Jorge Pullin: Our speaker today is Francesco xeni who will speak about high performance spin for new marks.
Francesco Gozzini: Okay.
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.
Francesco Gozzini: i'd like to mention that many results, based on previous work done here in Mercedes.
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.
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.
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.
Francesco Gozzini: In this story, I will present you a new IT performance code for competition integration API URL.
Francesco Gozzini: In that will show you the very first applications.
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.
For the Community.
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.
Francesco Gozzini: So in covariance take your G we work with graphs and triangulation made by forcing business the trader and other geometrical objects.
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.
Francesco Gozzini: We representation of G on the faces, while we color the edges with minors.
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.
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.
Francesco Gozzini: Is the state some and the partition function is the some overall bike degrees of freedom of this beam from.
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.
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.
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.
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.
Francesco Gozzini: and
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.
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.
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.
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.
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.
Francesco Gozzini: removed from the integration.
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.
Francesco Gozzini: formula can be implemented on the computer.
Francesco Gozzini: way to proceed, was put forward by bit theology.
Francesco Gozzini: We can split the previous formula is converting some over what I call the shells.
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.
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.
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.
Francesco Gozzini: In this picture, you can see, the next steps of the splitting so the non compact integrals these boxes.
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.
Francesco Gozzini: The strength on the right.
Francesco Gozzini: format, the 15 JC most of the for the left.
Francesco Gozzini: This is the complete formula, and you can see that.
Francesco Gozzini: It is defined as the infield limiting in this parameter delta as that I call the number of shares.
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.
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.
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.
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.
For.
Francesco Gozzini: The American challenges more completely.
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.
Francesco Gozzini: In the shares are cut off on these beans so.
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.
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.
Abhay Vasant Ashtekar: Right, but you, in passing, you just mentioned that if you.
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.
Francesco Gozzini: yeah yeah yes so.
Francesco Gozzini: The Fulani to show the full P amp between these limits.
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.
Francesco Gozzini: These elements of essence to see.
Francesco Gozzini: Then, that the disarm is in fact infinite because.
Carlo Rovelli: I can, I can I can I just interject maybe they said.
Carlo Rovelli: Well you're just.
Carlo Rovelli: saying is that this infinite number of terms is not saying he's not saying that.
Abhay Vasant Ashtekar: Right, but do you do good exactly that was my.
Abhay Vasant Ashtekar: But are used, but are you saying it is gorgeous and in spite of the treatment.
Francesco Gozzini: He is converting because the Sam the dap lumpy to is well defined when it is well defined, of course, so.
Abhay Vasant Ashtekar: But I mean it's a submission, this is a fact.
Francesco Gozzini: it's a fact is a it's a different way of writing the writing.
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.
Carlo Rovelli: that's here.
Carlo Rovelli: Sorry, this is a single vertex.
Abhay Vasant Ashtekar: single what exactly is fixed up.
Carlo Rovelli: Oh good feelings that this is fine, it yeah yeah.
Abhay Vasant Ashtekar: It single what exactly what I didn't get.
Francesco Gozzini: Thank you.
Abhay Vasant Ashtekar: Thank you know that's fine.
Francesco Gozzini: I will talk about divergent series, but these are different topics.
Carlo Rovelli: there's not yet the some over the the gay, which is a Bible, do you think about that.
Thank you.
Francesco Gozzini: Okay, thanks for the clarifying question.
Francesco Gozzini: So doing medical challenges.
Francesco Gozzini: For computing a single vertex amplitude.
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.
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.
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.
Francesco Gozzini: shape parameter because.
We know that.
Francesco Gozzini: drew me to this limit.
Francesco Gozzini: To the number of shares going to.
Abhay Vasant Ashtekar: infinity but, of course.
Francesco Gozzini: One wants to.
Francesco Gozzini: To get good convergence with a low number of shares to compute things quickly.
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.
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.
Francesco Gozzini: and continue with that after that we have to compute the single worst examples for all the combination of biking determinism faces.
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.
Francesco Gozzini: So disease disease, like a daunting task, but it can be done.
Francesco Gozzini: And this is what.
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.
Francesco Gozzini: The library specifically to perform these competitions.
