speeds so Theresa the convergence, so I stopped with application, I can I can do. 541 01:11:22,290 --> 01:11:32,790 Francesco Gozzini: Some of the first result, so the learning Center synthetic is basically completed now in understood in the session, now we have a clear picture of what is going on. 542 01:11:33,390 --> 01:11:43,440 Francesco Gozzini: With our approximations so we found that we have as many as a parameter, we can trust a few shares up to Las Vegas of that, indeed, the. 543 01:11:44,760 --> 01:11:48,360 Francesco Gozzini: uses morning near these practical, from the point of your lyrics. 544 01:11:49,380 --> 01:11:50,820 Francesco Gozzini: For the nazca free. 545 01:11:52,890 --> 01:11:54,210 Okay, we had the. 546 01:11:55,290 --> 01:12:09,510 Francesco Gozzini: discussion about that, but I think that our maker, is our switches that, in this particular case, so we've free vertices and Euclidean memory data that are noisy dental quarter constraints. 547 01:12:10,530 --> 01:12:11,250 Francesco Gozzini: and 548 01:12:13,260 --> 01:12:19,560 Francesco Gozzini: I also have computed the bike expectation values and compared it with the corresponding classical geometry. 549 01:12:20,940 --> 01:12:35,430 Francesco Gozzini: For the divergent series, we have some means of possible convergence, these are just the means of course there's the analysis of the result is three key use case and there is, of course, the resulting the return to that states that desire to 30 words. 550 01:12:36,630 --> 01:12:52,170 Francesco Gozzini: STDs interesting to see that we was more line is the parameter the suppose the convergence is way faster and, in general, working with this morning music parameter improves the convergence and the stability of the reasons. 551 01:12:53,490 --> 01:13:01,650 Francesco Gozzini: I would like to conclude with some ideas about the next steps so some possible improvements to the call include the. 552 01:13:02,430 --> 01:13:18,750 Francesco Gozzini: More tools for computing with your vertices that gpu integration and then API integration with Julia and better documentation and, of course, if you happen to look at the code and to see if possible improvements do not hesitate to let me know. 553 01:13:19,830 --> 01:13:30,450 Francesco Gozzini: Regarding future computation there are many interesting possibilities hearing mention these so as on one was saying was suggesting would be interesting to. 554 01:13:31,440 --> 01:13:46,380 Francesco Gozzini: completed computer dynamic us before we learn English amanda data, then, to see if, in that case the armpits are suppressed or not in these would be stronger the answer I think, to the flatness problem. 555 01:13:48,120 --> 01:13:49,620 Francesco Gozzini: Also, in the spirit. 556 01:13:49,620 --> 01:13:50,280 Seth K Asante: Of the. 557 01:13:50,310 --> 01:13:57,120 Francesco Gozzini: work by mankind set to be nice to test the Wednesday night miss reading terminal dynamical segments. 558 01:13:58,170 --> 01:14:05,550 Francesco Gozzini: In through an ongoing work with the power of visual me is the computation of the minimum graph. 559 01:14:05,580 --> 01:14:12,180 Francesco Gozzini: With creating boundary and also competing of server barkin boundary of servers and also we need to. 560 01:14:12,630 --> 01:14:15,000 Francesco Gozzini: apply a Monte Carlo techniques for nuts. 561 01:14:15,000 --> 01:14:21,870 Francesco Gozzini: grass or even think about, for example, the normalization thing, and if you have any suggestion. 562 01:14:22,980 --> 01:14:24,630 Francesco Gozzini: I have received it. 563 01:14:26,940 --> 01:14:46,860 Francesco Gozzini: So, to conclude I have developed a new code for computing duration up around features that is efficient scalable and into the very first tester I have attained interesting results about the aeration or some topics, the flatness provenance for screen forms and the divergent series of. 564 01:14:48,810 --> 01:14:55,530 Francesco Gozzini: The code is free and publicly available, so you can find it and and his address and. 565 01:14:57,420 --> 01:15:09,540 Francesco Gozzini: I hope that it will be used by other researchers to learn new things about quantum gravity and also to experiment with a PR and model in a light and you interesting results. 