CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Jonny Evans, 2022/02/08, 16h 30m, Symplectic cohomology of compound Du Val singularities
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6493
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6493<p>(Joint with Y. Lekili) If someone gives you a variety with a singular point, you can try and get some understanding of what the singularity looks like by taking its “link”, that is you take the boundary of a neighbourhood of the singular point. For example, the link of the complex plane curve with a cusp $y^2 = x^3$ is a trefoil knot in the 3-sphere. I want to talk about the links of a class of 3-fold singularities which come up in Mori theory: the compound Du Val (cDV) singularities. These links are 5-dimensional manifolds. It turns out that many cDV singularities have the same 5-manifold as their link, and to tell them apart you need to keep track of some extra structure (a contact structure). We use symplectic cohomology to distinguish the contact structures on many of these links.</p>Sat, 27 Nov 2021 11:27:19 +0000Tue, 08 Feb 2022 16:30:00 +0000Tue, 08 Feb 2022 17:30:00 +0000<a target='_content' href="http://jde27.uk">Jonny Evans</a>University of LancasterGeometria em LisboaJohn Stout, 2022/02/07, 15h, Infinite Distance Limits and Information Theory
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6534
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6534<p>The classical information metric provides a unique notion of distance on the space of probability distributions with a well-defined operational interpretation: two distributions are far apart if they are readily distinguishable from one another. The quantum information metric generalizes this to the space of quantum states, and thus defines a notion of distance on an arbitrary continuous family of quantum field theories via their vacua that is proportional to the metric on moduli space when restricted appropriately. We study this metric and its operational interpretation in a variety of examples.</p>Fri, 07 Jan 2022 18:54:05 +0000Mon, 07 Feb 2022 15:00:00 +0000Mon, 07 Feb 2022 16:00:00 +0000John StoutHarvard UniversityString TheoryGiancarlo Urzua, 2022/01/25, 16h 30m, What is the right combinatorics for spheres in K3 surfaces?
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6510
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6510<p>Together with Javier Reyes, in <a data-saferedirecturl="https://www.google.com/url?q=https://arxiv.org/abs/2110.10629&source=gmail&ust=1639997883828000&usg=AOvVaw0DqRoFYOoj5DvqB2_i007H" href="https://arxiv.org/abs/2110.10629" target="_blank">https://arxiv.org/abs/2110.<wbr />10629</a> we have been able to construct compact 4-manifolds $3\mathbb{CP}^2\#(19-K^2)\overline{\mathbb{CP}}^2$ with complex structures for $K^2=1,2,3,4,5,6,7,8,9$. The cases $K^2=7,9$ are completely new in the literature, and this finishes with the whole range allowed by the technique of Q-Gorenstein smoothing (rational blow-down). But one can go further: Is it possible to find minimal exotic $3\mathbb{CP}^2\#(19-K^2)\overline{\mathbb{CP}}^2$ for $K^2\geq10$? Here it would be much harder to prove the existence of complex structures, but, as a motivation, there is not even one example for $K^2 > 15$, and very few for $10 \leq K^2 \leq 15$ (see e.g. works by Akhmedov, Park, Baykur). In this talk I will explain the constructions in connection with the geography of spheres arrangements in $K3$ surfaces, where the question of the title arises. We do not have an answer. So far we have been implementing what we know in computer searches, finding these very rare exotic surfaces for $K^2=10,11,12$. This is a new and huge world which promises more findings, we have explored very little.</p><p> </p>Sun, 19 Dec 2021 11:36:10 +0000Tue, 25 Jan 2022 16:30:00 +0000Tue, 25 Jan 2022 17:30:00 +0000<a target='_content' href="http://www.mat.uc.cl/~urzua/">Giancarlo Urzua</a>Pontificia Universidad Católica de ChileGeometria em LisboaMarija Tomašević, 2022/01/24, 15h, Holographic Complexity of Quantum Black Holes
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6508
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6508<p>We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields with large central charge in the presence of the black hole, including the backreaction corrections to the BTZ metric. Our results show that Volume Complexity admits a consistent quantum expansion and correctly reproduces known limits. On the other hand, the generalized Action Complexity fails to account for the additional contributions from bulk quantum fields and does not lead to the correct classical limit. Furthermore, we show that the doubly-holographic setup allows computing the complexity coming purely from quantum fields - a notion that has proven evasive in usual holographic setups. We find that in holographic induced-gravity scenarios the complexity of quantum fields in a black hole background vanishes to leading order in the gravitational strength of CFT effects.</p>Fri, 10 Dec 2021 10:24:15 +0000Mon, 24 Jan 2022 15:00:00 +0000Mon, 24 Jan 2022 16:00:00 +0000Marija TomaševićUniversity of BarcelonaString TheoryAnders Hansen, 2022/01/20, 17h, Why things don’t work — On the extended Smale's 9th and 18th problems (the limits of AI) and methodological barriers
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6506
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6506<p>The alchemists wanted to create gold, Hilbert wanted an algorithm to solve Diophantine equations, researchers want to make deep learning robust in AI, MATLAB wants (but fails) to detect when it provides wrong solutions to linear programs etc. Why does one not succeed in so many of these fundamental cases? The reason is typically methodological barriers. The history of science is full of methodological barriers — reasons for why we never succeed in reaching certain goals. In many cases, this is due to the foundations of mathematics. We will present a new program on methodological barriers and foundations of mathematics, where — in this talk — we will focus on two basic problems: (1) The instability problem in deep learning: Why do researchers fail to produce stable neural networks in basic classification and computer vision problems that can easily be handled by humans — when one can prove that there exist stable and accurate neural networks? Moreover, AI algorithms can typically not detect when they are wrong, which becomes a serious issue when striving to create trustworthy AI. The problem is more general, as for example MATLAB's linprog routine is incapable of certifying correct solutions of basic linear programs. Thus, we’ll address the following question: (2) Why are algorithms (in AI and computations in general) incapable of determining when they are wrong? These questions are deeply connected to the extended Smale’s 9th and 18th problems on the list of mathematical problems for the 21st century.</p>Fri, 14 Jan 2022 13:49:32 +0000Thu, 20 Jan 2022 17:00:00 +0000Thu, 20 Jan 2022 18:00:00 +0000<a target='_content' href="https://www.damtp.cam.ac.uk/research/afha/anders/">Anders Hansen</a>Faculty of Mathematics and Department of Applied Mathematics and Theoretical Physics, University of CambridgeMathematics, Physics & Machine LearningGiorgio Trentinaglia, 2022/01/19, 17h, Simplicial vector bundles and representations up to homotopy
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6499
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6499<p>The classical Dold–Kan correspondence for simplicial objects in an abelian category is one of the cornerstones of homological algebra. When the abelian category is that of vector spaces, it gives a full identification between simplicial vector spaces and chain complexes of vector spaces vanishing in negative degrees. The Grothendieck construction for fibered categories, on the other hand, is a cornerstone of category theory. It relates the fibered category point of view with the pseudo-functor point of view and lies at the heart of the theory of stacks. Our main result can be understood as a far-reaching simultaneous generalization of both ideas within the contexts of linear algebra and differential geometry. In our result, simplicial vector spaces and chain complexes of vector spaces are replaced respectively by vector fibrations over a given (higher) Lie groupoid <i>G</i> and by representations up to homotopy of <i>G</i>. (Joint work with Matias del Hoyo.)</p>Sat, 27 Nov 2021 23:48:24 +0000Wed, 19 Jan 2022 17:00:00 +0000Wed, 19 Jan 2022 18:00:00 +0000<a target='_content' href="https://www.math.tecnico.ulisboa.pt/~gtrentin/">Giorgio Trentinaglia</a>Instituto Superior Técnico, LisbonTopological Quantum Field TheoryAmine Asselah, 2022/01/19, 16h, Intersection of the traces of two independent walks in high dimensions
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6545
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6545<p>We discuss deviations for the number of intersections of two independent infinite-time ranges in dimensions five and more. This settles a conjecture of van den Berg, Bolthausen and den Hollander. Moreover, we obtain the scenario leading to this deviation. (joint work with B.Schapira). </p>Mon, 17 Jan 2022 14:33:09 +0000Wed, 19 Jan 2022 16:00:00 +0000Wed, 19 Jan 2022 17:00:00 +0000<a target='_content' href="https://perso.math.u-pem.fr/asselah.amine/">Amine Asselah</a>Paris-Est CréteilProbability and Stochastic AnalysisHossein Movasati, 2022/01/18, 16h 30m, A quest for new theories of automorphic forms: Gauss-Manin connection in disguise
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6477