Francesco Gozzini: It includes the computation of laurentian imperial lampeter in bfm.
Francesco Gozzini: queries disco efficient, and it was wonderful it is.
Francesco Gozzini: For.
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.
Francesco Gozzini: If we increase the average boundary spin and the number of shares in the vertex, so there is.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Francesco Gozzini: Another results.
Abhay Vasant Ashtekar: Sorry, good too, but do you understand that the difference why there is a difference, I mean.
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.
Abhay Vasant Ashtekar: guess.
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.
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.
Francesco Gozzini: The boundary space for the Euclidean case, our own genius so they are all equal and.
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.
Francesco Gozzini: The configuration that was founded by my colleagues here in marcell has the boundaries piece five and two.
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.
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.
Carlo Rovelli: Can I can I get a comment here.
Carlo Rovelli: Is my just because I think many people.
Carlo Rovelli: don't know this terminology because it's pretty exciting game so here up then endurance and do not mean that.
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.
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.
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.
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.
Carlo Rovelli: The boundary has a property that it can be immersed in a up in four dimensional space.
Carlo Rovelli: simple example is to imagine the transition from nothing to a full sphere full scale and we must.
Carlo Rovelli: Be so careful not confused, this will be presenting lengthy.
Abhay Vasant Ashtekar: But, at the very good so you're saying that everywhere, the.
Abhay Vasant Ashtekar: representation refrigeration to see.
Abhay Vasant Ashtekar: Right it's just only the boundary yeah.
Carlo Rovelli: Alright, so that is the classification of possible baldo data that you won't see that there are lots of places.
Carlo Rovelli: Yes.
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.
Francesco Gozzini: So, if we take the duration theory is we are doing this.
Abhay Vasant Ashtekar: Now, but now there's not a lot in general included right because you're talking about.
Abhay Vasant Ashtekar: lorenzen Euclidean as Carver explained.
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.
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.
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.
yeah sure.
Abhay Vasant Ashtekar: So this is.
Francesco Gozzini: This is presenting the paper.
Abhay Vasant Ashtekar: That I referenced in recording or so the statement is that there is a large class of these large class of.
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.
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.
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.
Abhay Vasant Ashtekar: So that will disappear if I just use a generic boundary data without looking at specific ones.
Carlo Rovelli: That came with the scenes.
Carlo Rovelli: screens the the amplitude is exponential.
Abhay Vasant Ashtekar: And, but we'll see is that.
Abhay Vasant Ashtekar: Once he is that in the new relics that these exposures.
Francesco Gozzini: are present, yes.
Abhay Vasant Ashtekar: Yes, okay good Thank you so much okay thanks.
and
Francesco Gozzini: Okay, so we were at the point where we see that in the the plot on the left is not completed.
Francesco Gozzini: In the end, they one wants to go to higher values of Lambda in high gear number of ships.
Francesco Gozzini: So I was starting roughly two okay to introduce or saw what they call the flatness problem.
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.
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.
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.
Francesco Gozzini: That is the force the Defense dangles to be zero.
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.
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.
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.
Francesco Gozzini: And we can pause boundary data that correspond both to flatter in the Court configurations.
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.
Francesco Gozzini: So we the the last year in the case of the BF vertex and.
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.
Francesco Gozzini: We find that in the integral.
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.
Francesco Gozzini: The acid into curvature constraints of the flatness program are not seeing this case.
Abhay Vasant Ashtekar: i'm sorry.
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.
Francesco Gozzini: yeah, this is a delicate point so.
Francesco Gozzini: Indeed, in classical BF theory.
The.
Francesco Gozzini: The connection, that is.
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.
Francesco Gozzini: But still, one can I can do the quantum theory and can try to to construct.
Francesco Gozzini: boundary data that corresponds to geometries that non that have different angles.
Francesco Gozzini: On the internal triangle, the eternal zero in this is what we're looking at.
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.
Francesco Gozzini: A yeah, this is a bit confusing if we if we consider a BF theory.
Francesco Gozzini: But the point is that.
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.
Abhay Vasant Ashtekar: Maybe we can come back and i'm still confused.
Francesco Gozzini: Okay okay we'll try to be more clear.
lead.