566 01:15:11,100 --> 01:15:14,130 Francesco Gozzini: So I stopped hearing things for your attention. 567 01:15:23,160 --> 01:15:24,330 Jorge Pullin: Oh, more questions. 568 01:15:25,530 --> 01:15:38,790 Simone: And maybe I have one question so first of all, let me stress that the improvement that your code made on the original version of the code is really amazing as you've shown. 569 01:15:39,210 --> 01:15:53,670 Simone: much higher speeds and more stable, this is really good, and so this is good news for the new metrics by we recently also heard some other very nice news for the new metrics, and this was this method use the. 570 01:15:55,590 --> 01:15:57,600 Simone: Live she symbols that. 571 01:15:59,190 --> 01:16:09,600 Simone: machine Hong Wang Chung presented the recently to us, which also seem to be extremely powerful and promising and I was wondering if. 572 01:16:11,490 --> 01:16:17,220 Simone: The metal you're using is in a in a sense, maybe some advantages respect to the other, maybe it's more. 573 01:16:17,940 --> 01:16:29,250 Simone: It cannot go as high and spins but it's maybe more precise in that it doesn't require to reconstruct the symbol, so I was wondering if maybe the two methods could work together with yours. 574 01:16:30,600 --> 01:16:33,750 Simone: Improving the way they look for. 575 01:16:34,890 --> 01:16:47,940 Simone: The critical points in the team bolts, and then, once that has been proved the continuing with their technique to push the spins even higher, do you think that could be some collaborations between these two types of methods. 576 01:16:49,560 --> 01:16:58,950 Francesco Gozzini: Yes, I would say that these are like complimentary meters, because we have the two codes that do very different. 577 01:17:00,630 --> 01:17:06,030 Francesco Gozzini: Things and they use very different techniques, so the techniques that we use are. 578 01:17:07,590 --> 01:17:11,430 Francesco Gozzini: Our most suited for the spins not to hike. 579 01:17:13,020 --> 01:17:14,160 Francesco Gozzini: But we need, we can. 580 01:17:15,510 --> 01:17:16,860 Francesco Gozzini: Do we can do. 581 01:17:17,880 --> 01:17:30,930 Francesco Gozzini: Very few approximations apart from the fact that we are competing in funny number of shares, but as long as we have these under control that we don't have to care about, for example, the position of southern points or have. 582 01:17:32,310 --> 01:17:51,300 Francesco Gozzini: or the other things because these are for free once you can we compute everything, while, of course, we cannot get to spins as high as they do with them more thicker limited, and so they want academy to can. 583 01:17:51,690 --> 01:17:52,590 Francesco Gozzini: investigate. 584 01:17:53,010 --> 01:17:55,590 Francesco Gozzini: The semi classical limiting and more effective way. 585 01:17:57,240 --> 01:17:58,110 than our code. 586 01:17:59,370 --> 01:18:00,990 Francesco Gozzini: Once one. 587 01:18:02,550 --> 01:18:18,120 Francesco Gozzini: Has a good understanding my opinion work once one has a good understanding of the southern point structure of of the model that you are computing so the these are complimentary approaches, in my opinion, yes, as you were saying. 588 01:18:24,720 --> 01:18:25,260 Jorge Pullin: questions. 589 01:18:27,810 --> 01:18:29,550 Abhay Vasant Ashtekar: I just requested by. 590 01:18:29,580 --> 01:18:31,590 Abhay Vasant Ashtekar: I just have a really strong strong request. 591 01:18:32,040 --> 01:18:43,350 Abhay Vasant Ashtekar: Good people just stick to the word repeated and lorenzen in one sense and not keep changing because it's very confusing to outside world and where to communicate with the outside world, so I think. 