Sebastian Steinhaus (he/him): Yeah.
Jorge Pullin: yeah. Share his screen and go ahead.
Sebastian Steinhaus (he/him): Hello.
Sebastian Steinhaus (he/him): it says Host. Has disabled participants screen sharing.
Sebastian Steinhaus (he/him): Okay? So I'm I'm great that now, my desktop, take some time before I can actually share my screen. So
Sebastian Steinhaus (he/him): but
Sebastian Steinhaus (he/him): yeah, it will take some time, but it will come to my screen will come back at some point. but anyway, so I'm happy that I have this opportunity to
Sebastian Steinhaus (he/him): to give this presentation about American methods in spin phones, because I wanted to recapitulate a little bit about the methods and the techniques and the progress that we in the community have made over the last few years, and in particular about the aspects of
Sebastian Steinhaus (he/him): like explicit evaluation of vertex amplitudes on the one hand, and then the new effective models that we are developing that utilize semi-classical methods.
Sebastian Steinhaus (he/him): And in these various aspects I actually want to a little bit share. Then my own perspective on that and was hopefully new, interesting insights for all of you, and maybe some future techniques. So II have a few things to say about Monte Carlo, for example. So I hope this will be interesting for you
Sebastian Steinhaus (he/him): and I would give a very, very brief introduction, because this talk is mostly not about the specific of the physical. Some part is some part is not. It's more about numerical letters, but the problem will be spinning up on gravity as a non perturbative part of geometries, and particularly calculations, is where the numerical part will come. I will interpret the 2 complex as a regulator, and the system, and the key part of our spin phones is that we have quantum geometric building blocks
Sebastian Steinhaus (he/him): which we derive from constraint, logic of quantum field theory.
Sebastian Steinhaus (he/him): and we have a discrete area spectrum, the physical content of our theory, our transition amplitude, which, of course, we then want to compute, and one of the most important results that we still have is that for a single building block in what some has called, you know, last J limit, we re obtained this to gravity, retro gravity.
Sebastian Steinhaus (he/him): And also, importantly, the actually using quantum, and it becomes more and more apparent on the last few years. It's actually an important physical insight that we should actually not implement. Actually, they don't make a reference to background geometries, and we aim to implement a few more.
Sebastian Steinhaus (he/him): However, the challenge that we face is actually computing things in this approach.
Sebastian Steinhaus (he/him): In particular, if you look at the partition function that is usually written in this way, there are 2 challenges that we face. So one thing is, of course, the key. Important dynamical building block, which is the verdict number 2, which I pictorially drawn here, which can imagine here for a 4 simplex, as the contraction of 5 enter 5 can imagine to be dual to fuzzy tetrahedron.
Sebastian Steinhaus (he/him): This calculation can actually be extremely challenging. And I will talk about this. The other part is that actually the sum over representations intertwine us which encodes the geometry of our building blocks is the second part that is highly challenging. And this is actually
Sebastian Steinhaus (he/him): also the key point about he's not determined the calculations that they typically require a lot of numerical resources. And often we make progress in those calculations from Meta, analytical understanding. And I will try to keep this message or get this message across, doing this talk in both of these aspects.
Sebastian Steinhaus (he/him): and start them by highlighting. Briefly what I think are some of the progress that we made over the last few years. So, first of all, there are some resources for additional reading voice, introductory reading. There are the handbook of articles in particular. That's the article by and on, one about how to perform high performance computing calculations.
Sebastian Steinhaus (he/him): and then also some aspects is covered in my article with Seth Asante and Bianca didfish.
Sebastian Steinhaus (he/him): for example, about effective spin forms. About the explicit calculation when it's coming to there. Of course the asset to the phone package, or particularly assets for next package for Eclf K model, as basically the pico of of that direction and there's also A/C to the Fpu, where we have contributed a little bit, and we want to publish more tools. Hopefully soon.
Sebastian Steinhaus (he/him): The other part is, of course, about utilizing the semiclassical insights. One of those directions are effective spin phones, whichever mentioned about later on.
Sebastian Steinhaus (he/him): also, of course, the complex critical points which both heavily emphasized.
Sebastian Steinhaus (he/him): under which conditions, and actually that one can recover length, version, conference, or at least semi classical length or semi-classics, which look like length, virtual solutions for larger trying conditions, for larger complexes, which is like building and extending obviously the results that we have for such a long time
Sebastian Steinhaus (he/him): in a bit of a similar veins what we call the type of presentation for spin forms and I also work on what's called restricted spin phones. The respected part I won't talk much about, but I will mention the hybrid presentation a little bit to link effective spin forms to the, and a very recent result by acceleration operators for series conversions, which is, if you are summing many, many contributions.
Sebastian Steinhaus (he/him): For example, in this it's difficult to see whether the system converges or not, and they found actually rather old.
Sebastian Steinhaus (he/him): I think, from the fifties and sixties methods that can actually help understand or accelerate the conversions of disease. And there's also investigations into Monte Carlo methods. So there's the Markov chain, Monte Carlo. Let's just timers and random sampling for dealer and dependent model has been used as well. So I want to cover some of these aspects during my talk in particular.
Sebastian Steinhaus (he/him): in the first part, talk about the explicit evaluation of spin from amplitudes. Then talk about building these effective models. This part about whether, actually, one could use Monte Carlo. Is there any potential for Monte Carlo? I might only very briefly touch upon. And then I want to give you a summary outlook.
Sebastian Steinhaus (he/him): So as I mentioned in the beginning, the semi classical properties of sprint forms is one of the most important results that we have. And if we're looking at a just a single vertex, the vertex amplitude as critical points which dominate for large representations. And we have, like a plethora of results, from which we have and obtained that
Sebastian Steinhaus (he/him): basically just go to the points
Sebastian Steinhaus (he/him): correspond either to genetic forces, and if they do, they will say with eventually action, which is an impressive and very important result, that you can actually recover discrete gravity from this other voice, rather abstract view.
Sebastian Steinhaus (he/him): So this, of course, like a very, very important system to check. The other aspect is also the better geometries which we talk to talk about. Yes, an important ingredient for these derivations article here, and boundary data, particularly in touch lines which I will usually represent here by these little mops
Sebastian Steinhaus (he/him): on on the edges of the representations. And then these group integrations.
Sebastian Steinhaus (he/him): So what is so important about these critical points. And why do they dominate? Well, because if you do not satisfy these critical point equations, you get excellential subtraction away from the critical points. And I've tried to show this here on the right hand side. So this is already from explicit evaluation of S into ef
Sebastian Steinhaus (he/him): for different boundary data. So one is the Equilateral for Simplex, and it's also be scales to take click to take care of the typical scaling behavior. So the blue curve is actually the equilibrium. And then you have several more and more non closing
Sebastian Steinhaus (he/him): configuration. So I've chosen the boundary data in these situations, such that the tetrahedron are actually much better. They do not close anymore, and they they become exponentially suppressed. And the more and I'm closing they are the more exponentially suppressed they become
Sebastian Steinhaus (he/him): so. The question is beyond these semi-classical methods, how can we actually perform or evaluate these workers?
Sebastian Steinhaus (he/him): So the first example is, the J. Simple or Vpf. Versus amplitude. More precisely if you have written it, or if you have that convergence under 2 with bombing data in all the models for network basis. And so 15 J simple, it is called because it depends on 10 spins. These would correspond to the 10 areas of your
Sebastian Steinhaus (he/him): of your 4 Simplex.