Francesco Gozzini: him.
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.
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.
Francesco Gozzini: The name is nice to see from next because there's still many DSM meters come from the previous version.
Francesco Gozzini: The new library use a sufficient data structures and multiple parallel position, I used to achieve maximum perform.
Francesco Gozzini: So the library is written, you see, but it provides an interface in the language Julia.
Francesco Gozzini: So essentially analysis, there is a fuel injector activity.
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.
Francesco Gozzini: A single vertex with many different values of the sharepoint.
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.
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.
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.
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.
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.
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.
Francesco Gozzini: I use this notation here in the States some, there is the contraction of these vertex dangers.
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.
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.
Francesco Gozzini: Importantly, the vertex Sam sorry easily parallelizable or are embarrassingly parallel and.
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.
Francesco Gozzini: notice that 1000 cpu which is just a very modest number in the domain of high performance computing.
Francesco Gozzini: And not only that.
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.
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.
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.
Francesco Gozzini: Okay.
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.
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.
Francesco Gozzini: We, the previous work for each day, only no values of Lambda in low value of the number of shares.
Francesco Gozzini: Within the new code, we can study.
Francesco Gozzini: We can reach very large values of Lambda in many shares from we can study many interesting phenomena, for example.
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.
Francesco Gozzini: So here is a lot of the new coda with the Burberry me the parameters set to 0.3.
Francesco Gozzini: So the blue line shows the analytic value of the same topics and.
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.
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.
Francesco Gozzini: So.
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.
Francesco Gozzini: The more we increase Lambda the more shares, we need, and the more the computation experience.
Francesco Gozzini: springs are pretty large in the speaker on indeed for the last point, the boundaries piece are afforded to hundreds.
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.
Francesco Gozzini: Two shells.
Francesco Gozzini: Here at 15 are start not to be enough to get conversions to the true value of the API.
Francesco Gozzini: Is plot required about three days and 300 cpu usage.
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.
Francesco Gozzini: We move now to the case of gamma 2.0 which is not so nice.
Francesco Gozzini: So.
Francesco Gozzini: Now we see that for shares are not enough to get the.
To get to the value of the same topics.
Francesco Gozzini: We can see that.
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.
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.
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.
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.
Francesco Gozzini: So this is a like the new results for the rotation, as some topics and I moved to the flatness problem.
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.
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.
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.
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.
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.
Francesco Gozzini: It is also possible to compute the, for example, the simple biker sellable.
Francesco Gozzini: The average lifespan.
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.
Francesco Gozzini: And so we can see the flat cases, so if we impose that flat boundary data.
Francesco Gozzini: These blocks shows the ronnie some.
Francesco Gozzini: were a jumper signals an interval of slowly changing phase in this pollination of the action so.
Francesco Gozzini: These jumper corresponds to a certain point, and indeed if we feel that the data to announce.
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.
Francesco Gozzini: Of the geometrical.
Francesco Gozzini: Body carrier, so the meaning of this plot is that.
Francesco Gozzini: We have a flat geometry in.
Francesco Gozzini: For the space and these as particular.
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.
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.
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.
Francesco Gozzini: So.
Francesco Gozzini: These.
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.
Francesco Gozzini: And Euclidean boundary the sound, is it six.
Abhay Vasant Ashtekar: Which is, what are the trends in the boundary data, the two.
Abhay Vasant Ashtekar: cases the flat case and the non flat case.
Francesco Gozzini: In the flat case and these perfectly flat triangulation so in in for the.
Abhay Vasant Ashtekar: For the master data you're talking about boundaries right.
Francesco Gozzini: A yes so.
Francesco Gozzini: So that.
Francesco Gozzini: We can we can define the triangulation in in flat space.
Francesco Gozzini: Okay, so we take free for simplicity and We grew them, we can do them at in.
Francesco Gozzini: If we set certain values of the areas.
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.
Francesco Gozzini: Not to embed this fish for simplicity, seeing flat space, but.
Francesco Gozzini: To construct them in a way that deficit thing.
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.
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.
Abhay Vasant Ashtekar: Is that what is happening.
Abhay Vasant Ashtekar: Or are you using the same boundary data and finding to sunset side at once.