592 01:18:44,400 --> 01:18:57,660 Abhay Vasant Ashtekar: I think, usually by Euclidean or Romanian one means positive signature was a definite signature and the lorenzen is minus plus plus plus signature and there should be no other use of these terms, I think you should change the terminology that really, really would. 593 01:18:58,590 --> 01:19:01,530 Simone: Why do we have other users don't understand. 594 01:19:05,880 --> 01:19:08,070 Simone: Why is it different understand why is it different. 595 01:19:16,350 --> 01:19:18,390 Simone: But that's exactly what happens when you take. 596 01:19:19,890 --> 01:19:33,420 Simone: boundary data you're actually it's only the so three subgroup of the Orange cancer group that is giving you a critical points, this is why, even though the model is laurentian he has a critical behavior for Korean boundary data. 597 01:19:35,670 --> 01:19:37,590 Abhay Vasant Ashtekar: model is not Indian, so why do you call it, you. 598 01:19:38,880 --> 01:19:40,590 Simone: know is the boundary data, these are you. 599 01:19:40,860 --> 01:19:41,640 Abhay Vasant Ashtekar: know, but I think. 600 01:19:41,820 --> 01:19:44,400 Abhay Vasant Ashtekar: The way it is also just said is really. 601 01:19:44,910 --> 01:19:46,380 Abhay Vasant Ashtekar: You know Okay, what is a model. 602 01:19:47,460 --> 01:19:48,330 Abhay Vasant Ashtekar: That was being said today. 603 01:19:49,950 --> 01:19:50,790 Simone: OK OK OK. 604 01:19:52,320 --> 01:19:53,490 Abhay Vasant Ashtekar: But he was that you know. 605 01:19:53,520 --> 01:19:53,820 Simone: Maybe. 606 01:19:54,030 --> 01:19:56,460 Abhay Vasant Ashtekar: Very important is that you know you. 607 01:19:56,880 --> 01:19:58,170 Abhay Vasant Ashtekar: make up a symbol right. 608 01:19:59,040 --> 01:19:59,310 Okay. 609 01:20:00,810 --> 01:20:04,920 Abhay Vasant Ashtekar: Do your makeup something which is not just. 610 01:20:06,690 --> 01:20:08,400 Simone: Okay, no, no, I understand, thank you. 611 01:20:09,030 --> 01:20:17,700 Carlo Rovelli: bye I mean I i've weaknesses those kinds of talks in which people just get it wrong when they're presented for this reason, so I. 612 01:20:18,090 --> 01:20:19,020 Simone: Okay Okay, thank you. 613 01:20:19,860 --> 01:20:23,670 Francesco Gozzini: yeah maybe Indeed it was a source of confusion. 614 01:20:25,560 --> 01:20:26,940 Yes, so thanks for. 615 01:20:28,860 --> 01:20:42,300 Simone: Responding right why, because these are, and also with the Berkeley more than maybe I don't remember it is funny that even though the model is orange and it meets critical behavior for boundary data which are Euclidean so ever since. 616 01:20:42,810 --> 01:20:47,850 Jonathan Engle: it's actually quite understood that, because this you can audrey data it's not only. 617 01:20:48,150 --> 01:21:01,530 Jonathan Engle: boundary data for Euclidean for simplex in embedded in Euclidean space it's also a boundary data for a degenerate Lorenz Ian but it's also better data for degenerate for simplex embedded and Lorenzo in space that's flat. 618 01:21:03,420 --> 01:21:03,780 Simone: Wait. 619 01:21:04,380 --> 01:21:05,520 Jonathan Engle: that's interesting thing is. 620 01:21:05,610 --> 01:21:17,310 Jonathan Engle: If you give me if you give me any Euclidean any Euclidean for simplex you can reassemble all of the tetrahedral so that they're all flat within a within the. 621 01:21:18,360 --> 01:21:26,880 Jonathan Engle: Three elements within the three dimensional plane and it's a, it has to do with it has to do with the self duality structure of the. 622 01:21:27,000 --> 01:21:27,870 Simone: Look sure. 623 01:21:28,860 --> 01:21:30,330 Carlo Rovelli: explain that to me one day. 624 01:21:31,650 --> 01:21:32,040 Carlo Rovelli: Long. 625 01:21:32,490 --> 01:21:48,780 Simone: I mean, of course, he gets back to buy anything but sometimes you might come as a surprise that is still a critical behaviors I was just wanting to remind the I didn't mean that there's anything new, no, no sorry didn't mean to I completely agree to all the well understood is. 626 01:21:51,000 --> 01:21:51,300 Muxin Han: That. 627 01:21:51,990 --> 01:21:55,650 Carlo Rovelli: How said yeah model has the same. 628 01:21:56,790 --> 01:21:57,480 You know. 629 01:22:00,660 --> 01:22:02,040 Hal Haggard: Well we've only in. 630 01:22:03,390 --> 01:22:05,160 Carlo Rovelli: The you're not there yet so. 631 01:22:05,310 --> 01:22:08,520 Hal Haggard: yeah we've only investigated a Euclidean eerie. 