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6477<p>In this talk I will consider a moduli space of projective varieties enhanced with a certain frame of its cohomology bundle. In many examples such as elliptic curves, abelian varieties and Calabi-Yau varieties, and conjecturally in general, this moduli space is a quasi-affine variety. There are certain vector fields on this moduli which are algebraic incarnation of differential equations of automorphic forms. Using these vector fields one can construct foliations with algebraic leaves related to Hodge loci. The talk is based on my book "Modular and Automorphic Forms & Beyond, Monographs in Number Theory, World Scientific (2021)" in which the Tupi name ibiporanga (pretty land) for such a moduli space is suggested.</p>Tue, 04 Jan 2022 10:23:40 +0000Tue, 18 Jan 2022 16:30:00 +0000Tue, 18 Jan 2022 17:30:00 +0000Hossein MovasatiInstituto Nacional de Matemática Pura e AplicadaGeometria em LisboaKiril Hristov, 2022/01/17, 15h, 4d $N = 2$ supergravity observables from Nekrasov partition functions
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6487
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6487<p>We reinterpret the OSV formula for the on-shell action/entropy function of asymptotically flat BPS black holes as a fixed point formula that is formally equivalent to a recent gluing proposal for asymptotically AdS$_4$ black holes. This prompts a conjecture that the complete perturbative answer for the most general gravitational building block of 4d $N = 2$ supergravity at a single fixed point takes the form of a Nekrasov-like partition function with equivariant parameters related to the higher-derivative expansion of the prepotential. In turn this leads to a simple localization-like proposal for a set of supersymmetric partition functions in (UV completed) 4d $N = 2$ supergravity theories. The conjecture is shown to be in agreement with a number of available results for different BPS backgrounds with both Minkowski and AdS asymptotics. In particular, it follows that the OSV formula comes from the unrefined limit of the general expression including only the so-called $\mathbb{W}$ tower of higher derivatives, while the on-shell action of pure (Euclidean) AdS$_4$ with round $S^3$ boundary comes from the NS limit that includes only the $\mathbb{T}$ tower.</p>Mon, 10 Jan 2022 10:07:38 +0000Mon, 17 Jan 2022 15:00:00 +0000Mon, 17 Jan 2022 16:00:00 +0000Kiril HristovSofia UniversityString TheoryDan Roberts, 2022/01/13, 17h, The Principles of Deep Learning Theory
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6498
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6498<p>Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data.</p><p>This talk is based on a book, <em><a href="https://arxiv.org/pdf/2106.10165.pdf">The Principles of Deep Learning Theory</a></em>, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.</p><p> </p>Thu, 13 Jan 2022 22:34:40 +0000Thu, 13 Jan 2022 17:00:00 +0000Thu, 13 Jan 2022 18:00:00 +0000<a target='_content' href="https://physics.mit.edu/faculty/dan-roberts/">Dan Roberts</a>MIT, Center for Theoretical PhysicsMathematics, Physics & Machine LearningDavide Gabrielli, 2022/01/12, 16h, A double limite for the current of particle systems. The order does not matter
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6538
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6538<p>We consider diffusive particle systems evolving on a lattice of mesh $1/N$ and study the large deviations for the current on a time window $[0,T]$. We consider two different asymptotics. In the first case we send before $N\to +\infty$ with a diffusive hydrodynamic rescaling keeping $T$ fixed, and then send $T\to +\infty$. In the second case we send before $T\to +\infty$ keeping $N$ fixed and then send $N\to +\infty$.</p>Mon, 10 Jan 2022 09:43:10 +0000Wed, 12 Jan 2022 16:00:00 +0000Wed, 12 Jan 2022 17:00:00 +0000<a target='_content' href="http://people.disim.univaq.it/~gabriell/">Davide Gabrielli</a>University of L'AquilaProbability and Stochastic AnalysisLars Sektnan, 2022/01/11, 16h 30m, Blowing up extremal Kähler manifolds
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6491
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6491<p>Extremal Kähler metrics were introduced by Calabi in the 80’s as a type of canonical Kähler metric on a Kähler manifold, and are a generalisation of constant scalar curvature Kähler metrics in the case when the manifold admits automorphisms. A natural question is when the blowup of a manifold in a point admits an extremal Kähler metric. We completely settle the question in terms of a finite dimensional moment map/GIT condition, generalising work of Arezzo-Pacard, Arezzo-Pacard-Singer and Székelyhidi. Our methods also allow us to deal with a certain semistable case that has not been considered before, where the original manifold does not admit an extremal metric, but is infinitesimally close to doing so. As a consequence of this, we solve the first non-trivial special case of a conjecture of Donaldson. This is joint work with Ruadhaí Dervan.</p>Wed, 12 Jan 2022 18:32:19 +0000Tue, 11 Jan 2022 16:30:00 +0000Tue, 11 Jan 2022 17:30:00 +0000<a target='_content' href="https://sites.google.com/cirget.ca/lars-sektnan/">Lars Sektnan</a>University of GothenburgGeometria em LisboaMakiko Sasada, 2022/01/05, 16h, On Varadhan’s decomposition theorem in a general setting
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6531
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6531<p>We rigorously formulate and prove for a relatively general class of interactions the characterization of shift-invariant closed L2-forms for a large scale interacting system. Such characterization of closed forms has played an essential role in proving the hydrodynamic limit of nongradient systems. The universal expression in terms of conserved quantities was sought from observations for specific models, but a precise formulation or rigorous proof up until now had been elusive. To obtain this, we first prove the universal characterization of shift-invariant closed “local” forms in a completely geometric way, that is, in a way that has nothing to do with probability measures. Then, we apply the result to characterize the L2-forms. Our result is applicable for many important models including generalized exclusion processes, multi-species exclusion processes, exclusion processes on crystal lattices and so on. This talk is based on a joint work with Kenichi Bannai and Yukio Kametani (https://arxiv.org/abs/2009.04699), and a joint work with Kenichi Bannai (https://arxiv.org/abs/2111.08934).</p>Mon, 03 Jan 2022 20:02:52 +0000Wed, 05 Jan 2022 16:00:00 +0000Wed, 05 Jan 2022 17:00:00 +0000<a target='_content' href="https://sites.google.com/view/makikosasada/home">Makiko Sasada</a>University of TokyoProbability and Stochastic AnalysisEva Miranda, 2021/12/21, 16h 30m, Looking at the Euler flows through a contact mirror
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6365
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6365<p>The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [6, 7, 8] launched a programme to address the global existence problem for the Euler and Navier-Stokes equations based on the concept of universality. Inspired by this proposal, we show that the stationary Euler equations exhibit several universality features, in the sense that, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension [1].</p><p>A key point in the proof is looking at the h-principle in contact geometry through a contact mirror, unveiled by Etnyre and Ghrist in [4] more than two decades ago. We end this talk addressing a question raised by Moore in [5] : “Is hydrodynamics capable of performing computations?”. The universality result above yields the Turing completeness of the steady Euler flows on a 17-dimensional sphere. Can this result be improved? In [2] we construct a Turing complete steady Euler flow in dimension 3. Time permitting, we discuss this and other generalizations for t-dependent Euler flows contained in [3].</p><p>In all the constructions above, the metric is seen as an additional "variable" and thus the method of proof does not work if the metric is prescribed.</p><p>Is it still possible to construct a Turing complete Euler flow on a 3-dimensional space with the standard metric? Yes, see our recent preprint <a data-saferedirecturl="https://www.google.com/url?q=https://arxiv.org/abs/2111.03559&source=gmail&ust=1636795092908000&usg=AOvVaw2wiNLbApigMgm6ZBiUTXs1" href="https://arxiv.org/abs/2111.03559" target="_blank">https://arxiv.org/abs/2111.<wbr />03559</a> (joint with Cardona and Peralta).</p><p>This talk is based on several joint works with Cardona, Peralta-Salas and Presas.</p><p>[1] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Universality of Euler flows and flexibility of Reeb embeddings, arXiv:1911.01963.<br />[2] R. Cardona, E. Miranda, D. Peralta-Salas, F. Presas. Constructing Turing complete Euler flows in dimension 3. PNAS May 11, 2021 118 (19) e2026818118; <a data-saferedirecturl="https://www.google.com/url?q=https://doi.org/10.1073/pnas.2026818118&source=gmail&ust=1636795092908000&usg=AOvVaw2Lilygt45rCtDHdj4HRWKP" href="https://doi.org/10.1073/pnas.2026818118" target="_blank">https://doi.org/10.1073/pnas.<wbr />2026818118</a>.<br />[3] R. Cardona, E. Miranda and D. Peralta-Salas, Turing universality of the incompressible Euler equations and a conjecture of Moore, <em>International Mathematics Research Notices</em>, rnab233, <a data-saferedirecturl="https://www.google.com/url?q=https://doi.org/10.1093/imrn/rnab233&source=gmail&ust=1636795092908000&usg=AOvVaw3sUXTOwEhwYUrub__1OPKY" href="https://doi.org/10.1093/imrn/rnab233" target="_blank">https://doi.org/10.1093/imrn/<wbr />rnab233</a><br />[4] J. Etnyre, R. Ghrist. Contact topology and hydrodynamics I. Beltrami fields and the Seifert conjecture. Nonlinearity 13 (2000) 441–458.<br />[5] C. Moore. Generalized shifts: unpredictability and undecidability in dynamical systems. Nonlinearity 4 (1991) 199–230.<br />[6] T. Tao. On the universality of potential well dynamics. Dyn. PDE 14 (2017) 219–238.<br />[7] T. Tao. On the universality of the incompressible Euler equation on compact manifolds. Discrete Cont. Dyn. Sys. A 38 (2018) 1553–1565.<br />[8] T. Tao. Searching for singularities in the Navier-Stokes equations. Nature Rev. Phys. 1 (2019) 418–419.</p>Wed, 22 Dec 2021 14:55:37 +0000Tue, 21 Dec 2021 16:30:00 +0000Tue, 21 Dec 2021 17:30:00 +0000<a target='_content' href="https://web.mat.upc.edu/eva.miranda/nova/">Eva Miranda</a>Universitat Politècnica de CatalunyaGeometria em LisboaVladimir M. Stojanovic, 2021/12/15, 17h, Lie-algebraic aspects of quantum control: gate realization and W-to-GHZ state conversion