Francesco Gozzini: No, the boundary data in the case of reinforce our disputes.
Carlo Rovelli: Yes, this is what was happening.
Abhay Vasant Ashtekar: Namely the outage at a.
Carlo Rovelli: Different time they did.
Abhay Vasant Ashtekar: That because I did not do what was happening, thank you very much yeah.
Carlo Rovelli: The different boundary data yeah.
Abhay Vasant Ashtekar: Different budget.
Abhay Vasant Ashtekar: So that's.
Abhay Vasant Ashtekar: The devil is dominated by white space, but the other boundary data for, which is why.
Abhay Vasant Ashtekar: Thank you so much good.
Carlo Rovelli: job of saying how we construct guess how he gets this is about.
Abhay Vasant Ashtekar: Right exactly that but.
Abhay Vasant Ashtekar: That, thank you very much, both of you okay things.
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.
Carlo Rovelli: yeah yeah yeah.
Muxin Han: Not a counter example.
Carlo Rovelli: machine he standing over an internal.
Carlo Rovelli: J.
Muxin Han: Yes, it's it's some momentum about the the horizontal axis is the box in.
Francesco Gozzini: So.
Simone: In this planet storming just brought in the distribution.
Simone: Of the internal spins.
Simone: Right sorry.
Muxin Han: Not so it's not a counterexample.
Jonathan Engle: sushi.
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.
Muxin Han: Okay, I think the left, the Left Party for something over I think it looks.
Francesco Gozzini: Like a normalized, of course.
Right okay.
Muxin Han: Okay, thanks, thank you, thank.
Carlo Rovelli: You want to see in Thailand in terms of boundary data.
Carlo Rovelli: The fact that there is, there is a subtle point implies that if you put a waste bucket.
Carlo Rovelli: Central.
Muxin Han: Okay okay I.
Get.
Seth K Asante: It.
Francesco Gozzini: Okay, I continue.
Francesco Gozzini: Sorry, are there any other question, yes.
Seth K Asante: Yes, I had a question up front of previous go like on the Left sorry okay.
Seth K Asante: The Left plot what the why exits pressure sounds.
Seth K Asante: Wang what's it.
Francesco Gozzini: what's the liberal into adding y the.
Francesco Gozzini: y axis is the value of the employee to the party, it is just normalize to define value archaeopteryx.
Francesco Gozzini: Okay.
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.
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.
Muxin Han: One can already predict that there is a peek at at the box in corresponding to the geometrical oxygen because.
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.
Muxin Han: So i'm.
Muxin Han: From the US and politics, we know that there definitely is a.
Carlo Rovelli: People she's not it's not the, this is the.
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.
Carlo Rovelli: it's a it's a sum of all the terms up to that particular exit so it's really a.
Carlo Rovelli: it's really it's really a the.
Carlo Rovelli: End of those related is oscillation is fascinating less.
Carlo Rovelli: Less past so so so so something that.
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.
Muxin Han: Right right.
Muxin Han: and
Carlo Rovelli: and actually the we cancel.
Carlo Rovelli: Tony.
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.
Right.
Francesco Gozzini: To the right plot is.
Muxin Han: is basically implying the Left plot.
Francesco Gozzini: Indeed, I think, is the contrary, because the right bra is is just the Left plot.
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.
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.
Francesco Gozzini: Because it does.
Francesco Gozzini: He speak is not there is no meaning in the sense that it is just a way of.
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.
Carlo Rovelli: This is an assumption of xp embedded itself is an oscillating thing.
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.
Carlo Rovelli: At some point the ups and down frequencies slows down.
Carlo Rovelli: So your fascination there is no association association again, so this is a way of capturing window solution is less.
Francesco Gozzini: let's.
See.
Muxin Han: Yes, but I I.
Muxin Han: Just think that i'm, this is not not really a counter example of.
Muxin Han: Of the flatness it's it's just a.
Muxin Han: At least for from the right plot from the right plot.
Muxin Han: It is just like usual which we know what we know from the US and politics.
Francesco Gozzini: Okay, I think that.
Carlo Rovelli: It is in.
Muxin Han: Because I mean from the US and politics, we know that at the fox being there is a bump.