632 01:22:09,510 --> 01:22:09,990 yeah. 633 01:22:11,100 --> 01:22:20,220 Hal Haggard: So so yeah we haven't looked at this issue, yet, although that's certainly a direction set that started to go I don't know, do you have set and results I don't know about stuff. 634 01:22:21,630 --> 01:22:29,730 Seth K Asante: not yet I mean we just starting to understand lawrenson reggie it's it's very different from Euclidean so. 635 01:22:30,840 --> 01:22:35,880 Seth K Asante: Yes, i'm excited this year have to come over before we can do, effective spin phones like we did before. 636 01:22:37,740 --> 01:22:38,070 yeah. 637 01:22:39,750 --> 01:22:42,390 Seth K Asante: But if I may, I have a question for Francesca. 638 01:22:44,520 --> 01:22:56,700 Seth K Asante: very nice talk Francesca it's it's very nice to see all these nice mercury results, I had a question about the barista functions that you use for a new marriage. 639 01:22:57,240 --> 01:23:10,080 Seth K Asante: And what's the interpretation that because I saw like you have the 15 Jason will multiply it by this some of these booster functions and the function somehow implementing some constraints. 640 01:23:11,280 --> 01:23:17,730 Seth K Asante: Their lines and like I just I was just wondering, the interpretation of the sophistication you mean. 641 01:23:18,750 --> 01:23:20,010 Francesco Gozzini: In. 642 01:23:21,030 --> 01:23:22,650 Francesco Gozzini: Yes, the. 643 01:23:22,740 --> 01:23:26,970 Francesco Gozzini: The average American interpretation, if you if you want to see that so. 644 01:23:28,650 --> 01:23:31,260 Francesco Gozzini: Technically, we are just deleting. 645 01:23:34,200 --> 01:23:49,140 Francesco Gozzini: The model into pieces and there is one piece, that is, the 15 J that corresponds to so true BF theory and there is this piece that that the buzzer buzzer function that. 646 01:23:50,130 --> 01:24:02,190 Francesco Gozzini: Basically, the the core the all the non compact part of the model, and there is a dramatic an interpretation in the sense that if you just take the 15 day. 647 01:24:03,990 --> 01:24:06,870 Francesco Gozzini: You a modem router functions you. 648 01:24:07,890 --> 01:24:20,970 Francesco Gozzini: You suppress also this some requests piece, we are back to the FDR and we know that these as critical points for Euclidean i'm sorry I keep saying. 649 01:24:21,450 --> 01:24:24,510 Francesco Gozzini: But for Euclidean boundary that and. 650 01:24:25,860 --> 01:24:36,210 Francesco Gozzini: The booster functions in the splitting have the role of introducing critical points that corresponds to geometries that are non. 651 01:24:37,170 --> 01:24:50,250 Francesco Gozzini: Euclidean saw in particular, there is a recent work bye bye Simone and Theodore and others that show that the critical points of the booster functions correspond to the dre dre that. 652 01:24:51,720 --> 01:25:08,250 Francesco Gozzini: can be boosted the from one frame to when other so from you see that is wanting to China on the left and one on the right, and these are show critical points when when you compute. 653 01:25:09,780 --> 01:25:14,670 Francesco Gozzini: These things we've created on Monday, after the show critical points when you can do a booster. 654 01:25:15,840 --> 01:25:25,470 Francesco Gozzini: From this data, you drawn to this that's right so basically all the all the non compactness of the model is called Mr functions. 