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6496
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6496<p>In this talk I will try to demonstrate the use of Lie-algebraic concepts in the quantum control of interacting qubit arrays, with examples from both operator (gate)- and state control. I will start from the basics of quantum control and briefly review the Lie-algebraic underpinnings of the concept of complete controllability. I will then specialize to qubit arrays with Heisenberg-type interactions, summarizing the conditions for their complete controllability and showing a few examples of gate realization. The second part of the talk will be devoted to a rather unconventional use of Lie-algebraic concepts within a dynamical-symmetry-based approach to the deterministic conversion between W- and Greenberger-Horne-Zeilinger (three-qubit) states. The underlying physical system consists of three neutral atoms subject to several external laser pulses, where the atomic ground- and a highly-excited Rydberg state play the role of the two relevant logical qubit states.</p>Mon, 20 Dec 2021 10:26:39 +0000Wed, 15 Dec 2021 17:00:00 +0000Wed, 15 Dec 2021 18:00:00 +0000Vladimir M. StojanovicTU DarmstadtTopological Quantum Field TheorySourav Roychowdhury, 2021/12/13, 15h, Non-Abelian T-dual of Klebanov-Tseytlin background and its Penrose limits
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6483
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6483<p>In this talk I will discuss Klebanov-Tseytlin background and its non-Abelian T-dual geometry. In particular I will show that the T-dual background admits pp-wave geometry in the neighbourhood of appropriate null geodesic. I will make comments on possible dual gauge theory for our pp-wave background.</p>Mon, 03 Jan 2022 09:42:51 +0000Mon, 13 Dec 2021 15:00:00 +0000Mon, 13 Dec 2021 16:00:00 +0000Sourav RoychowdhuryChennai Mathematical InstituteString TheoryPier Luigi Dragotti, 2021/12/09, 17h, Computational Imaging for Art investigation and for Neuroscience
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6472
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6472<p>The revolution in sensing, with the emergence of many new imaging techniques, offers the possibility of gaining unprecedented access tothe physical world, but this revolution can only bear fruit through the skilful interplay between the physical and computational worlds. This is the domain of computational imaging which advocates that, to develop effective imaging systems, it will be necessary to go beyond the traditional decoupled imaging pipeline where device physics, image processing and the end-user application are considered separately. Instead, we need to rethink imaging as an integrated sensing and inference model. In this talk we cover two research areas where computational imaging is likely to have an impact.</p><p>We first focus on the heritage sector which is experiencing a digital revolution driven in part by the increasing use of non-invasive, non-destructive imaging techniques. These new imaging methods provide a way to capture information about an entire painting and can give us information about features at or below the surface of the painting. We focus on Macro X-Ray Fluorescence (XRF) scanning which is a technique for the mapping of chemical elements in paintings. After describing in broad terms the working of this device, a method that can process XRF scanning data from paintings is introduced. The method is based on connecting the problem of extracting elemental maps in XRF data to Prony's method, a technique broadly used in engineering to estimate frequencies of a sum of sinusoids. The results presented show the ability of our method to detect and separate weak signals related to hidden chemical elements in the paintings. We then discuss results on the Leonardo’s<em> The Virgin of the Rocks</em> and show that our algorithm is able to reveal, more clearly than ever before, the hidden drawings of a previous composition that Leonardo then abandoned for the painting that we can now see.</p><p>In the second part of the talk, we focus on two-photon microscopy and neuroscience. To understand how networks of neurons process information, it is essential to monitor their activity in living tissue. Multi-photon microscopy is unparalleled in its ability to image cellular activity and neural circuits, deep in living tissue, at single-cell resolution. However, in order to achieve step changes in our understanding of brain function, large-scale imaging studies of neural populations are needed and this can be achieved only by developing computational tools that can enhance the quality of the data acquired and can scan 3-D volumes quickly. In this talk we introduce light-field microscopy and present a method to localize neurons in 3-D. The method is based on the use of proper sparsity priors, novel optimization strategies and machine learning.</p><p>This is joint work with A. Foust, P. Song, C. Howe, H. Verinaz, J. Huang and Y.Su from Imperial College London, and C. Higgitt and N. Daly from The National Gallery in London</p>Sun, 12 Dec 2021 20:36:18 +0000Thu, 09 Dec 2021 17:00:00 +0000Thu, 09 Dec 2021 18:00:00 +0000<a target='_content' href="https://www.imperial.ac.uk/people/p.dragotti">Pier Luigi Dragotti</a>Department of Electrical and Electronic Engineering, Imperial College, LondonMathematics, Physics & Machine LearningStefan Grosskinsky, 2021/12/08, 16h, Feynman-Kac particle models for cloning algorithms
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6507
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6507<p>Dynamic large deviations for additive path functionals of stochastic processes have attracted recent research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical 'cloning' algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we use Feynman-Kac models to establish fully rigorous bounds on systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization and related to the propagation of chaos for mean-field models. Our results apply to a large class of jump processes on locally compact state space, and provide a framework that can also be used to evaluate and improve the efficiency of algorithms. This is joint work with Letizia Angeli, Adam Johansen and Andrea Pizzoferrato.</p>Sun, 05 Dec 2021 23:22:36 +0000Wed, 08 Dec 2021 16:00:00 +0000Wed, 08 Dec 2021 17:00:00 +0000<a target='_content' href="https://stefangrosskinsky.com">Stefan Grosskinsky</a>Universität AusburgProbability and Stochastic AnalysisCiprian Manolescu, 2021/12/07, 16h 30m, Khovanov homology and the search for exotic 4-spheres
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6373
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6373<p>A well-known strategy to disprove the smooth 4D Poincare conjecture is to find a knot that bounds a disk in a homotopy 4-ball but not in the standard 4-ball. Freedman, Gompf, Morrison and Walker suggested that Rasmussen’s invariant from Khovanov homology could be useful for this purpose. I will describe three recent results about this strategy: that it fails for Gluck twists (joint work with Marengon, Sarkar and Willis); that an analogue works for other 4-manifolds (joint work with Marengon and Piccirillo); and that 0-surgery homeomorphisms provide a large class of potential examples (joint work with Piccirillo).</p>Thu, 09 Dec 2021 13:55:32 +0000Tue, 07 Dec 2021 16:30:00 +0000Tue, 07 Dec 2021 17:30:00 +0000<a target='_content' href="https://web.stanford.edu/~cm5/">Ciprian Manolescu</a>Stanford UniversityGeometria em LisboaNathan Benjamin, 2021/12/06, 15h, Harmonic analysis of $2d$ CFT partition functions
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6439
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6439<p>We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space $H/SL(2,\mathbb{Z})$, and of target space moduli space $O(c, c; \mathbb{Z})\backslash O(c, c; \mathbb{R})/O(c) × O(c)$. This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to $AdS_3$ gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.</p>Mon, 03 Jan 2022 15:05:52 +0000Mon, 06 Dec 2021 15:00:00 +0000Mon, 06 Dec 2021 16:00:00 +0000Nathan BenjaminPrinceton UniversityString TheorySoledad Villar, 2021/12/02, 17h, Equivariant machine learning structure like classical physics
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6456
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6456<p>There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make use of high-order tensor objects, and some apply symmetry-enforcing constraints. Different physical laws obey different combinations of fundamental symmetries, but a large fraction (possibly all) of classical physics is equivariant to translation, rotation, reflection (parity), boost (relativity), and permutations. Here we show that it is simple to parameterize universally approximating polynomial functions that are equivariant under these symmetries, or under the Euclidean, Lorentz, and Poincaré groups, at any dimensionality $d$. The key observation is that nonlinear $O(d)$-equivariant (and related-group-equivariant) functions can be expressed in terms of a lightweight collection of scalars–scalar products and scalar contractions of the scalar, vector, and tensor inputs. These results demonstrate theoretically that gauge-invariant deep learning models for classical physics with good scaling for large problems are feasible right now.</p>Fri, 03 Dec 2021 14:16:36 +0000Thu, 02 Dec 2021 17:00:00 +0000Thu, 02 Dec 2021 18:00:00 +0000<a target='_content' href="https://www.ams.jhu.edu/villar/">Soledad Villar</a>Mathematical Institute for Data Science at Johns Hopkins UniversityMathematics, Physics & Machine LearningStefan Czimek, 2021/12/02, 14h 30m, The characteristic gluing problem of general relativity