Francesco Gozzini: But this man is not.
Francesco Gozzini: This is not a bump in the amplitude this bump is just.
Francesco Gozzini: A way of showing that there is a southern point it has it has nothing to.
Muxin Han: Other one is.
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.
Francesco Gozzini: What I can see, of course.
Muxin Han: Is a pig it's like a bank of the in the space of scenes that's what I can see.
Muxin Han: And and and this part one can predict, we found from the automatic.
Francesco Gozzini: Okay, maybe the picture is a bit misleading.
Francesco Gozzini: And of course the from remix we don't ever we just have indications that there is some.
Simone: speeches are misleading I think these pictures are really good because.
Muxin Han: They know I don't think a.
Simone: True.
Simone: picture we just did you see highly.
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.
Simone: To make that the presence of the subtle point more visible.
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.
Nice good question Latin.
Muxin Han: War, maybe, maybe we can discuss later.
Francesco Gozzini: yeah I think I think we can discuss it.
Jonathan Engle: Further question on that this is Jonathan.
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.
Jonathan Engle: class of the classical value, so there is a definitely a contribution from there, but the thing about the the the.
Jonathan Engle: flatness problem or the accidental curvature constraint, it has to do with.
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.
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.
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.
Simone: Maybe john.
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.
Simone: You are doing an integral of a function that has a point at which the gradient vanishes.
Simone: So why is there no exponentially suppress, how can that happen.
Muxin Han: Actually, complex.
Jonathan Engle: Yet you have a discreet some it's a discreet some and the you have.
Simone: To evaluate which these happens it's a real it's not a complex.
Jonathan Engle: Really.
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.
Carlo Rovelli: These.
Simone: Are the pneumatic shows that this doesn't happen, the reason to these new medical interpreting.
This is.
Simone: But anyway.
Carlo Rovelli: that's not happened, I see but.
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.
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.
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.
Simone: But at least.
Simone: let's agree that these numerical method it's useful to highlight certain properties of the integral and.
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.
Simone: Maybe maybe we can agree on that.
Jonathan Engle: Yes, no I agree it's a very clever method, yes and.
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.
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.
Carlo Rovelli: with lung the higher and higher and higher.
Carlo Rovelli: that's what happened in Michigan in bianca and how calculations right that you do.
Carlo Rovelli: suppress.
Carlo Rovelli: The contribution of.
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.
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.
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.
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.
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.
Muxin Han: yeah that's exactly yeah exactly i'm sorry i'm sorry I confuse that you had before.
Muxin Han: and
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.
Muxin Han: or not I don't know.
Carlo Rovelli: I think it is, I think that they.
say.
Carlo Rovelli: to you.
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.
Carlo Rovelli: There is.
Abhay Vasant Ashtekar: Someone is the situation as follows.
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.
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.
Carlo Rovelli: At which.
Abhay Vasant Ashtekar: There is a there is a.
Abhay Vasant Ashtekar: Normal five geometry that's what I understood so maybe.
Abhay Vasant Ashtekar: Somebody can correct me a bit briefly, maybe, without going to technicalities.
Carlo Rovelli: Was I think that, without bianca.
Carlo Rovelli: bianca how's it going it's much simpler.
Abhay Vasant Ashtekar: yeah is it much simpler example my.
Carlo Rovelli: model in which much farther than than what Francesco company account because because anything credence.
Abhay Vasant Ashtekar: yeah.
Abhay Vasant Ashtekar: But it's pretty pretty Euclidean in the usual sense of the word.
Carlo Rovelli: Nothing.
Carlo Rovelli: But there one sees that the theory has a regime that correspond to the classical language.
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.
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.
Carlo Rovelli: So you don't see the glass of the limit anymore.
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.
Carlo Rovelli: fact like like that.
Abhay Vasant Ashtekar: So it's up to here i'm completely on the same wavelength, but it's the.
Carlo Rovelli: Next statement.
Carlo Rovelli: The next point the way I understand it, is that this field is a part of this progress until I find.
Carlo Rovelli: A physics.
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.
Carlo Rovelli: Right is it bigger or anything like they just get a three part people.
Carlo Rovelli: Or how many health and.
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.