655 01:25:26,460 --> 01:25:30,000 Simone: Now, do you mind if I add something also it. 656 01:25:30,000 --> 01:25:32,070 Simone: is very clear answer already but. 657 01:25:32,490 --> 01:25:40,230 Simone: You know, said this question you you just ask the haunted me for as long as these, the composition was introduced. 658 01:25:40,710 --> 01:25:49,440 Simone: and interaction, the answer as Francesco said is quite Nice, they have the interpretation of boosting editor hearing from one frame to the other. 659 01:25:49,800 --> 01:25:53,100 Simone: But what is really non trivial is, what do you mean by boosting a tetrahedron. 660 01:25:53,730 --> 01:26:02,220 Simone: And, of course, what do you mean there is a notion of booze that is associated to the normal to the theater either being the electric part of simple by vectors. 661 01:26:02,520 --> 01:26:06,300 Simone: Which is what, if you want a better model is built on except that. 662 01:26:06,720 --> 01:26:14,430 Simone: You seen the booster functions, on the one side, you have the minimal spins like in the model, but on the other side on have minimal spins. 663 01:26:14,730 --> 01:26:22,110 Simone: And so the generators of the Lawrence group on their keys they're not in the circles, if you want, if you want to don't satisfy the warm up. 664 01:26:22,740 --> 01:26:31,020 Simone: So how this this notion of a simple by factors come into play as well it's actually quite interesting. 665 01:26:31,590 --> 01:26:38,460 Simone: And it's also resonates with some of the other analyses that also seen had been doing, because the face of the spinners player rule so anyway. 666 01:26:38,820 --> 01:26:47,940 Simone: I encourage you, if you're interested in this question three this last paper that we had because they think it's quite nice what happens, so thank you for the advertisement that you allow me to do. 667 01:26:52,050 --> 01:26:52,560 Things. 668 01:26:55,920 --> 01:26:56,370 Muxin Han: So. 669 01:26:57,690 --> 01:27:05,370 Muxin Han: I have a comment and it relates to comparing the flatness result you show those plots and and. 670 01:27:07,050 --> 01:27:15,150 Muxin Han: And the result we have earlier analytically by awesome article, and also the new result of john and water. 671 01:27:16,140 --> 01:27:25,590 Muxin Han: I think the confusion one one of the point computing come from is that most of time we already a result are focusing on. 672 01:27:26,190 --> 01:27:33,750 Muxin Han: single critical point and we are now analyze single critical point and look at that, as in politics and find the platinum but. 673 01:27:34,200 --> 01:27:45,720 Muxin Han: Here here what you do numerical is corresponding to multiple critical points because here you don't really do have the nordics and we don't do a stationary face and you just sign in numerically. 674 01:27:46,350 --> 01:27:54,600 Muxin Han: The amplitude and then, of course, on to something over multiple critical points and you got multiple phases. 675 01:27:55,800 --> 01:28:06,960 Muxin Han: And, and so so that's why the amplitude you don't really see the complexity of the action and then the the because the flatness is critically critically depend on the complexity. 676 01:28:07,350 --> 01:28:14,880 Muxin Han: Of the action but here's into some overly critical point and you don't really see this this complexity and I think that's confusing come from. 677 01:28:15,480 --> 01:28:34,920 Muxin Han: And also, and one of the point I also want mentioned because we we actually played with your your earlier data with one and try to fit those data and and we find because you're speaking is not large. 678 01:28:36,120 --> 01:28:58,560 Muxin Han: Its maximum of 30 skin so it's hard to say that the disarming over students and the total antidote polynomial you suppress or or or exponentially surprised actually we tried both essential eating and eating fried chicken feed your data, the same way, so yeah that's that's two comments. 