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6503
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6503<p>In this talk we introduce and solve the characteristic gluing problem for the Einstein vacuum equations. We prove that obstructions to characteristic gluing come from an infinite-dimensional space of conservation laws along null hypersurfaces for the linearized equations at Minkowski. We show that this obstruction space splits into an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges. We identify the 10 gauge-invariant charges to be related to the energy, linear momentum, angular momentum and center-of-mass of the spacetime. Based on this identification, we explain how to characteristically glue a given spacetime to a suitably chosen Kerr black hole spacetime. As corollary we get an alternative proof of the Corvino-Schoen spacelike gluing to Kerr. Moreover, we apply our characteristic gluing method to localise characteristic initial data along null hypersurfaces. In particular, this yields a new proof of the Carlotto-Schoen spacelike localization where our method yields no loss of decay, thus resolving an open problem in this direction. We also outline further applications. This is joint work with S. Aretakis (Toronto) and I. Rodnianski (Princeton).</p>Tue, 30 Nov 2021 15:55:23 +0000Thu, 02 Dec 2021 14:30:00 +0000Thu, 02 Dec 2021 15:30:00 +0000Stefan CzimekBrown UniversityMathematical RelativityJean Van Schaftingen, 2021/12/02, 14h, Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold (**postponed**)
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6480
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6480<p>Ginzburg-Landau type functionals provide a relaxation scheme to construct harmonic maps in the presence of topological obstructions. They arise in superconductivity models, in liquid crystal models (Landau-de Gennes functional) and in the generation of cross-fields in meshing. For a general compact manifold target space we describe the asymptotic number, type and location of singularities that arise in minimizers. We cover in particular the case where the fundamental group of the vacuum manifold in nonabelian and hence the singularities cannot be characterized univocally as elements of the fundamental group.</p><p>We obtain similar results for \(p\)-harmonic maps with \(p\) going to \(2\).</p><p>The results unify the existing theory and cover new situations and problems.</p><p>This is a joint work with Antonin Monteil (Paris-Est Créteil, France), Rémy Rodiac (Paris-Saclay, France) and Benoit Van Vaerenbergh (UCLouvain).</p>Mon, 29 Nov 2021 17:52:42 +0000Thu, 02 Dec 2021 14:00:00 +0000Thu, 02 Dec 2021 15:00:00 +0000Jean Van SchaftingenUniversité Catholique de LouvainLisbon WADE — Webinar in Analysis and Differential EquationsJeffrey Kuan, 2021/12/01, 16h, Joint moments of multi-species q-Boson
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6504
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6504<p>The Airy_2 process is a universal distribution which describes fluctuations in models in the Kardar--Parisi--Zhang (KPZ) universality class, such as the asymmetric simple exclusion process (ASEP) and the Gaussian Unitary Ensemble (GUE). Despite its ubiquity, there are no proven results for analogous fluctuations of multi--species models. Here, we will discuss one model in the KPZ universality class, the q--Boson. We will show that the joint multi--point fluctuations of the single--species q--Boson match the single--point fluctuations of the multi--species q--Boson. Therefore the single--point fluctuations of multi--species models in the KPZ class ought to be the Airy_2 process. The proof utilizes the underlying algebraic structure of the multi--species q--Boson, namely the quantum group symmetry and Coxeter group actions.</p>Tue, 30 Nov 2021 19:06:49 +0000Wed, 01 Dec 2021 16:00:00 +0000Wed, 01 Dec 2021 17:00:00 +0000<a target='_content' href="https://www.math.tamu.edu/~jkuan/">Jeffrey Kuan</a>Texas A&M UniversityProbability and Stochastic AnalysisAlfonso Zamora, 2021/11/30, 16h 30m, E-polynomials and geometry of character varieties
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6474
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6474<p>Quasi-projective complex algebraic varieties (not necessarily smooth or compact) carry, following Deligne, mixed Hodge structures whose numerical information is encoded in the $E$-polinomial, which provides substantial geometrical (topological plus complex) information about these varieties; important examples being character varieties. Let $G$ be a complex algebraic group and let $\mathcal{X}_{\Gamma}G$ be the $G$-character variety of a finitely presented group $\Gamma$. Exploring a new path between the previously known arithmetical and geometrical methods to compute $E$-polynomials we provide a concrete relation, in terms of plethystic functions, stratifications of the character variety as an affine GIT quotient and combinatorics, between the generating series for $E$-polynomials of $\mathcal{X}_{\Gamma}G$ for $G=GL(n,\mathbb{C})$ and the series of the subset of irreducible representation conjugacy classes $\mathcal{X}_{\Gamma}^{irr}G$. This yields explicit (stratified) expressions for the $E$-polynomials of several groups $\Gamma$, for low values of $n$. For the case $\Gamma=F_{r}$, the free group of rank $r$, we prove the equality of the $E$-polynomials for $\mathcal{X}_{r}SL_{n}$ and $\mathcal{X}_{r}PGL_{n}$, for any $n,r\in\mathbb{N}$. This settles a conjecture of Lawton-Muñoz and provides evidence on topological mirror symmetry conjectures for Langlands dual groups.</p><p>These results are joint work with Carlos Florentino and Azizeh Nozad.</p>Wed, 01 Dec 2021 23:10:47 +0000Tue, 30 Nov 2021 16:30:00 +0000Tue, 30 Nov 2021 17:30:00 +0000<a target='_content' href="https://blogs.upm.es/azamorasaiz/">Alfonso Zamora</a>Polytechnic University of MadridGeometria em LisboaShira Chapman, 2021/11/29, 15h, Holographic Complexity and de Sitter Space
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6446
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6446<p>We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. We comment on the implications of these results towards understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon.</p>Tue, 30 Nov 2021 22:45:38 +0000Mon, 29 Nov 2021 15:00:00 +0000Mon, 29 Nov 2021 16:00:00 +0000Shira ChapmanBen Gurion University of the NegevString TheoryMilton Jara, 2021/11/26, 14h, Sharp convergence of Markov chains
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6468
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6468<p>We show how to use entropy methods to obtain sharp estimates on the convergence of finite-state Markov chains to their stationary states.</p>Thu, 18 Nov 2021 11:33:04 +0000Fri, 26 Nov 2021 14:00:00 +0000Fri, 26 Nov 2021 15:00:00 +0000Milton JaraInstituto de Matemática Pura e AplicadaRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsSuman Ravuri, 2021/11/25, 17h, Skilful precipitation nowcasting using deep generative models of radar
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6473
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6473<p>Precipitation nowcasting, the high-resolution forecasting of precipitation up to two hours ahead, supports the real-world socioeconomic needs of many sectors reliant on weather-dependent decision-making. State-of-the-art operational nowcasting methods typically advect precipitation fields with radar-based wind estimates, and struggle to capture important non-linear events such as convective initiations. Recently introduced deep learning methods use radar to directly predict future rain rates, free of physical constraints. While they accurately predict low-intensity rainfall, their operational utility is limited because their lack of constraints produces blurry nowcasts at longer lead times, yielding poor performance on rarer medium-to-heavy rain events. Here we present a deep generative model for the probabilistic nowcasting of precipitation from radar that addresses these challenges. Using statistical, economic and cognitive measures, we show that our method provides improved forecast quality, forecast consistency and forecast value. Our model produces realistic and spatiotemporally consistent predictions over regions up to 1,536 km × 1,280 km and with lead times from 5–90 min ahead. Using a systematic evaluation by more than 50 expert meteorologists, we show that our generative model ranked first for its accuracy and usefulness in 89% of cases against two competitive methods. When verified quantitatively, these nowcasts are skillful without resorting to blurring. We show that generative nowcasting can provide probabilistic predictions that improve forecast value and support operational utility, and at resolutions and lead times where alternative methods struggle.</p>Thu, 25 Nov 2021 23:26:41 +0000Thu, 25 Nov 2021 17:00:00 +0000Thu, 25 Nov 2021 18:00:00 +0000<a target='_content' href="https://www.linkedin.com/in/suman-ravuri-81928082/">Suman Ravuri</a>DeepMindMathematics, Physics & Machine LearningDenis Bonheure, 2021/11/25, 15h, Equilibrium configuration of a rectangular obstacle immersed in a channel flow
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=6492