Sebastian Steinhaus (he/him): Yeah. So here, up to J, 4, 5, and then you have 5 additional ones which come from the expansion of the Internet wires. So the the ultimate basis of the wires, which are again interrupt, we can again see as representation labels which correspond to the recoupling or participants into a intermediate one and then into the other 2 remaining ones. So that's why it depends on 50 labels.
Sebastian Steinhaus (he/him): And very importantly, it can be written as this closed formula on the right hand side. Yes, one summation there was parameter X. And the nice thing is, it is the final song. It is constrained by the labels and it is some, or it is here a product of 5, 6 trace symbols. Which are also some coupling symbols. And the good. The positive thing is
Sebastian Steinhaus (he/him): that typically for what? Typically for whatever programming language you're looking for, there will be some package which is highly optimized for computing these 6 J symbols, which is, of course, like one lesson always. If you wanted to calculations. If someone has done already optimized, they probably have done a better job than you. But also, let's be honest, we're not computer. We're not computer scientists. So
Sebastian Steinhaus (he/him): it's usually a good idea to rely on. Someone else was extensively optimized, and that this calculation that can be done is actually at the core of many of the calculations that are that are about
Sebastian Steinhaus (he/him): right. So. But the calculation that I showed you before, for which you get these com. These critical points and the recovery of the virtual action were not done in the basis they were done in the coherent state based for coherent wires and you can rewrite them, or you can write on this amplitude here. In a close form.
Sebastian Steinhaus (he/him): and which is also very nice. You can use the properties of the coherent States, for example, down here. Where you say where you realize that you can rewrite the same expression in the fundamental representation of SE. 2, system, one half representation, and take the whole expression to the power to J. And this expression is just the contraction of the coherent States. On the boundary and wedge in between the grouping
Sebastian Steinhaus (he/him): integrations and these objects here intertwine is, you have to explicitly integrate over the issue. Yeah, so so these are, I've done 5 integrations. But one of them is actually gauge this gauge symmetry. You can absorb one of these integrations. So you're left with 4. But
Sebastian Steinhaus (he/him): the problem is, these are well, it's 4 A/C 2 integrations. SU. 2 is 3 dimensional. So this would be a 12 dimensional, simultaneous integration of these highly oscillatory functions. Yeah, so these are cosine and sines up to a certain power. So you can imagine. If you make J very large, this oscillates very rapidly.
Sebastian Steinhaus (he/him): Now you can try to explicitly calculate this via America integration. But the convergence is very slow, and it's probably not even going to work. They should pick all the setting for the stationary phase analysis, because what you could do is that you exponentiate this expression? So you have each of the lock of this, and you can then get to J into the front, and then the whole station can take place. So
Sebastian Steinhaus (he/him): And that's very well. But, like the American integration is pretty much hopeless. And the key in insight to to to actually compute this, then, is to perform the integration analytically. So the object here is what we are well familiar with as the hard projector. So you have the tensor product of several representations of issue, and you can perform the integration and expand this, as is some over interference.
Sebastian Steinhaus (he/him): And there's also
Sebastian Steinhaus (he/him): works out. If you have the coherent states on one side, which is means that here you have something like a change of basis expanded in this label iota, which is just a coupling basis. And then another part which goes into the vertex. So the so you basically do this transformation for each group integration here on the on the boundary.
Sebastian Steinhaus (he/him): And what you obtain is this new expression here on the right hand side. So now we see we have again the so called 15 Json, but that we have previously at the center, which we can relatively easily compute.
Sebastian Steinhaus (he/him): And also now we have this, some over these intertwine labels here contracted with these change of basis from the basically from the human intertwiners to the basis. Or you can say it's the coherent expanded in that basis of this.
Sebastian Steinhaus (he/him): So what we have done now we have traded the group integrations for a sum or finite labels, and in particular. For example, if you would say that all of the spins in the system are spin one half.
Sebastian Steinhaus (he/him): this is extremely easy to do, because then
Sebastian Steinhaus (he/him): you have in touch minus basically just run from 0 to one. So you just have 2 to the 5, some variables sum over. It's very easily done right? And it's a much better process.
Sebastian Steinhaus (he/him): Of course
Sebastian Steinhaus (he/him): you've I mean there's no free lunch. So if you make the spins now overall larger, what also happens is that your intertwine arrange grows. So if your spins become larger and larger, you will also have more internal names for some more, so this will become more and more costly. And actually, it grows exponentially.
Sebastian Steinhaus (he/him): Right? There's one wave.
Sebastian Steinhaus (he/him): You can optimize this, which is what's so called tense network methods. And this would basically mean that you interpret this 15 Jason would here in the center as a 5 bail and tensor. So you have your labels. And you, you think that these are basically tenser labels.
Sebastian Steinhaus (he/him): Or you could say, it's a it's a 5 dimensional array, and you're contracting it with 5 vectors. And this is faster, because, what you basically do is linear algebra operations. So what you can, what is basically done. Then there are pre-existing packages for that as well, you are transforming your 15, that we are, you know, 15 J symbol into, for example, in matrix. And then you do matrix multiplication with the vector and this is in many languages much faster than, for example, writing it for you.
Sebastian Steinhaus (he/him): Yeah. The trade off again, is your training commutation of time with memory. So you also can't do this indefinitely, because the 50 J symbol and it's various transformations must fit into memory. But I mean.
Sebastian Steinhaus (he/him): the positive thing is, we had a calculation previously that was very difficult, and we traded it for something that can be done.
Sebastian Steinhaus (he/him): and in particular we traded this group of integrations for a sum over finite orthonormal intertwinners.
Sebastian Steinhaus (he/him): The situation gets worse enough. Open Renzi dependent models. The Soc amplitude, because now we have basically a 24 dimensional integration for Iso C elements in the Quero State representation. There are also spinner variables and just suppressing all of these things.
Sebastian Steinhaus (he/him): I've also dropped one integration explicitly. Because constraints, it's important if you do several forcing Vcs together in the independent model that they do along a common spatial micro service.
Sebastian Steinhaus (he/him): And this integration, again, in the quick and state representation which is useful for obtaining the semiclassical amplitude, or then including the asymptotic expansion. With this way, now, you have essentially group elements, and this is, of course, much more challenging because you have now a non compact group and a much higher dimension integration.
Sebastian Steinhaus (he/him): But the crucial insight by Simon is well. Simona was like 7 years ago that one can decomp policy as interesting integration. So the first thing is, one can use just the properties of soc presentation theory to split these representation to 2. And what this does is introduce it introduces a sum over auxiliary as you 2 spends.
Sebastian Steinhaus (he/him): and Simon is key inside. My was that you can use the Katambi composition SN. To C. And right Sm. 2 c. As a S as an Se. 2. Integration, a boost integration, and then another se, 2 integration.
Sebastian Steinhaus (he/him): So in particular, if you look at a single edge off the Eca and water. Yeah, so this would be here. Next, something like the projector.
Sebastian Steinhaus (he/him): You have. Basically here the data. And here the data at the left hand side, it goes to one vertex in the right hand, side to another. So here you have the map, and here the S into C integration. And here. Now these auxiliary spins, called L, which come from splitting. See sso to C representation matrix.
Sebastian Steinhaus (he/him): Now you decompose
Sebastian Steinhaus (he/him): the asset C group element into SU, 2 goes in SU. 2 on both sides and perform the sc. 2 integrations again, analytically. So the first part here and so.