679 01:29:00,180 --> 01:29:00,600 I have. 680 01:29:02,670 --> 01:29:06,090 Muxin Han: And and, by the way, thanks for simoni for mentioning our work. 681 01:29:09,450 --> 01:29:10,560 Francesco Gozzini: Okay yeah I think that. 682 01:29:11,700 --> 01:29:12,870 Francesco Gozzini: thanks for your comments. 683 01:29:14,460 --> 01:29:17,490 Francesco Gozzini: it's tricky to feed the. 684 01:29:19,440 --> 01:29:26,370 Francesco Gozzini: numerical data in this case is when you don't have many points, of course, so, in fact, we didn't try. 685 01:29:27,570 --> 01:29:28,020 Francesco Gozzini: To. 686 01:29:29,940 --> 01:29:38,550 Francesco Gozzini: do that, I mean this is the first thing that one can try to do but indeed we tried to base our analysis to. 687 01:29:40,710 --> 01:29:47,550 Francesco Gozzini: On a different method is this algorithm to search for southern points because, indeed the fitting it. 688 01:29:48,150 --> 01:30:04,200 Francesco Gozzini: Is not conclusive at all I didn't do that, for example, for the divergence or or converges from the main on in the last class because I tried to fit with something convergent and in Florida and try to feed with something divergent that in toward the end so. 689 01:30:05,610 --> 01:30:06,390 Francesco Gozzini: So. 690 01:30:10,650 --> 01:30:18,120 Francesco Gozzini: I think that there were there was no value in in these fields, but I can try to. 691 01:30:21,090 --> 01:30:29,640 Francesco Gozzini: I can also try to the different blogs in with more data points and maybe I can I can try to answer your questions in the forum. 692 01:30:31,590 --> 01:30:48,300 Simone: will be nice if we can continue the discussion things, maybe, but other difficulties also that they also relate the data once your resume maybe so you have to feed, having in mind that you only want to look at the upper bounds of this lesions support. 693 01:30:48,390 --> 01:31:04,860 Francesco Gozzini: yeah yeah, this is another thing that sometimes you'll see late, so I might maybe at some particular value of Lambda the value is very low, but this is just because of the simulations right, not for the same topic ski. 694 01:31:06,360 --> 01:31:06,660 Things. 695 01:31:09,360 --> 01:31:11,250 Jonathan Engle: like to ask another question about the. 696 01:31:13,230 --> 01:31:18,480 Jonathan Engle: So we were talking about i'm about how the I mentioned again how the Euclidean. 697 01:31:19,530 --> 01:31:24,870 Jonathan Engle: boundary data is actually degenerate boundary data and and there's another. 698 01:31:26,190 --> 01:31:34,320 Jonathan Engle: case of degenerate boundary data that's not suppressed analytically and that I think they're called vector geometries is third class and so. 699 01:31:35,310 --> 01:31:45,480 Jonathan Engle: i'm wondering first have you checked numerically whether the back, whether boundary data, corresponding to vector geometries is of course that's probably still going to be not suppressed, but. 700 01:31:45,900 --> 01:31:58,170 Jonathan Engle: i'm at least you have some sense of of these three different classes of boundary data, the Lorenz Ian Euclidean and the vector geometries is there any relative dominance among them. 701 01:32:00,630 --> 01:32:03,960 Francesco Gozzini: And this is an interesting question, I think that, as far as. 702 01:32:05,490 --> 01:32:13,500 Francesco Gozzini: For single vertex case this is pretty clear, so this has been done by simonon patrons are Joe and others. 703 01:32:14,760 --> 01:32:17,760 Francesco Gozzini: But if we consider more vertices then. 704 01:32:19,500 --> 01:32:36,930 Francesco Gozzini: I think that we have still a lot to understand and, indeed, it can be that the contribution of active geometries in this case or cases is substantial, but for the moment, I have no fault of the way of quantifying it. 705 01:32:39,510 --> 01:32:45,300 Abhay Vasant Ashtekar: So, can you remind us what someone and Pietro concluded for a single vertex what is the. 706 01:32:46,560 --> 01:32:49,710 Abhay Vasant Ashtekar: switch and which has some time in it and sub sub document. 