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=6492<p>Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may be asymmetric. We show that this is not the case for a Poiseuille flow in an unbounded 2D channel, at least for small Reynolds number and flow rate. We consider both the cases of vertically moving obstacles and obstacles rotating around a fixed pin.</p><p>This presentation is based on a joint work with F. Gazzola and P. Galdi.</p>Mon, 22 Nov 2021 15:11:00 +0000Thu, 25 Nov 2021 15:00:00 +0000Thu, 25 Nov 2021 16:00:00 +0000<a target='_content' href="http://homepages.ulb.ac.be/~dbonheur/">Denis Bonheure</a>Francqui Research Professor (Francqui Foundation) and Université Libre de BruxellesRoom P3.10, Mathematics BuildingPartial Differential EquationsMilton Jara, 2021/11/25, 14h, Sharp convergence of Markov chains
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6467
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6467<p>We show how to use entropy methods to obtain sharp estimates on the convergence of finite-state Markov chains to their stationary states.</p>Thu, 18 Nov 2021 11:33:29 +0000Thu, 25 Nov 2021 14:00:00 +0000Thu, 25 Nov 2021 15:00:00 +0000Milton JaraInstituto de Matemática Pura e AplicadaRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsAmol Aggarwal, 2021/11/24, 16h, Asymptotics in the Stochastic Six-Vertex Model
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6497
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6497<p>The stochastic six-vertex model is an example of a discrete random surface, which can be viewed as an interacting particle system that is discrete in both space and time. In this talk we describe several asymptotic properties for this model, including its relation to asymmetric simple exclusion processes, its limit shapes, local statistics, and translation-invariant Gibbs measures</p>Tue, 23 Nov 2021 00:05:28 +0000Wed, 24 Nov 2021 16:00:00 +0000Wed, 24 Nov 2021 17:00:00 +0000<a target='_content' href="https://www.claymath.org/people/amol-aggarwal">Amol Aggarwal</a>Columbia UniversityProbability and Stochastic AnalysisEly Kerman, 2021/11/23, 16h 30m, On symplectic capacities and their blind spots
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6384
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6384<p>In this talk I will discuss a joint work with Yuanpu Liang in which we establish some results concerning the symplectic capacities defined by Gutt and Hutchings using $S^1$-equivariant symplectic homology. Our primary result settles a version of the recognition question in the negative. We prove that the Gutt-Hutchings capacities, together with the volume, do not constitute a complete set of symplectic invariants for star-shaped (in fact convex) domains with smooth boundary. We also prove that, even for star-shaped domains with smooth boundaries, these capacities are mutually independent and are independent from the volume. The constructions that demonstrate these independence properties are not exotic. They are convex and concave toric domains. The new tool used here is a significant simplification of the formulae of Gutt and Hutchings for the capacities of convex/concave toric domains, that holds under an additional symmetry assumption. This allows us to identify new mutual blind spots of the capacities which are then used to construct the desired examples.</p>Wed, 24 Nov 2021 11:36:34 +0000Tue, 23 Nov 2021 16:30:00 +0000Tue, 23 Nov 2021 17:30:00 +0000<a target='_content' href="https://faculty.math.illinois.edu/~ekerman/index.html">Ely Kerman</a>University of Illinois Urbana-ChampaignGeometria em LisboaMilton Jara, 2021/11/22, 14h, Sharp convergence of Markov chains
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6466
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6466<p>We show how to use entropy methods to obtain sharp estimates on the convergence of finite-state Markov chains to their stationary states.</p>Thu, 18 Nov 2021 11:33:57 +0000Mon, 22 Nov 2021 14:00:00 +0000Mon, 22 Nov 2021 15:00:00 +0000Milton JaraInstituto de Matemática Pura e AplicadaRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsMilton Jara, 2021/11/19, 14h, Sharp convergence of Markov chains
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6465
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=6465<p>We show how to use entropy methods to obtain sharp estimate on the convergence of finite-state Markov chains to their stationary states.</p>Thu, 18 Nov 2021 11:34:23 +0000Fri, 19 Nov 2021 14:00:00 +0000Fri, 19 Nov 2021 15:00:00 +0000Milton JaraInstituto de Matemática Pura e AplicadaRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsGiovanni Bellettini, 2021/11/18, 14h, On a conjecture of De Giorgi on the first variation of the Modica-Mortola functional
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6479
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6479<p>We shall discuss some (not so recent) results on a 1991 conjecture of De Giorgi concerning the Gamma limit of the square norm of the first variation of the Modica-Mortola functionals, and its relation with the Willmore functional.</p>Wed, 10 Nov 2021 10:44:46 +0000Thu, 18 Nov 2021 14:00:00 +0000Thu, 18 Nov 2021 15:00:00 +0000<a target='_content' href="https://cvgmt.sns.it/person/47/">Giovanni Bellettini</a>ICTP and Università di SienaLisbon WADE — Webinar in Analysis and Differential EquationsBrian R. Williams, 2021/11/17, 17h, Exceptional super Lie algebras in twisted M-theory
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6481
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6481<p>With Saberi and Raghavendran we constructed, in the BV formalism, the minimal, holomorphic, twist of 11-dimensional supergravity. Amazingly, on flat space, the theory shares a close relationship to an exceptional simple super Lie algebra called $E(5,10)$. Motivated by holographic duality, I’ll turn attention to symmetries of the theories on M2 and M5 branes. In the twisted setting, we find that the superconformal algebra enhances to other infinite-dimensional exceptional super Lie algebras. I will discuss further extensions of these exceptional algebras to factorization algebras and applications to pinning down correlation functions in M-theory.</p>Sat, 20 Nov 2021 22:49:32 +0000Wed, 17 Nov 2021 17:00:00 +0000Wed, 17 Nov 2021 18:00:00 +0000<a target='_content' href="https://www.sites.google.com/view/brianrwilliams/home">Brian R. Williams</a>University of EdinburghTopological Quantum Field TheoryVincent Vargas, 2021/11/17, 16h, Liouville conformal field theory: from probability theory to the conformal bootstrap
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6486
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6486<p>Liouville conformal field theory was introduced by Polyakov in 1981 as an essential ingredient in his path integral construction of string theory. Since then Liouville theory has appeared in a wide variety of contexts ranging from random conformal geometry to 4d Yang-Mills theory with supersymmetry. Recently, a probabilistic (or constructive) construction of Liouville theory was provided using the 2d Gaussian Free Field. This construction can be seen as a rigrous construction of the 2d path integral introduced in Polyakov's 1981 work. In contrast to this construction, modern conformal field theory is based on representation theory and the so-called bootstrap procedure (based on recursive techniques) introduced in 1984 by Belavin-Polyakov-Zamolodchikov. In particular, a bootstrap contruction for Liouville theory has been proposed in the mid 90's by Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ). The aim of this talk is to review ongoing work which aims at showing the equivalence between the probabilistic (or path integral) construction and the bootstrap construction of Liouville theory. Based on numerous joint works with F. David, C. Guillarmou, A. Kupiainen, R. Rhodes.</p>Tue, 16 Nov 2021 00:16:20 +0000Wed, 17 Nov 2021 16:00:00 +0000Wed, 17 Nov 2021 17:00:00 +0000<a target='_content' href="https://www.math.ens.fr/~vargas/">Vincent Vargas</a>Université de GenèveProbability and Stochastic AnalysisHenrique Bursztyn, 2021/11/16, 16h 30m, Revisiting and extending Poisson-Nijenhuis structures
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6387
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6387<p>Poisson-Nijenhuis structures arise in various settings, such as the theory of integrable systems, Poisson-Lie theory and quantization. By revisiting this notion from a new viewpoint, I will show how it can be naturally extended to the realm of Dirac structures, with applications to integration results in (holomorphic) Poisson geometry.</p>Wed, 17 Nov 2021 10:41:04 +0000Tue, 16 Nov 2021 16:30:00 +0000Tue, 16 Nov 2021 17:30:00 +0000<a target='_content' href="https://w3.impa.br/~henrique/">Henrique Bursztyn</a>Instituto Nacional de Matemática Pura e AplicadaGeometria em LisboaMichael Arbel, 2021/11/11, 17h, Annealed Flow Transport Monte Carlo
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6455
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6455<p>Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NF) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps — as in SMC, but also relies on NF which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman-Kac measure which simplifies to the law of a controlled diffusion for expressive NF. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.</p>Thu, 11 Nov 2021 20:58:55 +0000Thu, 11 Nov 2021 17:00:00 +0000Thu, 11 Nov 2021 18:00:00 +0000<a target='_content' href="https://michaelarbel.github.io/">Michael Arbel</a>INRIA Grenoble Rhône-AlpesMathematics, Physics & Machine LearningSam Olesker-Taylor, 2021/11/10, 16h, Random Walks on Random Cayley Graph
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6476