Sebastian Steinhaus (he/him): and by that I just mean do the same as before, use the hard projector, and expand it as the sun over inter tyres the first part here you can exchange it with the because you can put it over this one. And what you essentially get is a an contract with itself. And that's just so that one is already done for. It's nice
Sebastian Steinhaus (he/him): and the right hand side you do the same thing, and you get a different intertwine label. It's just K here, and we are left now with this expression, where you have the boost left, and this is often called, I think, the Boost Matrix, which on the right hand side, has, like the original J on the left-hand side. It has the other L, and here's the remaining booster left.
Sebastian Steinhaus (he/him): The important thing is.
Sebastian Steinhaus (he/him): Now, you don't have the integrations anymore. You have 4 oned left. This is still not enough, because if I remember correctly, one has to use arbitrary precision. Floating point data to compute this. But I might be wrong about this.
Sebastian Steinhaus (he/him): But the important thing is, you don't have 4. But we have basically for one integration. So you can do this beforehand. And then so
Sebastian Steinhaus (he/him): what we were left with then is now again this expression, and again, here in the center, you have your original fifth sc. 2, 15 base symbol. However, this is now in the auxiliary response, and here you have to boost integrations.
Sebastian Steinhaus (he/him): And here, on the left hand side again, degree and boundary data. The challenge here, of course, is that now these things are in principle or computable, but these computations are still not. And you now have to additionally some overall of these data in particular, these observable data.
Sebastian Steinhaus (he/him): Fortunately, over these particularly spins in the middle you can perform something called a shell sum. So these Lf, they start at the boundary value J, and essentially run up to infinity.
Sebastian Steinhaus (he/him): Right, if you would have the sum to infinity. To get conversions would, of course, be very difficult.
Sebastian Steinhaus (he/him): but fortunately it converges after the field coming. But this that does mean that in sum over the various possibilities of these l's up to a certain above jf, up to a certain Delta.
Sebastian Steinhaus (he/him): you know. And so
Sebastian Steinhaus (he/him): so again, what I want to get across is from the identical insights it was possible to turn this integral on this
Sebastian Steinhaus (he/him): very difficult expression into something that is computable. This is still a lot of effort and required a lot of insights and optimizations. For example, we do not want to compute
Sebastian Steinhaus (he/him): don't want to complete things multiple times if you only need once, for example. So that's why they introduced hash papers for 6 base symbols, right? Because you need 6 races to compute these 15 Jones. So they are a lot of insights and optimizations that culminate in the development of next.
Sebastian Steinhaus (he/him): which, in addition, comes with all the care that you have to put into this to get all the factors, and so on right. So this was a very great effort, and it made.
Sebastian Steinhaus (he/him): like the Lorentzian Pond regime, also for several synthesis accessible, even though it is at high cost.
Sebastian Steinhaus (he/him): and it is a high cost, because you have these, all these additional sounds, and just to name a few of the results that we that came out with this? So this now the verification explicit verification of model up to very high
Sebastian Steinhaus (he/him): which means you have a
Sebastian Steinhaus (he/him): a larger truncation that has also bio triangles at which you can locate curvature, for example, Alaric calculus, and it turns out that the is exponentially suppressed. If you blow the boundary up and make it very large if the boundary data leads to a curved solution in the bulb.
Sebastian Steinhaus (he/him): and was the first American confirmation of that the diverse behavior was investigated also in great detail, their tools to search for critical points and mentioned before using contraction of interference, pencil networks as a method, and also Monte Carlo methods were used
Sebastian Steinhaus (he/him): as well to accelerate some of these.
Sebastian Steinhaus (he/him): Some of these calculations, and there has also been this year an article about how to form these calculations.
Sebastian Steinhaus (he/him): We here again are working. So the intention for that is a bit different. And I might explain Slater. So particular, my speech student has built a 2 complex constructor where that I just move that you basically tell it. I have several possibilities. And they are. And then the code basically assigns.
Sebastian Steinhaus (he/him): what are the triangles? What are the spins? What are the variables that you must assign to this?
Sebastian Steinhaus (he/him): And we also work on slightly different, but for the major work on this you have to see. This paper from 2017, where this is quoting that detail.
Sebastian Steinhaus (he/him): I also worked on fire there, and I see 2 birds, multitudes
Sebastian Steinhaus (he/him): and we also use these results from here in a paper this year to extrapolate some point number 2, the same classical regime. I'll be it only in
Sebastian Steinhaus (he/him): in the case where the action where you actually don't have an oscillating behavior.
Sebastian Steinhaus (he/him): So this is now the part that I finish about the explicit vertex commission calculation. Are there any questions?
Sebastian Steinhaus (he/him): Okay? If that's not the case, let me continue towards building effective models.
Sebastian Steinhaus (he/him): because
Sebastian Steinhaus (he/him): what I tried to get across now as well was that if you increase, the calculations become more and more difficult in many cases you have an exponential growth of the numerical cost. And this is obviously a problem. And I think we need longer triangulations to make contact with continuing physics, and if you want this situation, you will have a plethora of configurations to some over, and eventually becomes not feasible of repeating these calculations of change.
Sebastian Steinhaus (he/him): So I think it is necessary that we also have physically motivated approximations. One would be that the android comes simpler to compute
Sebastian Steinhaus (he/him): or themselves, and maybe we can exclude that level of configuration, even though we have to be careful with that and one possible route which I think has gone through the over the last few years are using the semiclassical analysis. One would be using semi-classical amplitudes as a valid approximation for larger presentations.
Sebastian Steinhaus (he/him): and say that. Well, maybe we only need to consider critical points
Sebastian Steinhaus (he/him): for large presentations. I put this in quotation marks, large screens. I could have also said, because I don't exactly know what large would mean, or when this is a good approximation.
Sebastian Steinhaus (he/him): But I think
Sebastian Steinhaus (he/him): both of these ideas could accelerate American calculations a lot. So when are such approximations justified? Question which, of course, you would want to validate in the full model.
Sebastian Steinhaus (he/him): But let's see what we found out so far, and I think important results was the last few years where the one has the complex critical points and the effect is platforms. So both the complex critical points in particular, you and Thompson Group. Is the asymptotic analysis of spit phones on larger complexes, with the important insight that you get, or that you could eat more than just to view critical points.
Sebastian Steinhaus (he/him): to get the correct results more than just to be in particular points contribute
Sebastian Steinhaus (he/him): particular. These these complex critical points corresponds to non flat configurations. And
Sebastian Steinhaus (he/him): yeah, so and but this you see, that they still contribute even at very large scale. So they consider, for example, spins of the size of 10 to 11, which is like,
Sebastian Steinhaus (he/him): yeah, and highly impressive.
Sebastian Steinhaus (he/him): CC, that even small. There is an angle that's the contribute, and you have a configuration that corresponds to that. And of course, then the large that is, an angle becomes eventually the expansion. But it is important to include these things in order to recover the virtual action under certain conditions from the spin for model. And that's just shamelessly taking the plot.
Sebastian Steinhaus (he/him): Any other insight which I think hinges on this, which I'm trying to build a spin for model by retaining is key features like in the screen area spectrum and basically do an area. So you you need to replace the full and choose by the exponentiated area Reggie action and
Sebastian Steinhaus (he/him): then introduce given constraints which are peak on shape matching
Sebastian Steinhaus (he/him): order to recover length for Chicago, and then which conditions in a similar vein as soliciting constraints. And
Sebastian Steinhaus (he/him): and the key point is here that they've discussed the mechanism. Between these growing constraints, which are these Gaussians and the oscillatory behavior of the amplitudes which depends on the music parameter gamma. And this is a result that has paid multiple times, that if you make up small you know, the flatness problem becomes less severe, and this seems also to be the case here. That is important to cover this. And the argument is.