Abhay Vasant Ashtekar: The disagreement is on whether this is an interesting indication that something is that that there is possibly a.
Abhay Vasant Ashtekar: Non trivial.
Abhay Vasant Ashtekar: Point of stupid to sleep as descent right.
Abhay Vasant Ashtekar: So semi classical approximation is good, are in fact the shows that that, in fact, is a non flat.
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.
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.
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.
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.
I guess, thank you for the interference.
Abhay Vasant Ashtekar: yeah these are very helpful for those of us who are not experts Thank you so to.
Francesco Gozzini: reply to simoni yet the plots are exactly the same if you put the imaginary part.
So.
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.
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.
Francesco Gozzini: Thanks Jonathan so to be clear, of course, we are not buying the numeric the metrics.
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.
Francesco Gozzini: Something more to understand.
Carlo Rovelli: I see how can I can I ask.
Hal Haggard: yeah go ahead Carla i'm here.
Carlo Rovelli: Can I ask you what I was hoping, you would say something.
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.
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.
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.
Hal Haggard: is also on this call and young postdoc and a wonderful person and he did a huge body of the numeric.
Hal Haggard: So I wanted to make sure his name got mentioned.
Hal Haggard: The money you're unmuted and we can hear you.
Francesco Gozzini: Okay, thanks everybody for all the comments, is a very interesting discussion, and I see that.
Francesco Gozzini: There are many interesting means.
Francesco Gozzini: If everybody agree, let me just continue.
Hongguang Liu: To ask a single question which type of data are you using.
Hongguang Liu: you're using Euclidean under data organization bounder did.
Francesco Gozzini: They are Euclidean.
Hongguang Liu: Okay, that is a luxury car.
Francesco Gozzini: Yes.
Hongguang Liu: Okay, so okay.
Francesco Gozzini: So I have more plots on these delta free so.
Francesco Gozzini: So here, for example, in the spirit of.
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.
Francesco Gozzini: The semi classical limited in both flood ks and the curve Kazan.
Francesco Gozzini: agrees with.
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.
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.
Francesco Gozzini: This is a very long number, and this is probably due to just numerically.
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.
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.
Francesco Gozzini: semi classical.
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.
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.
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.
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.
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.
Francesco Gozzini: And the amplitude should be divergent that because the internal physicists form a bubble.
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.
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.
Francesco Gozzini: And this is the formula.
Francesco Gozzini: With the new coil we can compute these divergent series, so we fix or your genius cut off of an Internet speeds.
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.
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.
Francesco Gozzini: So I show you the plots of these men an amputated computer, we were very musical Stan set to 0.1.
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.
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.
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.
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.
Francesco Gozzini: We have also some plots of around the barbarian music parameter.
Francesco Gozzini: handle this last plot is interesting because it shows that the convergence and I call this convergence, even in a priori the.
Francesco Gozzini: amplitude are divergent but you see these convert this towards the last day at the I guess cut off normalized one.
Francesco Gozzini: is much better with the low value some very nice.
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.
Francesco Gozzini: At the same value of the boundary speeds so Theresa the convergence, so I stopped with application, I can I can do.
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.
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.
Francesco Gozzini: uses morning near these practical, from the point of your lyrics.
Francesco Gozzini: For the nazca free.
Okay, we had the.
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.
Francesco Gozzini: and
Francesco Gozzini: I also have computed the bike expectation values and compared it with the corresponding classical geometry.
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.
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.
Francesco Gozzini: I would like to conclude with some ideas about the next steps so some possible improvements to the call include the.
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.
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.
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.
Francesco Gozzini: Also, in the spirit.
Seth K Asante: Of the.
Francesco Gozzini: work by mankind set to be nice to test the Wednesday night miss reading terminal dynamical segments.
Francesco Gozzini: In through an ongoing work with the power of visual me is the computation of the minimum graph.
Francesco Gozzini: With creating boundary and also competing of server barkin boundary of servers and also we need to.
Francesco Gozzini: apply a Monte Carlo techniques for nuts.
Francesco Gozzini: grass or even think about, for example, the normalization thing, and if you have any suggestion.
Francesco Gozzini: I have received it.
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.
Francesco Gozzini: The code is free and publicly available, so you can find it and and his address and.