707 01:32:51,360 --> 01:32:59,580 Francesco Gozzini: So maybe maybe simoni can answer that but basically a vector geometry is is a geometry, that is not rigid. 708 01:33:00,750 --> 01:33:02,130 Francesco Gozzini: But it's still not small. 709 01:33:02,970 --> 01:33:04,110 Abhay Vasant Ashtekar: But, which is dominant in. 710 01:33:04,560 --> 01:33:06,600 Simone: The answer, they have the same power law. 711 01:33:08,010 --> 01:33:10,950 Simone: director geometry as a single we confirm the. 712 01:33:10,950 --> 01:33:28,320 Simone: Exactly the analysis OK, so the only difference is that the feasts of the vector geometry configurations is a pure gauge depends on the orientation of the data, whereas in their education, these two critical points and therefore you have. 713 01:33:29,010 --> 01:33:33,930 Simone: Like a gauge independent notion of the installations, but the power rule is the same. 714 01:33:34,350 --> 01:33:35,490 Abhay Vasant Ashtekar: By the same for all three. 715 01:33:36,570 --> 01:33:43,590 Francesco Gozzini: yeah yeah yeah, so this is very subtle, because in is an interplay of phases and not of scaling. 716 01:33:44,730 --> 01:33:45,120 and 717 01:33:46,560 --> 01:33:48,240 Francesco Gozzini: This is something that we have to think about. 718 01:33:50,490 --> 01:33:53,730 Francesco Gozzini: Now you have to have answered your question, Joe. 719 01:33:56,790 --> 01:33:57,090 Jonathan Engle: Thank you. 720 01:34:01,140 --> 01:34:01,830 Jorge Pullin: For questions. 721 01:34:07,050 --> 01:34:13,110 Jorge Pullin: So I have a question as an outsider what does it mean that the boundary data itself is Euclidean or lawrenson. 722 01:34:15,900 --> 01:34:19,110 Francesco Gozzini: him so if we take the example of. 723 01:34:20,400 --> 01:34:33,810 Francesco Gozzini: Obvious single vertex so for simplex the first simplex can be embedded in Euclidean space for the mission of space or in binkowski four dimensional space in the first case we speak of. 724 01:34:35,130 --> 01:34:44,310 Francesco Gozzini: Euclidean for simplex and in the second case, we speak of laurentian forcing mix in the boundary data means that you. 725 01:34:46,230 --> 01:35:06,240 Francesco Gozzini: You construct this geometry, either in the Euclidean space or in duration space and then you look at the areas you compute the areas and the normals of all the data, either on the boundary of these for CBC and you construct tickle your estate and then you put to the. 726 01:35:08,520 --> 01:35:11,010 quantum theory and you can you can. 727 01:35:18,600 --> 01:35:21,420 Jorge Pullin: metric and unexperienced the curvature and. 728 01:35:22,770 --> 01:35:23,430 Francesco Gozzini: Yes. 729 01:35:25,980 --> 01:35:35,970 Simone: way is that you take the 10 spins that define the area of the first simplex out of these you can invert for length, if you want in principle. 730 01:35:36,480 --> 01:35:44,670 Simone: And then you can compute the formula for the square the volume using the kaley expression, and you can check whether the square volume is positive or definite. 731 01:35:45,540 --> 01:35:54,780 Simone: They will give you so, in other words, is the triangular inequality satisfied by the spins that determine whether your configuration is Euclidean already gives you an option if you want. 732 01:35:55,890 --> 01:35:56,910 Simone: An orange a boundary. 733 01:35:57,810 --> 01:36:03,750 Carlo Rovelli: And I give you an example is everybody's confused about that, let me give you an example, that is, it might be clarifying. 734 01:36:04,620 --> 01:36:24,810 Carlo Rovelli: tikka tikka laurentian situation our universe okay take cosmology and imagine the university's three sphere that's a possibility, take the simplest possible to angle triangulation factory sphere, have a choice here right, you can triangulate three sphere with five. 735 01:36:27,390 --> 01:36:28,080 Carlo Rovelli: The trader. 