Sebastian Steinhaus (he/him): for example, here on this side, and we'll try to explain this a bit better later on is, if you make on a smaller
Sebastian Steinhaus (he/him): the the oscillations
Sebastian Steinhaus (he/him): of your amplitude become less, and the Gauss, the these fluid constraints, these these weak implementation, simplicity, constraint, as is, it is argued.
Sebastian Steinhaus (he/him): actually work, and are not washed out by the oscillations.
Sebastian Steinhaus (he/him): So why is it necessary? So why is it necessary that we that you know we need also more than just these real critical points, and I think it has to do with the relation between area, rich calculus and names which. So if we just look at the area before dimensions, it is a rather simple expression where you have the areas of your triangles, times, depth, angles.
Sebastian Steinhaus (he/him): in the bulk, and then you have some boundary terms. The boundary terms are not that important for what you want to discuss here now, but they're important for the variation principle.
Sebastian Steinhaus (he/him): and the relation. Now between length and area. Rich. Chicago has been starting with detail. And there's, for example, the paper by Bianca and Simona, from 2,007, in which they derive area angle variables, and already argued that these variables are more suitable for making contact with 3 4 models and names. Reggie and Error, Richie, are like very different theories, even though they look similar.
Sebastian Steinhaus (he/him): right? Because the action is actually the same.
Sebastian Steinhaus (he/him): And just that the areas are functions of the links as well as your deficit language, whereas an area where she, the deficit angles are functions of the areas.
Sebastian Steinhaus (he/him): And if you now completely create a promotion, for example, for triangle areas, and your equation tells you that Epsilon of T equals to 0. So the deficit angle, the one that encodes the curvature of the triangulation, at least in their local distribution. The fashion must be flat.
Sebastian Steinhaus (he/him): and this is due to the case. Because of the if you vary the the heathen angles which make up the deficit angles these variations actually vanish if multiplied by the areas, and some over all the triangles, then of the
Sebastian Steinhaus (he/him): of your awesome, flexible
Sebastian Steinhaus (he/him): which is, of course, which is very different from you, would get the derivative of the area, and many cases the absolute equal to 0 can be a solution.
Sebastian Steinhaus (he/him): But that depends very much on the bonding data.
Sebastian Steinhaus (he/him): And then these simplicity constraints in in spin forms, which is a theory that has fundamentally area variables. So it is more like, or it is at least should suggest it to think that rather than area, Reggie actually emerges in the center classical limits, the simplicity constraints should reduce area to names, Reggie.
Sebastian Steinhaus (he/him): And this is the argument that is being pursued by effective platforms. So they say, well, let's take. Let's do area virtual calculus plus 3 constraints as follows, so areas of the fundamental variables and a 4 simplex is not uniquely determined by its 10 areas. I can give you is 10 areas. But they can be multiple links, configuration
Sebastian Steinhaus (he/him): configurations for the same area.
Sebastian Steinhaus (he/him): Yeah. So what you would do is that you look for for links, configurations that give you the 10 areas. And there can be situations in which there are multiple of those.
Sebastian Steinhaus (he/him): Now, if you take 2 4 sympathies and you glue them.
Sebastian Steinhaus (he/him): Actually becomes very strict, because in this situation, as I've drawn here the 2 blue must agree on all of the 6 catch links.
Sebastian Steinhaus (he/him): And if they do, you basically, you're here saying that the tetrahedron, as seen from the 2 4 simply C's has the same length, so that these distances between these vertices are the same as seen from these vertices. So your metric is continuous
Sebastian Steinhaus (he/him): area calculus. You only have the 4 final areas that must agree, and in principle you can have 2 forcing disease.
Sebastian Steinhaus (he/him): Now that actually do not agree on how these, all these different heater can look which can lead to discontinuities or 14 degrees of freedom.
Sebastian Steinhaus (he/him): And if you continue this, if you build a larger triangulation, you typically have more triangles than you have edges.
Sebastian Steinhaus (he/him): So the constraints are now put in place to post simplicity and meeting. And what they say is that okay, I have my temporary one, and I have this 4 areas. This is not enough to specify completely, but if I additionally have 2 angles
Sebastian Steinhaus (he/him): at 2, that angles which are located at edges that share a vertex in the tetrahedron. Then I can specify the tetrahedron, and I now weekly implement shape mentioned by saying, Well, these angles should match in the 2 in the tetrahedron, as seen from the 2.
Sebastian Steinhaus (he/him): I think to force emphasis.
Sebastian Steinhaus (he/him): So they should agree. But I can only implement that weekly via a Gaussian, because these
Sebastian Steinhaus (he/him): these angles actually do not create. So there would be a second class constraint that you can't implement sharply. So you have to impose really deeply by the gossip.
Sebastian Steinhaus (he/him): And now you essentially have a competing effect. You can have the Gaussian from glue to these facilities together, which should be shape matching. But you also have your other tools that are oscillate potentially, very rapidly controlled by using parameter down.
Sebastian Steinhaus (he/him): As, for example, you can derive from the amplitude
Sebastian Steinhaus (he/him): of from the Semitic expansion of the body substitute.
Sebastian Steinhaus (he/him): So if the oscillation are too strong, you can wash off the Gaussian and therefore not implement shape management, and you get reduced to area virtues. And therefore the flatness problem, the flatness problem emerges eventually. If you make in particular, then everything much larger. So
Sebastian Steinhaus (he/him): so so this is, of course, like very, very interesting suggestion. And the question, though, is, Can we find a similar representation and argue for a similar mechanism in the full split phones.
Sebastian Steinhaus (he/him): And I think we can. So think about glue, how gluing enforcement from works. I will do everything. Basically as you 2, we have, because it's simpler. And I don't have to worry that much about conversion of the expressions. So in principle. This is how to verify. You have your 15 J. Simple, and you glue them by summing over these shared data
Sebastian Steinhaus (he/him): means a champion does plan
Sebastian Steinhaus (he/him): I can just do the reverse that I have before and reintroduce the group variables cause I can jump back and forth between those and
Sebastian Steinhaus (he/him): and also, when we want to introduce the coherent state data, this is just a resolution of the identity on these on these black things that we put here.
Sebastian Steinhaus (he/him): Yeah, so what we can do is we can integrate over these coherent data.
Sebastian Steinhaus (he/him): which is the resolution of the identity and arrive at the coherent coherent state representation of the spin-form amplitude.
Sebastian Steinhaus (he/him): Yeah. And from this you could already say that well, here on the left-hand side, on the right hand side, I have now
Sebastian Steinhaus (he/him): spin forms, express integral data. And let's just say that all the Buddhist contains were pretty large
Sebastian Steinhaus (he/him): and the expressions here should come from. But, like the main revolutions, should now come from the critical points
Sebastian Steinhaus (he/him): of like either these of these of these vertices.
Sebastian Steinhaus (he/him): which could in principle possible. But what could happen is that other area, this amplitude, and this image here could not agree on the shape of it in between. So you might still get a contribution from this.
Sebastian Steinhaus (he/him): But this contribution would typically come from the intersection.
Sebastian Steinhaus (he/him): So you might have to evaluate both of these amateurs away from their particular points. To get the main contribution to this
Sebastian Steinhaus (he/him): and together with Seth and and Jose, we we thought about that. We could do something a bit different and just reintroduce another set of coherent data again, and implement something which would be that we call green constraints similar to effective. Which is this object here in between. So essentially, we have basically added another group integration and another set of coherent data which is counterintuitive because these are terrible integrals.