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6476<p>We investigate mixing properties of RWs on random Cayley graphs of a finite group G with k ≫ 1 independent, uniformly random generators. Denote this Gₖ. Assume that 1 ≪ log k ≪ log |G|. Aldous and Diaconis (1985) conjectured that the RW exhibits cutoff for any group G whenever k ≫ log |G| and further that the time depends only on k and |G|. This was verified for Abelian groups by Dou and Hildebrand (1994, 1996). Their upper bound holds for all groups. We establish cutoff for the RW on Gₖ for all Abelian groups when 1 ≪ k ≲ log |G|, subject to some 'almost necessary' conditions. We also exhibit a non-Abelian matrix group which contradicts the second part of the AD conjecture. Lastly, we upper bound the mixing time of a RW on a nilpotent group by that of the RW on a corresponding Abelian group.</p>Mon, 08 Nov 2021 21:22:02 +0000Wed, 10 Nov 2021 16:00:00 +0000Wed, 10 Nov 2021 17:00:00 +0000<a target='_content' href="https://mathematicalsam.wordpress.com">Sam Olesker-Taylor</a>University of BathProbability and Stochastic AnalysisCarlos Florentino, 2021/11/09, 16h 30m, The geometry of commuting varieties of reductive groups
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6416
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6416<p>Let $R_r(G)$ be the (connected component of the identity of the) variety of commuting $r$-tuples of elements of a complex reductive group $G$. We determine the mixed Hodge structure on the cohomology of the representation variety $R_r(G)$ and of the character variety $R_r(G)/G$, for general $r$ and $G$. We also obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomials, Poincaré polynomials and Euler characteristics of these representation and character varieties. In the character variety case, this gives the counting polynomial over finite fields, and some results also apply to character varieties of nilpotent groups.</p><p>This is joint work with S. Lawton and J. Silva (arXiv:2110.07060).</p>Wed, 10 Nov 2021 10:57:46 +0000Tue, 09 Nov 2021 16:30:00 +0000Tue, 09 Nov 2021 17:30:00 +0000<a target='_content' href="http://cfloren.wikidot.com/start">Carlos Florentino</a>Faculty of Sciences - University of LisbonGeometria em LisboaJoerg Teschner, 2021/11/08, 15h, Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6413
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6413<p>We study the Borel summation of the Gromov-Witten potential for the resolved conifold. The Stokes phenomena associated to this Borel summation are shown to encode the Donaldson-Thomas invariants of the resolved conifold, having a direct relation to the Riemann-Hilbert problem formulated by T. Bridgeland. There exist distinguished integration contours for which the Borel summation reproduces previous proposals for the non-perturbative topological string partition functions of the resolved conifold. These partition functions are shown to have another asymptotic expansion at strong topological string coupling. We demonstrate that the Stokes phenomena of the strong-coupling expansion encode the DT invariants of the resolved conifold in a second way. Mathematically, one finds a relation to Riemann-Hilbert problems associated to DT invariants which is different from the one found at weak coupling. The Stokes phenomena of the strong-coupling expansion turn out to be closely related to the wall-crossing phenomena in the spectrum of BPS states on the resolved conifold studied in the context of supergravity by D. Jafferis and G. Moore.</p>Wed, 10 Nov 2021 14:43:37 +0000Mon, 08 Nov 2021 15:00:00 +0000Mon, 08 Nov 2021 16:00:00 +0000Joerg TeschnerUniversity of HamburgString TheoryGeorge Em Karniadakis, 2021/11/04, 17h, Operator regression via DeepOnet: Theory, Algorithms and Applications
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6400
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6400<p>We will review physics-informed neural network and summarize available theoretical results. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. The universal approximation theorem of operators is suggestive of the potential of NNs in learning from scattered data any continuous operator or complex system. We first generalize the theorem to deep neural networks, and subsequently we apply it to design a new composite NN with small generalization error, the deep operator network (DeepONet), consisting of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, e.g., integrals, Laplace transforms and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. More generally, DeepOnet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously.</p>Fri, 05 Nov 2021 23:38:26 +0000Thu, 04 Nov 2021 17:00:00 +0000Thu, 04 Nov 2021 18:00:00 +0000<a target='_content' href="https://www.brown.edu/research/projects/crunch/george-karniadakis">George Em Karniadakis</a>Brown UniversityMathematics, Physics & Machine LearningMelanie Graf, 2021/11/04, 14h 30m, Singularity theorems in low regularity
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6471
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6471<p>The singularity theorems of R. Penrose and S. Hawking from the 1960s show that a spacetime satisfying certain physically reasonable curvature and causality conditions cannot be causal geodesically complete. Despite their great success these classical theorems still have some drawbacks, one of them being that they require smoothness of the metric while in many physical models the metric is less regular. In my talk I will present work on singularity theorems based on distributional energy conditions for metrics that are merely continuously differentiable – a regularity where one still has existence but not uniqueness for solutions of the geodesic equation. We will see that an approximation-based approach to the low-regularity issue is closely linked to establishing singularity theorems under weakened energy conditions and while the improvements necessary are still entirely straightforward in the present case, attempting to lower the regularity further would require some new methods.</p>Tue, 02 Nov 2021 11:43:55 +0000Thu, 04 Nov 2021 14:30:00 +0000Thu, 04 Nov 2021 15:30:00 +0000Melanie GrafUniversity of TübingenMathematical RelativityKelei Wang, 2021/11/04, 14h, Regularity of transition layers in Allen-Cahn equation
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6443
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6443<p> In this talk I will survey the regularity theory for transition layers in singularly perturbed Allen-Cahn equation, from zeroth order regularity to second order one. Some applications of this regularity theory will also be discussed, including De Giorgi conjecture, classification of finite Morse index solutions and construction of minimal hypersurfaces by Allen-Cahn approximation.</p>Wed, 13 Oct 2021 09:35:40 +0100Thu, 04 Nov 2021 14:00:00 +0000Thu, 04 Nov 2021 15:00:00 +0000<a target='_content' href="https://scholar.google.com.sg/citations?user=J6eOUc4AAAAJ&hl=en">Kelei Wang</a>Wuhan UniversityLisbon WADE — Webinar in Analysis and Differential EquationsLuisa Andreis, 2021/11/03, 17h, Phase transition in sparse random graphs and coagulation processes
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6470
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6470<p>Inhomogeneous random graphs are a natural generalization of the wellknown Erdös-Renyi random graph, where vertices are characterized by a type and edges are present independently according to the type of the vertices that they are connecting. In the sparse regime, these graphs undergo a phase transition in terms of the emergence of a giant component exactly as the classical Erd}os{R enyi model. In this talk we will present an alternative approach, via large deviations, to prove this phase transition. This allows a comparison with the gelation phase transition that characterizes some coagulation process and with phase transitions of condensation type emerging in several systems of interacting components. This is an ongoing joint work with Wolfgang Koenig (WIAS and TU Berlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Robert Patterson (WIAS).</p>Mon, 01 Nov 2021 17:57:25 +0000Wed, 03 Nov 2021 17:00:00 +0000Wed, 03 Nov 2021 18:00:00 +0000<a target='_content' href="https://sites.google.com/view/luisaandreis/home">Luisa Andreis</a>University of FlorenceProbability and Stochastic AnalysisPranav Chakravarthy, 2021/11/02, 16h 30m, Homotopy type of equivariant symplectomorphisms of rational ruled surfaces
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6368
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6368<p>In this talk, we present results on the homotopy type of the group of equivariant symplectomorphisms of $S^2 \times S^2$ and $CP^2$ blown up once, under the presence of Hamiltonian group actions of either $S^1$ or finite cyclic groups. For Hamiltonian circle actions, we prove that the centralizers are homotopy equivalent to either a torus or to the homotopy pushout of two tori depending on whether the circle action extends to a single toric action or to exactly two non-equivalent toric actions. We can show that the same holds for the centralizers of most finite cyclic groups in the Hamiltonian group. Our results rely on J-holomorphic techniques, on Delzant's classification of toric actions, on Karshon's classification of Hamiltonian circle actions on 4-manifolds, and on the Chen-Wilczynski smooth classification of $\mathbb Z_n$-actions on Hirzebruch surfaces.</p>Wed, 03 Nov 2021 16:46:10 +0000Tue, 02 Nov 2021 16:30:00 +0000Tue, 02 Nov 2021 17:30:00 +0000Pranav ChakravarthyHebrew University of JerusalemGeometria em LisboaLuiz Renato Fontes, 2021/10/27, 17h, Random walk in a birth-and-death dynamical environment
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6462