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.
Francesco Gozzini: So I stopped hearing things for your attention.
Jorge Pullin: Oh, more questions.
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.
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.
Simone: Live she symbols that.
Simone: machine Hong Wang Chung presented the recently to us, which also seem to be extremely powerful and promising and I was wondering if.
Simone: The metal you're using is in a in a sense, maybe some advantages respect to the other, maybe it's more.
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.
Simone: Improving the way they look for.
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.
Francesco Gozzini: Yes, I would say that these are like complimentary meters, because we have the two codes that do very different.
Francesco Gozzini: Things and they use very different techniques, so the techniques that we use are.
Francesco Gozzini: Our most suited for the spins not to hike.
Francesco Gozzini: But we need, we can.
Francesco Gozzini: Do we can do.
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.
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.
Francesco Gozzini: investigate.
Francesco Gozzini: The semi classical limiting and more effective way.
than our code.
Francesco Gozzini: Once one.
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.
Jorge Pullin: questions.
Abhay Vasant Ashtekar: I just requested by.
Abhay Vasant Ashtekar: I just have a really strong strong request.
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.
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.
Simone: Why do we have other users don't understand.
Simone: Why is it different understand why is it different.
Simone: But that's exactly what happens when you take.
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.
Abhay Vasant Ashtekar: model is not Indian, so why do you call it, you.
Simone: know is the boundary data, these are you.
Abhay Vasant Ashtekar: know, but I think.
Abhay Vasant Ashtekar: The way it is also just said is really.
Abhay Vasant Ashtekar: You know Okay, what is a model.
Abhay Vasant Ashtekar: That was being said today.
Simone: OK OK OK.
Abhay Vasant Ashtekar: But he was that you know.
Simone: Maybe.
Abhay Vasant Ashtekar: Very important is that you know you.
Abhay Vasant Ashtekar: make up a symbol right.
Okay.
Abhay Vasant Ashtekar: Do your makeup something which is not just.
Simone: Okay, no, no, I understand, thank you.
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.
Simone: Okay Okay, thank you.
Francesco Gozzini: yeah maybe Indeed it was a source of confusion.
Yes, so thanks for.
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.
Jonathan Engle: it's actually quite understood that, because this you can audrey data it's not only.
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.
Simone: Wait.
Jonathan Engle: that's interesting thing is.
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.
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.
Simone: Look sure.
Carlo Rovelli: explain that to me one day.
Carlo Rovelli: Long.
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.
Muxin Han: That.
Carlo Rovelli: How said yeah model has the same.
You know.
Hal Haggard: Well we've only in.
Carlo Rovelli: The you're not there yet so.
Hal Haggard: yeah we've only investigated a Euclidean eerie.
yeah.
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.
Seth K Asante: not yet I mean we just starting to understand lawrenson reggie it's it's very different from Euclidean so.
Seth K Asante: Yes, i'm excited this year have to come over before we can do, effective spin phones like we did before.
yeah.
Seth K Asante: But if I may, I have a question for Francesca.
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.
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.
Seth K Asante: Their lines and like I just I was just wondering, the interpretation of the sophistication you mean.
Francesco Gozzini: In.
Francesco Gozzini: Yes, the.
Francesco Gozzini: The average American interpretation, if you if you want to see that so.
Francesco Gozzini: Technically, we are just deleting.
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.
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.
Francesco Gozzini: You a modem router functions you.
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.
Francesco Gozzini: But for Euclidean boundary that and.
Francesco Gozzini: The booster functions in the splitting have the role of introducing critical points that corresponds to geometries that are non.
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.
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.
Francesco Gozzini: These things we've created on Monday, after the show critical points when you can do a booster.
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.
Simone: Now, do you mind if I add something also it.
Simone: is very clear answer already but.
Simone: You know, said this question you you just ask the haunted me for as long as these, the composition was introduced.
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.
Simone: But what is really non trivial is, what do you mean by boosting a tetrahedron.
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.
Simone: Which is what, if you want a better model is built on except that.
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.
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.
Simone: So how this this notion of a simple by factors come into play as well it's actually quite interesting.
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.
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.
Things.
Muxin Han: So.