Sebastian Steinhaus (he/him): But basically, the point was you wanted that each of the of the vertices have their own independent set of coherent data, and how well they fit together we put into this expression. Here's a growing constraint which will be while you have a certain set of of
Sebastian Steinhaus (he/him): normal like to see on the left hand side on the right hand side, and you just compare how well they fit together and call this the hybrid representation.
Sebastian Steinhaus (he/him): And actually, this, this.
Sebastian Steinhaus (he/him): this, this green constraint has actually very much the desired properties, because we computed what, for example, the absolute value of these, and they look very gross. So they have actually peaked matching data. And we were up in particular, Jose was able to derive and and into the formula for this, away from the particular ones.
Sebastian Steinhaus (he/him): Yeah, so essentially they could. They behave like Gaussians very much.
Sebastian Steinhaus (he/him): And for me the suggested there should be some intermediate regime in spiniform that at some point you could say that there are non-matching, serotizable vertices appear which, between which you adopt, led by growing constraints.
Sebastian Steinhaus (he/him): and in some sense I would expect the major contribution from this from coming from matching critical points which could be useful for guests, for guessing which configuration might be relevant. Our initial intention was, of course, that we want to use this
Sebastian Steinhaus (he/him): to optimize, calculate for the full speed, and the first idea has failed to explain on the on the next side, and it has to do with coherent state integrations. But you know this up to this point. This is like a nice confirmation of the effective spin form idea. I think from the full theory, even from the F theory, you could say
Sebastian Steinhaus (he/him): so. Our idea was to develop what's called a hybrid algorithm. So our idea was that we wanted to approximate now the full amplitude which I told you in the first part, which can be extremely difficult to compute just by the asymptotic formula.
Sebastian Steinhaus (he/him): and therefore we equipped each vertex with its own set of independent coherent data, and then I would argue that, but if the total expression is fine, I can exchange the order of integrations and perform the group integrations for us. And I have the formula, and then I'm just left with the coherent state integrations. precisely these N and Ms everywhere.
Sebastian Steinhaus (he/him): So this was this was my hope. This was my initial idea. However, these remain integrated are very challenging, and the hope was that the main contribution will only come from the matching critical points between those vertices, and we could just replace integration by a sum of critical points.
Sebastian Steinhaus (he/him): bitter rain can be difficult. As it turns out. If you just, for example, glue the 2 vertices together along a common tetrahedron, or you can do a chain of vertices, 4 vertices together. This actually works out.
Sebastian Steinhaus (he/him): however. if you
Sebastian Steinhaus (he/him): for more general contributions. For example, for the data. 3. Move where for the data, 3. Graph, where you include 3, 4 indices together, you get actually the wrong scaling behavior of averages right? So from
Sebastian Steinhaus (he/him): as well in the overall, adequate expansion, we can rapidly can calculate the scaling behavior. And this approximation
Sebastian Steinhaus (he/him): didn't give it to us. And is this kind of clear? Because
Sebastian Steinhaus (he/him): II should have known this because actually, if you try to investigate these expressions, typically get on local expressions, also because it is a gauge theory. And the point is that some of these coherent State integrations.
Sebastian Steinhaus (he/him): are in some sense gauge. So there will be some integrations which along which the value
Sebastian Steinhaus (he/him): at the integral does not actually change it. You can't do something like a stationary-based approximation for those.
Sebastian Steinhaus (he/him): and it is actually very difficult to determine those, if you if we can't approximation away from the critical points.
Sebastian Steinhaus (he/him): So so that was a bit of a setback, but at this is still thing, that it gives us valuable insight into what type of configurations might be. If you look at larger regulations and what we could still do is build like new effective models which could include, however, this is also very challenging because
Sebastian Steinhaus (he/him): of of geometries which one would have to integrate over. Alternatively, I think this might be
Sebastian Steinhaus (he/him): potentially more promising is going by other companies to the point.
Sebastian Steinhaus (he/him): because
Sebastian Steinhaus (he/him): in those calculations you consider the entire verbal amplitude, and you consider, the comments critical points
Sebastian Steinhaus (he/him): of those.
Sebastian Steinhaus (he/him): The question would be then, in particular, if you can approximate the full amplitude. When is this approximation ballot?
Sebastian Steinhaus (he/him): So there's a lot more work to to be done? But maybe there are some questions up to this point, because my second part.
Sebastian Steinhaus (he/him): let me just finish and talk about other main results.
Sebastian Steinhaus (he/him): So because I think from this area variables, area metrics, there's also a lot of interesting insights potentially in other developments. So in particular, Seth has worked a lot on this algorithm of actually to go from area configuration to algorithm to give it an area spits out the names configurations. It's actually this very impressive. And
Sebastian Steinhaus (he/him): I'm young and derived a continued limit of the linearized, effective spin phones which looks like like retic gravity around the flash space time around like that, Reggie. Gravity plus. I think it was fire terms which were method. So it's also very interesting.
Sebastian Steinhaus (he/him): There's now relation to area metrics and continues variables and the ransom configurations and violations. So they are mainly results. There's also this point about 7.5 already mentioned, these acceleration operators for convergence. And this brings me a little bit to the next point, which is the question of convergence, because one thing that we would want
Sebastian Steinhaus (he/him): what this will happen is if we have many contributions for highly facilitated some over that it doesn't converge.
Sebastian Steinhaus (he/him): And that's one problem.
Sebastian Steinhaus (he/him): And the other problem is, if we really wants to go to large triangulations for thousands of variables, how can we actually do that?
Sebastian Steinhaus (he/him): And this is important question. But maybe I stop here and that people ask questions if there are any.
Sebastian Steinhaus (he/him): Okay. Sorry.
Sebastian Steinhaus (he/him): I said this myself very often.
Sebastian Steinhaus (he/him): that
Sebastian Steinhaus (he/him): said very often that you can't, and very, very obviously, this is true to some extent, and I will explain what I mean by what I meant by this, and why this to some extent 2, or maybe not. So typically
Sebastian Steinhaus (he/him): if you're having a lettuce theory, and this is one of these successes of latest fewies is that you can move importance on the call sampling and use it to approximate high dimensional
Sebastian Steinhaus (he/him): like very simply, if you do scale a field TV, and we want to compute expectation values of observables.
Sebastian Steinhaus (he/him): you have the advantage that you have an action exponentially minus the actions that you have big, rotated. and you have an expression which you can interpret as a probability distribution.
Sebastian Steinhaus (he/him): so that you can approximate this integral by a finite number of samples.
Sebastian Steinhaus (he/him): which you have generated from the probability distribution. Right? So so essentially, what you say, what you do is that you. You create samples of 3 configurations from one over ZE to the minus s.
Sebastian Steinhaus (he/him): And because you've done so, and you have to be careful that you actually did this. But if you have done so, you can take this out and just evaluate the observable on those hidden configurations.
Sebastian Steinhaus (he/him): And to do this by essentially doing a random walk to configuration space, and you ask mobility, distribution, whether it's a small probability to accept a move or not. If it is not probable you always accept, if it's less probable you accept with a certain probability.
Sebastian Steinhaus (he/him): And the important thing is that your numerical costs grow with the samples. So how many samples you take and not with the system, size and system. Size doesn't matter obviously to some extent, because you will also need one samples to properly reflect that very large system. But this is a very huge turning point, obviously
Sebastian Steinhaus (he/him): but also Monte Carlo are more intricate than it seems initially because you have to give it proposal scheme that it must be a Gothic and satisfy detail balance, and where by detail balance, I just mean that you are actually
Sebastian Steinhaus (he/him): you are actually something with respect to this probability distribution, and not something else, which can completely distort your calculations and your results.