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6462<p>We consider a particle moving in continuous time as a Markov jump process; its discrete chain given by an ordinary random walk on Z^d (with finite second moments), and its jump rate at (x,t) given by a fixed function f of the state of a simple birth-and-death (BD) process at x on time t. BD processes at different sites are independent and identically distributed, and f is assumed non increasing and vanishing at infinity. We present an argument to obtain a CLT for the particle position when the environment is ergodic. In the absence of a viable uniform lower bound for the jump rate, we resort instead to stochastic domination, as well as to a subadditive argument to control the time spent by the particle to give n jumps (both ingredients rely on the monotonicity of f); and we also impose conditions on the initial (product) environmental initial distribution. We also discuss the asymptotic form of the environment seen by the particle. Joint work with Maicon Pinheiro and Pablo Gomes.</p>Tue, 26 Oct 2021 01:55:23 +0100Wed, 27 Oct 2021 17:00:00 +0100Wed, 27 Oct 2021 18:00:00 +0100<a target='_content' href="https://www.ime.usp.br/~lrenato/">Luiz Renato Fontes</a>Universidade de São PauloProbability and Stochastic AnalysisAndré Neves, 2021/10/26, 16h 30m, Minimal surfaces in hyperbolic manifolds
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6421
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6421<p>The study of geodesics in negatively curved manifolds is a rich subject which has been at the core of geometry and dynamical systems. Comparatively, much less is known about minimal surfaces on those spaces. I will survey some of the recent progress in that area.</p>Wed, 03 Nov 2021 10:01:07 +0000Tue, 26 Oct 2021 16:30:00 +0100Tue, 26 Oct 2021 17:30:00 +0100<a target='_content' href="https://math.uchicago.edu/~aneves/">André Neves</a>University of ChicagoGeometria em LisboaConstantino Tsallis, 2021/10/21, 17h, Statistical mechanics for complex systems
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6345
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6345<p>Together with Newtonian mechanics, Maxwell electromagnetism, Einstein relativity and quantum mechanics, Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics, with uncountable applications in science and technology. This theory applies formidably well to a plethora of physical systems. Still, it fails in the realm of complex systems, characterized by generically strong space-time entanglement of their elements. On the basis of a nonadditive entropy (defined by an index $q$, which recovers, for $q=1$, the celebrated Boltzmann-Gibbs-von Neumann-Shannon entropy), it is possible to generalize the BG theory. We will briefly review the foundations and applications in natural, artificial and social systems.</p><p>A Bibliography is available at <a href="http://tsallis.cat.cbpf.br/biblio.htm">http://tsallis.cat.cbpf.br/biblio.htm</a></p>Fri, 22 Oct 2021 07:39:55 +0100Thu, 21 Oct 2021 17:00:00 +0100Thu, 21 Oct 2021 18:00:00 +0100<a target='_content' href="https://www.santafe.edu/people/profile/constantino-tsallis">Constantino Tsallis</a>Group of Statistical Physics, CBPF and Santa Fe InstituteMathematics, Physics & Machine LearningEdgar Gasperín García, 2021/10/21, 14h 30m, Staticity and regularity for zero rest-mass fields near spatial infinity on flat spacetime
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6385
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6385<p>Linear zero-rest-mass fields generically develop logarithmic singularities at the critical sets where spatial infinity meets null infinity. Friedrich's representation of spatial infinity is ideally suited to study this phenomenon. These logarithmic singularities are an obstruction to the smoothness of the zero-rest-mass field at null infinity and, in particular, to peeling. In the case of the spin-2 field it has been shown that these logarithmic singularities can be precluded if the initial data for the field satisfies a certain regularity condition involving the vanishing, at spatial infinity, of a certain spinor (the linearised Cotton spinor) and its totally symmetrised derivatives. In this article we investigate the relation between this regularity condition and the staticity of the spin-2 field. It is shown that while any static spin-2 field satisfies the regularity condition, not every solution satisfying the regularity condition is static.</p>Mon, 18 Oct 2021 12:53:16 +0100Thu, 21 Oct 2021 14:30:00 +0100Thu, 21 Oct 2021 15:30:00 +0100Edgar Gasperín GarcíaInstituto Superior TécnicoSeminar room (2.8.3), Physics BuildingMathematical RelativitySimone Dovetta, 2021/10/21, 14h, Action versus energy ground states in nonlinear Schrödinger equations
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6343
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6343<p>The talk investigates the relations between normalized critical points of the nonlinear Schrödinger energy functional and critical points of the corresponding action functional on the associated Nehari manifold.</p><p>First, we show that the ground state levels are strongly related by the following duality result: the (negative) energy ground state level is the Legendre—Fenchel transform of the action ground state level. Furthermore, whenever an energy ground state exists at a certain frequency, then all action ground states with that frequency have the same mass and are energy ground states too. We see that the converse is in general false and that the action ground state level may fail to be convex. Next we analyze the differentiability of the ground state action level and we provide an explicit expression involving the mass of action ground states. Finally we show that similar results hold also for local minimizers, and we exhibit examples of domains where our results apply.</p><p>The matter of the talk refers to joint works with Enrico Serra and Paolo Tilli.</p><p> </p>Wed, 13 Oct 2021 08:46:50 +0100Thu, 21 Oct 2021 14:00:00 +0100Thu, 21 Oct 2021 15:00:00 +0100<a target='_content' href="https://www.researchgate.net/profile/Simone-Dovetta">Simone Dovetta</a>Università degli Studi di Roma "La Sapienza"Lisbon WADE — Webinar in Analysis and Differential EquationsInsuk Seo, 2021/10/20, 17h, Energy landscape and metastability of Ising/Potts model on lattice without external energy field
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6457
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6457<p>In this talk, we consider the Ising and Potts model defined on large lattices of dimension two or three at very low temperature regime. Under this regime, each monochromatic spin configuration is metastable in that exit from the energetic valley around that configuration is exponentially difficult. It is well-known that, under the presence of external magnetic fields, the metastable transition from a monochromatic configuration to another one is characterized solely by the appearance of a critical droplet. On the other hand, for the model without external field, the saddle structure is no longer characterized by a sharp droplet but has a huge and complex plateau structure. In this talk, we explain our recent research on the analysis of this energy landscape and its application to the demonstration of Eyring-Kramers formula for models on fixed two or three dimensional lattice (cf. <a href="https://arxiv.org/abs/2102.05565">https://arxiv.org/abs/2102.05565</a>) or models on growing two-dimensional lattice (cf. <a href="https://arxiv.org/abs/2109.13583">https://arxiv.org/abs/2109.13583</a>).<br />This talk is based on joint works with Seonwoo Kim.</p>Wed, 20 Oct 2021 00:24:06 +0100Wed, 20 Oct 2021 17:00:00 +0100Wed, 20 Oct 2021 18:00:00 +0100<a target='_content' href="http://www.math.snu.ac.kr/~insuk.seo/">Insuk Seo</a>Seoul National UniversityProbability and Stochastic AnalysisLuca Asselle, 2021/10/19, 16h 30m, A Morse complex for the Hamiltonian action in cotangent bundles
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6377
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6377<p>Critical points having infinite Morse index and co-index are invisible to homotopy theory, since attaching an infinite dimensional cell does not produce any change in the topology of sublevel sets. Therefore, no classical Morse theory can possibly exist for strongly indefinite functionals (i.e. functionals whose all critical points have infinite Morse index and co-index). In this talk, we will briefly explain how to instead construct a Morse complex for certain classes of strongly indefinite functionals on a Hilbert manifold by looking at the intersection between stable and unstable manifolds of critical points whose difference of (suitably defined) relative indices is one. As a concrete example, we will consider the case of the Hamiltonian action functional defined by a smooth time-periodic Hamiltonian $H: S^1 \times T^*Q \to \mathbb R$, where $T^*Q$ is the cotangent bundle of a closed manifold $Q$. As one expects, in this case the resulting Morse homology is isomorphic to the Floer homology of $T^*Q$, however the Morse complex approach has several advantages over Floer homology which will be discussed if time permits. This is joint work with Alberto Abbondandolo and Maciej Starostka.</p>Wed, 20 Oct 2021 14:32:23 +0100Tue, 19 Oct 2021 16:30:00 +0100Tue, 19 Oct 2021 17:30:00 +0100Luca AsselleRuhr University BochumGeometria em LisboaSergey Mozgovoy, 2021/10/18, 15h, Attractor invariants, brane tilings and crystals
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6395
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6395<p>Given a CY3-fold $X$, we define its refined DT invariants $\Omega_Z(d)$ by counting objects in the derived category $D^b(X)$, semistable with respect to a stability condition $Z$ and having Chern character $d$. Attractor invariants $\Omega_*(d)$ correspond to a special stability condition that depends on the Chern character $d$. They usually have a particularly simple form. If known, attractor invariants can be used to determine DT invariants for all other stability conditions using wall-crossing formulas or flow tree formulas. A wide class of non-compact toric CY3-folds is encoded by combinatorial data called brane tilings or by associated quivers with potentials. In this setting the derived category of $X$ can be substituted by the derived category of a quiver with potential and the counting problems can be reduced to representation theoretic problems and then solved under suitable conditions. I will survey known results about DT invariants and some new conjectures about attractor invariants in this setting. I will also explain how these formulas in the unrefined limit correspond to the counting of molten crystals associated with brane tilings.</p>Tue, 19 Oct 2021 21:37:45 +0100Mon, 18 Oct 2021 15:00:00 +0100Mon, 18 Oct 2021 16:00:00 +0100Sergey MozgovoyTrinity College DublinString TheoryClément Hongler, 2021/10/14, 17h, Neural Tangent Kernel