Muxin Han: I have a comment and it relates to comparing the flatness result you show those plots and and.
Muxin Han: And the result we have earlier analytically by awesome article, and also the new result of john and water.
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.
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.
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.
Muxin Han: The amplitude and then, of course, on to something over multiple critical points and you got multiple phases.
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.
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.
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.
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.
I have.
Muxin Han: And and, by the way, thanks for simoni for mentioning our work.
Francesco Gozzini: Okay yeah I think that.
Francesco Gozzini: thanks for your comments.
Francesco Gozzini: it's tricky to feed the.
Francesco Gozzini: numerical data in this case is when you don't have many points, of course, so, in fact, we didn't try.
Francesco Gozzini: To.
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.
Francesco Gozzini: On a different method is this algorithm to search for southern points because, indeed the fitting it.
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.
Francesco Gozzini: So.
Francesco Gozzini: I think that there were there was no value in in these fields, but I can try to.
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.
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.
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.
Things.
Jonathan Engle: like to ask another question about the.
Jonathan Engle: So we were talking about i'm about how the I mentioned again how the Euclidean.
Jonathan Engle: boundary data is actually degenerate boundary data and and there's another.
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.
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.
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.
Francesco Gozzini: And this is an interesting question, I think that, as far as.
Francesco Gozzini: For single vertex case this is pretty clear, so this has been done by simonon patrons are Joe and others.
Francesco Gozzini: But if we consider more vertices then.
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.
Abhay Vasant Ashtekar: So, can you remind us what someone and Pietro concluded for a single vertex what is the.
Abhay Vasant Ashtekar: switch and which has some time in it and sub sub document.
Francesco Gozzini: So maybe maybe simoni can answer that but basically a vector geometry is is a geometry, that is not rigid.
Francesco Gozzini: But it's still not small.
Abhay Vasant Ashtekar: But, which is dominant in.
Simone: The answer, they have the same power law.
Simone: director geometry as a single we confirm the.
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.
Simone: Like a gauge independent notion of the installations, but the power rule is the same.
Abhay Vasant Ashtekar: By the same for all three.
Francesco Gozzini: yeah yeah yeah, so this is very subtle, because in is an interplay of phases and not of scaling.
and
Francesco Gozzini: This is something that we have to think about.
Francesco Gozzini: Now you have to have answered your question, Joe.
Jonathan Engle: Thank you.
Jorge Pullin: For questions.
Jorge Pullin: So I have a question as an outsider what does it mean that the boundary data itself is Euclidean or lawrenson.
Francesco Gozzini: him so if we take the example of.
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.
Francesco Gozzini: Euclidean for simplex and in the second case, we speak of laurentian forcing mix in the boundary data means that you.
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.
quantum theory and you can you can.
Jorge Pullin: metric and unexperienced the curvature and.
Francesco Gozzini: Yes.
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.
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.
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.
Simone: An orange a boundary.
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.
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.
Carlo Rovelli: The trader.
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.
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.
Carlo Rovelli: So this is an example.
Carlo Rovelli: If you look at the dramatic of data of this for.
Carlo Rovelli: Of this fight that radio, this is an example of Euclidean what is called what what simonon good Francesca we call Euclidean.
Carlo Rovelli: boundary data.
Carlo Rovelli: For that particular State network or boundary simulation I think.
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.
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.
Francesco Gozzini: Yes, yeah yes you're right.
Jonathan Engle: That allows more embedding possibilities.
Jorge Pullin: But, but if i'm giving up three surface with a metric and an experience of curvature.
Jorge Pullin: y yc that's Euclidean or lawrenson.
Carlo Rovelli: Usually.
Simone: No, no.
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.
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.
Jorge Pullin: For simplex is the space time here we're talking about boundaries of that right So those are.
Jorge Pullin: So.
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.
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.
Simone: wonder whether you are for his Euclidean oriental medical depends on the spins of these boundary triangulation of the sphere.
Simone: that's right.
Carlo Rovelli: How many qualities.
Simone: right if they get any other registering any other legit disposition of s3 this wouldn't be true.
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.
Jorge Pullin: Any other questions.
Jorge Pullin: Okay let's thank the speaker again.