Sebastian Steinhaus (he/him): so yeah. The other thing is that
Sebastian Steinhaus (he/him): we also must explore a large configuration space. So this also means that you have to tune the acceptance rate. Yeah, you must be sure that your acceptance rate is not too low, because otherwise you don't explore anything while it's not too high. Because if it's too high, you basically accept every move which hopefully means it does explore a time space around, maybe a local maximum
Sebastian Steinhaus (he/him): so these are very different things, and you typically test them, for example, via thermalization to see what your average configuration typically is. And you want this to be almost always the the same unless there's a physical reason to not do that.
Sebastian Steinhaus (he/him): And important sampling can actually be highly efficient in studying systems with many degrees of freedom. If the results converge quickly, and there can be situations in particular. If you are the pretty good behavior of of the model, then it stops being being very fast.
Sebastian Steinhaus (he/him): But what about spin from stuff? So in spin forms, you then will have the sign problem.
Sebastian Steinhaus (he/him): The same problem means that you have many configurations contributing in your spin form or in your partition function that come with opposite signs or the time oscillate. So you have interference effects protection, and for interference effects. You have to account for these configurations
Sebastian Steinhaus (he/him): for interviews to work. If you just, for example, if you sample
Sebastian Steinhaus (he/him): and you forget some of these configurations
Sebastian Steinhaus (he/him): which you need to have interference with some other ones. You might do a wrong counting, and you get the wrong results, or, what would rather turn out is, if you repeat the simulation again, get different results. So it doesn't converge.
Sebastian Steinhaus (he/him): And this is, of course, a big problem. This is the problem of convergence. And you cannot even define important something, unfortunately. Yeah. Because if you're under 2, for example, can be negative or it can be complex, then you don't have a mobility distribution with which you can compare
Sebastian Steinhaus (he/him): whether to accept or objective. But what you can do is you can still try and apply the method by modifying the system.
Sebastian Steinhaus (he/him): And the first thing is about doing Monte Carlo and leftist Google. And these method is used, for example, to change. Integration controls
Sebastian Steinhaus (he/him): such that imaginary part of the system is constant, and this is currently very popular. If you look at gravitational paths and Nichols in Lorenzi, gravitational and cosmology.
Sebastian Steinhaus (he/him): And I think they are mostly studied for systems where you have very few variables.
Sebastian Steinhaus (he/him): but it might be mistaken. So it might be possible that all more variables are being using systems mobile, that's being exported. And the other potential is that you can choose or define a new probability distribution.
Sebastian Steinhaus (he/him): Now, so you can say that you take the constant distribution and do a random sampling.
Sebastian Steinhaus (he/him): and if you have many variables and they work over a large range. This can be already better than naively summing over everything.
Sebastian Steinhaus (he/him): The other is the so-called relating procedure, so you might have a complex amplitude. But you just say I sample with respect to the absolute value, and you shift the face into the observable.
Sebastian Steinhaus (he/him): and this procedure can be useful. If you want for something to measure the sign problem, because if you compute expectation advice, you also have to normalize it with the expectation value of the face, and if the expectation by the face is small. We have a huge sign problem.
Sebastian Steinhaus (he/him): and then often you can't trust your results, which is like very, very problematic
Sebastian Steinhaus (he/him): alternatively. And this can also go totally wrong is, you can guess, a suitable distribution, the suitable probability distribution for a system. And still the same problem can be there, and it might need
Sebastian Steinhaus (he/him): to convergence in particular.
Sebastian Steinhaus (he/him): the 2 you have this 15 Jason symbols.
Sebastian Steinhaus (he/him): Now, this change of variables, as you can take here from the paper by Ethel and Simona, from 2,007. This change of variables absolute value. It's nice to think about. Yes, actually, the absolute value squared.
Sebastian Steinhaus (he/him): This is actually a very nicely peaked distribution if you normalize it, and he has plotted, for example, for I think epilateral spins
Sebastian Steinhaus (he/him): 2 spends 100 spends 100, I think.
Sebastian Steinhaus (he/him): So I had the ideas that we could use the boundary data, these bounding data, these absolute value to to sample now relative to relevant intertwine labels, and for that I must modify the opportunity to do so. So.
Sebastian Steinhaus (he/him): So I want to compute the expression here on the left hand side. Why, I want to color sampling, and what I do now is I expand this function
Sebastian Steinhaus (he/him): and say, Well, I still sample with the interim labels. I have my 15 J. Symbol. and I have the contract. I have the. I still have these kind of variables here.
Sebastian Steinhaus (he/him): but what I do is II introduce just a a one. Essentially. So I say, well, I take the absolute value of this expression
Sebastian Steinhaus (he/him): normalize. So I've basically summed over this before to get a normalization and multiply it by the inverse to take care of that. So why am I doing this? I am modifying the expression such that I have now a probability distribution here of the interfinal labels with respect to which I can do a sampling process.
Sebastian Steinhaus (he/him): but because it changes the the expression I want to compliment. I have to modify the under 2 by essentially introducing this so I can now approximate this expression by the expression done here by essentially just evaluating this guy. Now for samples of the
Sebastian Steinhaus (he/him): and this I've I've tried this, and I've certainly need to do more testing. But I've tried this for the good advice on the tool, for all spins being equal.
Sebastian Steinhaus (he/him): And this is important, because, for example, if you do this for the equilateral boundary data, and you do something with the index minus, they are 2 J, plus one to the power. 5 combinations sum over.
Sebastian Steinhaus (he/him): Yeah. So you can already think, if you are spend 10, you have 21 to the power. 5 combinations. To sum over, which is a lot. That's why you're doing the network method.
Sebastian Steinhaus (he/him): because it's actually much faster
Sebastian Steinhaus (he/him): here I've plotted now the absolute value we scaled of that amplitude against the semi-pacific approximation. When you see very nicely how the full amplitude slowly approaches semantics for once as you go, if you make all the spends larger.
Sebastian Steinhaus (he/him): And then I did for spins 20 up to 80 10 months, with 10 to the 6 samples. So I have. Now we hear the Monte Carlo estimate. and you see, sometimes it's spot on, sometimes it's not spot on, and the the certain
Sebastian Steinhaus (he/him): I put in error bars to indicate the variance from the different ones.
Sebastian Steinhaus (he/him): So I was actually very impressed by these results. Also I the full calculations only up to spend 40, because that's essentially what I could suffer here, or what I could. The local Hpc, with doing the calculations.
Sebastian Steinhaus (he/him): which is, that's why C. 2 PM.
Sebastian Steinhaus (he/him): And then I went up. Bring them on a color estimate up to spends 80.
Sebastian Steinhaus (he/him): And you see, it's actually quite close to the to the semi classical amplitude. And there are 2 comments here. So you see that in some instances the error is quite large.
Sebastian Steinhaus (he/him): and also there's a certain gap still to the same classical result, so I can't say that the system has fully converged yet.
Sebastian Steinhaus (he/him): But there's another thing you have to keep in mind. So the with J to the power. 6. So if you are at J. 80,
Sebastian Steinhaus (he/him): you are. You have. This expression is already multiplied with 80 time, 80 to the power. 6. So this is, I think it's quite impressive for such a low number of samples.
Sebastian Steinhaus (he/him): So I'm really surprised how well this algorithm works.
Sebastian Steinhaus (he/him): and and so I'm really surprised by the good agreement at the fast convergence. And I compared this, for example, to random sampling, which is much, much worse in its convergence.