736 01:36:29,490 --> 01:36:41,160 Carlo Rovelli: And here, you have the boundary the five to eight la for a boundary of the universe of the four dimensional universe so you're translating to cost on surface. 737 01:36:41,970 --> 01:36:57,540 Carlo Rovelli: Of a tough time with unions and your intuitively you think this is a boundary from a ransom universe, because you arrange them, but if you take this to the sphere, this this for the joy girl obviously they can be embedded in flat out for. 738 01:36:59,070 --> 01:37:00,360 Carlo Rovelli: So this is an example. 739 01:37:01,560 --> 01:37:04,080 Carlo Rovelli: If you look at the dramatic of data of this for. 740 01:37:06,270 --> 01:37:15,870 Carlo Rovelli: Of this fight that radio, this is an example of Euclidean what is called what what simonon good Francesca we call Euclidean. 741 01:37:16,920 --> 01:37:18,000 Carlo Rovelli: boundary data. 742 01:37:20,580 --> 01:37:27,120 Carlo Rovelli: For that particular State network or boundary simulation I think. 743 01:37:27,420 --> 01:37:36,180 Jonathan Engle: is confused about something else, because he mentioned, of course, boundary data usually it would you would be specifying both the intrinsic geometry and the extrinsic curvature, but I think a key point here. 744 01:37:36,360 --> 01:37:43,500 Jonathan Engle: Is that when you're talking about Euclidean versus Lorenz Ian boundary data it's only peaked on the intrinsic geometry, not the extrinsic curvature and maybe that's what. 745 01:37:44,070 --> 01:37:46,440 Francesco Gozzini: Yes, yeah yes you're right. 746 01:37:47,070 --> 01:37:48,930 Jonathan Engle: That allows more embedding possibilities. 747 01:37:50,580 --> 01:37:54,960 Jorge Pullin: But, but if i'm giving up three surface with a metric and an experience of curvature. 748 01:37:56,460 --> 01:38:00,120 Jorge Pullin: y yc that's Euclidean or lawrenson. 749 01:38:04,290 --> 01:38:04,770 Carlo Rovelli: Usually. 750 01:38:05,790 --> 01:38:06,030 Simone: No, no. 751 01:38:07,230 --> 01:38:15,840 Simone: No, is it here we're talking about a philistine brexit for simple acts as a magical property because it's there's always a unique flood embedding of the forest simplex. 752 01:38:16,440 --> 01:38:28,140 Simone: And now, this flat embedding can be either Euclidean or laurentian depending on the value of the intrinsic geometry so it's really it, which is the spins if you want so it's really a magic appropriate of different simplex. 753 01:38:30,660 --> 01:38:35,280 Jorge Pullin: For simplex is the space time here we're talking about boundaries of that right So those are. 754 01:38:36,510 --> 01:38:36,810 Jorge Pullin: So. 755 01:38:37,620 --> 01:38:48,180 Simone: So Okay, so in Carlos terms the reggie triangulation on five tetrahedron can always be embedded in Florida or four as the boundary of a first simplex. 756 01:38:48,600 --> 01:38:56,130 Simone: And now, these can be either Ukrainian or laurentian In both cases, you can always be done in each unique and whether you can do it in the. 757 01:38:57,240 --> 01:39:05,010 Simone: wonder whether you are for his Euclidean oriental medical depends on the spins of these boundary triangulation of the sphere. 758 01:39:06,030 --> 01:39:06,390 Simone: that's right. 759 01:39:06,810 --> 01:39:07,710 Carlo Rovelli: How many qualities. 760 01:39:08,370 --> 01:39:13,920 Simone: right if they get any other registering any other legit disposition of s3 this wouldn't be true. 761 01:39:14,430 --> 01:39:29,640 Simone: You will need to specify also the extrinsic geometry to tell or other additional restrictions to tell whether you're doing a flat embedding or not a very simple it's it's actually that that's why they simply says or region that's why they are particularly useful. 762 01:39:33,210 --> 01:39:34,260 Jorge Pullin: Any other questions. 763 01:39:38,850 --> 01:39:40,470 Jorge Pullin: Okay let's thank the speaker again.