Sebastian Steinhaus (he/him): so, so, so. And in that regard I'm I'm
Sebastian Steinhaus (he/him): impressed by how well that works, and I have to do more testing to see how it works. But there. So what I want to say is that there is potential for Monte Carlo simulations and spin phones. But this is maybe only the first step. And another aspect which I think is important. The sign problem here is so present, and the sign problem is hidden in the global phase of the amplitude. So the the coherent voice is only defined up to a global phase.
Sebastian Steinhaus (he/him): You can take off the global phase, for example, by computing it for all spins one and then extrapolating it to higher ones.
Sebastian Steinhaus (he/him): So if you do the actual calculation, you get a real amplitude, plus a tiny imaginary part which comes from the
Sebastian Steinhaus (he/him): numerical accuracy of your simulations and this imaginary part with the Monte Carlo simulations.
Sebastian Steinhaus (he/him): I get this only to be a few out of magnitude, smaller than the real part. And there you see again the difficulties of Monte Carlo, because, determining this face is difficult with Monte Carlo methods. I can comment a bit more on this, on this later on. Sebastian, can you hear me?
Sebastian Steinhaus (he/him): Yeah, very briefly, because I think I'm slowly, briefly, because very opposite to Monte Carlo. It is very opposite in spirit and in perspective to Monte Carlo, because
Sebastian Steinhaus (he/him): in Monte Carlo what you essentially do is you have a big system with many variables. You throw it all onto a computer. And then you want to do a random walk, basically determining what are the most probable configurations that actually contribute.
Sebastian Steinhaus (he/him): and tensor networks are very opposite to that, because they want to rewrite everything in a local set of amplitudes
Sebastian Steinhaus (he/him): and locally manipulate the set of amplitudes as a tensor network.
Sebastian Steinhaus (he/him): And
Sebastian Steinhaus (he/him): do basically, yeah. So you, what you essentially do is you want to evaluate the partition function pass by explicitly summing over variables. And then.
Sebastian Steinhaus (he/him): you would talk and
Sebastian Steinhaus (he/him): yeah, and then reduce temptations by doing like basis transformations derive singular value decompositions.
Sebastian Steinhaus (he/him): I think I will just skip over this, but I just want to mention this for completeness sake. That we have worked in the past particular of turning spin forms into tensile language which is very challenging and particularly challenging for higher dimension systems.
Sebastian Steinhaus (he/him): The problem is in particular that you, if you have a system that has potentially infinitely infinite dimensional boundary spaces to turn into something finite. However, they are recent works and examples where this, for example, possible. And I wanted to highlight, for example, the recent work on 2 inventing on Budget costs which I have to look more closely into. And I remember this work, for example, for
Sebastian Steinhaus (he/him): from 2,020. So there are ideas where? So so this networks are techniques. If you find a virtual presentation to work and evaluate observables. But maybe let me just close here. Come to the summary and outlook.
Sebastian Steinhaus (he/him): and then face your questions. So in this talk I wanted to give you an overview of numerical methods and progress and sprint forms. I talked a lot about the explicit computation of vertical tools which particular culminated in the into the next package, which is making strides into exploring triangulation with several.
Sebastian Steinhaus (he/him): then you have effective models
Sebastian Steinhaus (he/him): the complex particular points. And that's much more easy to compute. And
Sebastian Steinhaus (he/him): actually, you look at. And you can, with that, explore larger triangulations with these semiclassical semaphores, approximations and actually study under which conditions length regime emerges. And I think a key point is that we have to focus on is, how can these 2 methods
Sebastian Steinhaus (he/him): be linked together? I think this is a very important method very important aspect about how we can bridge the gap between these methods and actually extract results from that. I briefly talked about the unknown potential of Monte Carlo.
Sebastian Steinhaus (he/him): And I want to make this clear. Spin forms.
Sebastian Steinhaus (he/him): I think, do suffer from the same problem. But we do not know how severe it is.
Sebastian Steinhaus (he/him): and it. It might be too severe to get something out of this, but we don't know yet, and by no means say that I have solved the design problem or not.
Sebastian Steinhaus (he/him): and does. The test is encouraging. And these effective models, for example, the hybrid presentation that I mentioned here might help us actually, maybe partially, yes.
Sebastian Steinhaus (he/him): probability distributions for Monte Carlo, for larger triangulations, at least for the intertwines.
Sebastian Steinhaus (he/him): It is not yet clear how to do it for the representation labels. But maybe there's something possible there as well.
Sebastian Steinhaus (he/him): something that I haven't talked about, because I also don't feel confident. Talking about this is quantum computing where there are first in terms of have been made and deep machine learning, cause I was for the latter. I do not.
Sebastian Steinhaus (he/him): can't say yet how to how this could advance our efforts there, and a bit of important issues. As I said, how can we combine this quantum and the semifinal visions.
Sebastian Steinhaus (he/him): And that's a very nice thing. I want to say that we are doing all of this, because eventually we want to study observables. Yeah, we want to study observables of space time. And, for example, but I worked on with my student, Alexander Johannes, too. Again.
Sebastian Steinhaus (he/him): is this backward dimension. So it's an effective dimension measure of quantum space, and from the spectrum for the past operator, which is to see, for example, whether you have what I mentioned on large fields, and then spin phones. It seems to depend very strongly on the scaling behavior of spin from other tools. How this had. How this? Because only in a simplified context.
Sebastian Steinhaus (he/him): you have to see.
Sebastian Steinhaus (he/him): And the other thing is Meta and spin phones. How can Meta, coupling? And importantly, how can we define meta gravity observables in spin forms, for example, correlation functions, for of massive scalar fields and Qa. And they are work in progress in this direction. So it says, Asante, looking at young Mills coupled to queue by spin phones, and with Alex.
Sebastian Steinhaus (he/him): we're looking at relational dynamics in device and spin forms for the master Scalar field. So at this point let me review and thank you for your attention.
Hal Haggard: Thank you, Sebastian.
Simone, please go ahead.
Simone SPEZIALE: Thanks. Can you hear me?
Hal Haggard: It seems he can't hear us. I'm gonna direct. Can you hear me?
Simone SPEZIALE: Hello!
Simone SPEZIALE: Hello! Can you hear me?
Hal Haggard: I can hear you. Well, Simone, it seems Sebastian can't hear you. Okay, thanks, I've direct, texted him.
Hal Haggard: It seems you can't hear any of us
Simone SPEZIALE: must have been a pretty lonely seminar for India.
Sebastian Steinhaus (he/him): Oh.
Sebastian Steinhaus (he/him): hmm!
Sebastian Steinhaus (he/him): Can you say something again? Can you try? Yes. Hello! Hello! Oh, no! I hear you.
Hal Haggard: You hear me? Okay, try again, Simone.
Simone SPEZIALE: can you hear me, too?
Simone SPEZIALE: Yes, yes. Okay. Sorry. I'll be good.
Simone SPEZIALE: so maybe. Okay. First start from something at the end. When you were talking about the sampling here of the coherent intertwiners. Your idea for the Monte Carlo.
Simone SPEZIALE: I wanted to understand. Yes, here you are, sampling over the labels of the orthonormal intertwiners. Right?
Simone SPEZIALE: Yes, and was that like although
Simone SPEZIALE: random sampling, or I missed this part like you're you're just selecting some random ones and something over only those. Or are you doing something else? It's it's important sampling. It's important sampling with respect to this distribution. Yeah,
Simone SPEZIALE: but but that's this is what I don't get. So if I see that as a distribution in the angles then I agree. That is like the previous picture you showed. Can you see one slide?
Simone SPEZIALE: Yes. So what is being plot here on the x-axis?
Sebastian Steinhaus (he/him): So these are the index ponder labels and the absolute value or the absolute value squared of this change of basis.
Sebastian Steinhaus (he/him): I see, okay, okay, very good. Very good. Okay, this is clear. Now, thank you. And I think from, you know, from your paper, from, I think, 2019 model, or was it later? I think you had? The idea of truncating the intertwine is by saying.
Sebastian Steinhaus (he/him): You only take the main part of these of these overlaps.
Simone SPEZIALE: I actually think we did to save time. Yeah, so okay, so this is consistent. We will. We were doing there. Okay, okay, very good. Thanks in
Simone SPEZIALE: no. Yes.
Sebastian Steinhaus (he/him): yeah, it's just so. So I'm doing the sampling such that you basically recover this, this overlap and a bit of details.
Sebastian Steinhaus (he/him): So I'm I'm choosing the acceptance rate to be, you know, a bit low enough that you really get this entire thing. And this, I think this is exactly what you need.
Sebastian Steinhaus (he/him): in order to come with these regards
Simone SPEZIALE: to approximately
Simone SPEZIALE: so. Okay, okay, then, more in general, I like very much your talk, and of course I appreciate that some of the results that we got are useful for you, and that's very nice that you keep pushing it, and some of the ideas you presented many ideas, and I hope that they will be successful. In particular, I think that 2 key open questions, at least for me, and I would like to hear your opinion about that concern as you see
Simone SPEZIALE: in relation to to length Reggae calculus, and the interplay between the the gluing and the critical points.
Simone SPEZIALE: my understanding is that for the time being he's
Simone SPEZIALE: lacking in the sense that the results show of machine that for whatever curve the solution we take there will be always a discrepancy with the value that you would expect, for from the Reggae action based on length, variables?
Simone SPEZIALE: So maybe the modifications that you are exploring in order to adopt from Monte Carlo may also give you a way of you know, testing how to maybe improve those bounds. I think that similar ideas were also investigated by Pedro few months ago, which he was wondering laying around similar lines how one could improve this matching here. So maybe
Simone SPEZIALE: that's another motivation for doing it. And I would like to hear your opinion about this discrepancy with the length regional calculus.
Sebastian Steinhaus (he/him): Yeah, definitely. So I'm I'm
Sebastian Steinhaus (he/him): and we
Sebastian Steinhaus (he/him): so so part of the motivations, of course, getting making things computable, but then also exploring whether you can obtain, for example, the eventually action for larger triangulations. And I think this discrepancy.
Sebastian Steinhaus (he/him): So so, in my opinion, if you, for example, if you choose the using parameter in a certain way, eventually, if the spins become too large. Eventually the practice problem hits you, and then you don't get anyone
Sebastian Steinhaus (he/him): but what I would guess is that we can probably look at some configurations, or some situations from which you can reasonably say that this looks like semi recipe, like virtual, is close to that. I would like to understand when this is possible, and maybe these motorcar methods can help us bridge the gap
Sebastian Steinhaus (he/him): the little bits.
Simone SPEZIALE: Yeah, I'm thinking that we can even be well, no, but maybe we can build slightly, even more ambitious in the sense that
Simone SPEZIALE: the
Simone SPEZIALE: since we don't have the connection with regical queues, length regional queues for curved solutions, I mean at least not an exact one. What that means is that we cannot invoke anymore. Regis, result to prove that there is a continuum limit, at least at the classical level that coincides with Gr, but because you're investigating medical methods, maybe you know you could.
Simone SPEZIALE: So the open question is, okay, then, is there something that could replace that?
Simone SPEZIALE: Could one still get consistent with Gr, even though at any finite spin, we're not really getting the rejection, but departures from it. And so medical methods could be also crucial because they could allow you to, you know, no longer need to invoke this results. You can just test directly. I don't know.
Simone SPEZIALE: So that makes them even more important, maybe.
Sebastian Steinhaus (he/him): Yeah, absolutely. Absolutely. Yeah. Yeah. I mean. But as you said, it probably would be more easy if you could just say we to know if you could cover
Sebastian Steinhaus (he/him): but I don't see them also as realistic. And one of the things that actually, personally, personally, and I don't know how to
Sebastian Steinhaus (he/him): but something that I am worried about the vector geometries. And this is something. If I recall correctly from the results that
Sebastian Steinhaus (he/him): and particularly, they make a choice of saying that some areas.
Sebastian Steinhaus (he/him): some triangle areas are actually fixed as function of the length, such that the the Jacobian of areas to length is invertible.
Sebastian Steinhaus (he/him): and under those conditions,
Sebastian Steinhaus (he/him): you at least can get closer to watching. Countless. But I mean, this is what worries me, and also like in effectors with but in general, is that if you have many more triangle variables.
Sebastian Steinhaus (he/him): You are potentially summing over many configurations
Sebastian Steinhaus (he/him): which probably would also include vector traumatries which,
Sebastian Steinhaus (he/him): yeah, could maybe destroy the behavior completely, somehow, actually, actually living in there. And I think this is positive.
Simone SPEZIALE: Yeah, I completely agree with that. I mean, that's that's a place where the models you are looking at are very different from the effective model. So how?
Simone SPEZIALE: Because in those you are expanding around the area calculus in which the the hydro angles are determined by the areas.
Simone SPEZIALE: Whereas in when you expand around BF that the areas and the angles are independent. So you also get these vector, geometry configurations that you don't in the other case. So
Simone SPEZIALE: yeah, I don't know if one wants to extend effective spin for models to include vector geometries, or rather find spin for model that has no vector. Geometry seems better option to me. But it's very unclear how to do that.
Sebastian Steinhaus (he/him): Yeah, thank you very much. Yep, maybe. Similarly, because this one idea that I sometimes had was that maybe there's situations in which the better phones do not contribute that much, and as far as I understand it, if you have Lorenz, these are actually isolated
Sebastian Steinhaus (he/him): from from vector geometries in the sense of this parameter space of of these normal vectors. So if for some reason, maybe the boundary data would prescribe geometry, maybe in those situations, vector, geometries might not play before. But II don't know what type of that is true. I mean tha that is true. If your for Simplex is Lorenzo.
Simone SPEZIALE: then there's no but the point is that you're gonna some over the Internet as well. And the more right? Exactly
Simone SPEZIALE: right.
Sebastian Steinhaus (he/him): And also the growing constraints
Sebastian Steinhaus (he/him): they don't inhibit that they are just information of doing threed space like things to the threed space together. So there's no restriction from there.
Simone SPEZIALE: right?
Hal Haggard: Because of the technical glitch. You probably didn't hear hear me? Thank you for the very nice seminar. Sebastian. Are there additional questions for Sebastian?
Hal Haggard: It looks like people are starting to leave just so, you know, cause it was in the chat Pietro. Donna said he had several questions, but had to go, and so he'll send them along to you directly.
Hal Haggard: Yeah, that's unfortunate. I'm afraid that's probably my headphones went to sleep mode and I had to turn them off and on again. And it wasn't a big problem. The only person who raised a hand during the talk was Simone. So we got through those questions.
Hal Haggard: Thank you again, Sebastian. Thank you. Everyone.
Sebastian Steinhaus (he/him): Yeah, thank you for listening, and I hope it was interesting.
Simone SPEZIALE: Yes, very much for me, at least. Thank you. And for me.