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6401
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6401<p>The Neural Tangent Kernel is a new way to understand the gradient descent in deep neural networks, connecting them with kernel methods. In this talk, I'll introduce this formalism and give a number of results on the Neural Tangent Kernel and explain how they give us insight into the dynamics of neural networks during training and into their generalization features.</p><p>Based off joint works with Arthur Jacot and Franck Gabriel.</p>Fri, 15 Oct 2021 07:44:09 +0100Thu, 14 Oct 2021 17:00:00 +0100Thu, 14 Oct 2021 18:00:00 +0100<a target='_content' href="http://hongler.org/">Clément Hongler</a>EPFLMathematics, Physics & Machine LearningJuraj Földes, 2021/10/14, 16h, Stochastic approach to boundary regularity of hypoelliptic PDEs
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6342
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6342<p>We will discuss the almost sure behavior of solutions of stochastic differential equations(SDEs) as time goes to zero. Our main general result establishes a functional law of the iterated logarithm (LIL) that applies in the setting of SDEs with degenerate noise satisfying the weak Hormander condition. We will introduce large deviations to provide some details of proofs. Furthermore, we apply the stochastic results to the problem of identifying regular points for hypoelliptic diffusions and obtain criteria for well posedness of degenerate equations.</p><p>This is a joint work with David Herzog and Marco Carfagnini</p>Wed, 06 Oct 2021 09:27:10 +0100Thu, 14 Oct 2021 16:00:00 +0100Thu, 14 Oct 2021 17:00:00 +0100<a target='_content' href="https://math.virginia.edu/people/jf8dc/">Juraj Földes</a>University of VirginiaLisbon WADE — Webinar in Analysis and Differential EquationsJean-Christophe Mourrat, 2021/10/13, 17h, Quantitative homogenization of interacting particle systems
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6442
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6442<p>I will discuss a class of interacting particle systems in continuous space. Such models are known to "homogenize", in the sense that the behavior of the cloud of particles is approximately described by a partial differential equation over large scales. In the talk, I will describe a first step towards making this result quantitative. The approach is inspired by recent developments in the homogenization of elliptic equations with random coefficients. Joint work with Arianna Giunti and Chenlin Gu.</p>Mon, 11 Oct 2021 23:03:19 +0100Wed, 13 Oct 2021 17:00:00 +0100Wed, 13 Oct 2021 18:00:00 +0100<a target='_content' href="https://cims.nyu.edu/~jcm777/">Jean-Christophe Mourrat</a>New-York UniversityProbability and Stochastic AnalysisTijana Radenković, 2021/10/13, 17h, Topological higher gauge theory — from 2BF to 3BF theory
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6424
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6424<p>We study a generalization of BF-theories in the context of higher gauge theory. We construct a topological state sum $Z$, based on the classical 3BF action for a general semistrict Lie 3-group and a triangulation of a 4-dimensional spacetime manifold. The 3BF action is constructed using a 2-crossed module which encodes a 3-group (as introduced by Picken and Faria Martins [<a href="#b1">1</a>]), while the state sum $Z$ is an example of Porter’s TQFT [<a href="#b2">2</a>] for $d=4$ and $n=3$. In order to verify that the constructed state sum is a topological invariant of the underlying manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum $Z$ remains the same. Our results are a generalization of the work done by Girelli, Pfeiffer, and Popescu [<a href="#b3">3</a>] for the case of state sum based on the classical 2BF action with the underlying 2-group structure.</p><ol><li><a id="b1" name="b1"> J. Faria Martins and R. Picken, Diff. Geom. Appl. 29, 179 (2011), </a><a href="https://arxiv.org/abs/0907.2566">arXiv:0907.2566</a><a id="b1" name="b1">.</a></li><li><a id="b2" name="b2">T. Porter, J. Lond. Math. Soc. (2)58, No. 3, 723 (1998), MR 1678163.</a></li><li><a id="b3" name="b3">F. Girelli, H. Pfeiffer and E. M. Popescu, Jour. Math. Phys. 49, 032503 (2008), </a><a href="https://arxiv.org/abs/0708.3051">arXiv:0708.3051</a><a id="b3" name="b3">.</a></li></ol>Sat, 16 Oct 2021 15:03:34 +0100Wed, 13 Oct 2021 17:00:00 +0100Wed, 13 Oct 2021 18:00:00 +0100<a target='_content' href="https://inspirehep.net/authors/1778027">Tijana Radenković</a>Institute of Physics, BelgradeTopological Quantum Field TheoryFelix Schlenk, 2021/10/12, 16h 30m, On the group of symplectomorphisms of starshaped domains
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6347
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6347<p><font color="black" face="Calibri,Helvetica,sans-serif" size="3">Take a simply connected compact domain $K$ in $\mathbb R^{2n}$ with smooth boundary. We study the topology of the group $\mathrm{Symp} (K)$ of those symplectomorphisms of $K$ that are defined on a neighbourhood of $K$. A main tool is a Serre fibration $\mathrm{Symp} (K) \to \mathrm{SCont} (\partial K)$ to the group of strict contactomorphisms of the boundary. The fiber is contractible if $K$ is 4-dimensional and starshaped, by Gromov's theorem. The topology (or at least the connectivity) of the group $\mathrm{SCont} (\partial K)$ can be understood in many examples. In case this group is connected, so is $\mathrm{Symp} (K)$. This has applications to the problem of understanding the topology of the space of symplectic embeddings of $K$ into any symplectic manifold. If $\mathrm{Symp} (K)$ is connected, then for embeddings that are not related by an ambient symplectomorphism there is not even an ambient symplectomorphism that maps one image to the other. </font></p><p><font color="black" face="Calibri,Helvetica,sans-serif" size="3">The talk is based on work with Joé Brendel and Grisha Mikhalkin.</font></p>Wed, 13 Oct 2021 12:52:45 +0100Tue, 12 Oct 2021 16:30:00 +0100Tue, 12 Oct 2021 17:30:00 +0100<a target='_content' href="http://members.unine.ch/felix.schlenk/index.html">Felix Schlenk</a>Université de NeuchâtelGeometria em LisboaMihalis Dafermos, 2021/10/07, 14h 30m, The black hole stability problem in general relativity
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6423
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6423<p>I will review the current status of the black hole stability problem in general relativity and discuss joint work Holzegel, Rodnianski and Taylor.</p>Tue, 05 Oct 2021 11:42:34 +0100Thu, 07 Oct 2021 14:30:00 +0100Thu, 07 Oct 2021 15:30:00 +0100Mihalis DafermosPrinceton and Cambridge UniversitiesMathematical RelativityMonica Clapp, 2021/10/07, 14h, Optimal partitions for the Yamabe equation
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6341
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6341<p>The Yamabe equation on a Riemannian manifold $(M,g)$ is relevant to the question of finding a constant scalar curvature metric on $M$ that is conformally equivalent to the given one.</p><p>An optimal $\ell$-partition for the Yamabe equation is a cover of $M$ by $\ell$ pairwise disjoint open subsets such that the Yamabe equation with Dirichlet boundary condition has a least energy solution on each one of these sets, and the sum of the energies of these solutions is minimal.</p><p>We will present some recent results obtained in collaboration with Angela Pistoia (La Sapienza Università di Roma) and Hugo Tavares (Universidade de Lisboa) that establish the existence and qualitative properties of such partitions.</p><p>If time allows, we will also present some results on symmetric optimal partitions obtained in collaboration with Angela Pistoia, and with Alberto Saldaña (UNAM) and Andrzej Szulkin (Stockholm University).</p><p> </p>Wed, 22 Sep 2021 21:45:29 +0100Thu, 07 Oct 2021 14:00:00 +0100Thu, 07 Oct 2021 15:00:00 +0100<a target='_content' href="https://www.matem.unam.mx/fsd/mclapp">Monica Clapp</a>Universidad Nacional Autónoma de MéxicoLisbon WADE — Webinar in Analysis and Differential EquationsMarielle Simon, 2021/10/06, 17h, Hydrodynamic limit for a facilitated exclusion process
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6432
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6432<p>In this talk I will present a one-dimensional exclusion process subject to strong kinetic constraints, which belongs to the class of cooperative kinetically constrained lattice gases. More precisely, its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. We will see that the macroscopic behavior of this microscopic dynamics, under periodic boundary conditions and diffusive time scaling, is ruled by a non-linear PDE belonging to free boundary problems (or Stefan problems). One of the ingredients is to show that the system typically reaches an ergodic component in subdiffusive time. Several questions are still open, I will also give some research directions.</p><p>Based on joint works with O. Blondel, C. Erignoux and M. Sasada</p>Wed, 06 Oct 2021 00:59:28 +0100Wed, 06 Oct 2021 17:00:00 +0100Wed, 06 Oct 2021 18:00:00 +0100<a target='_content' href="http://chercheurs.lille.inria.fr/masimon/">Marielle Simon</a>Inria, University of LilleProbability and Stochastic AnalysisBen Heidenreich, 2021/10/04, 16h 15m, The Weak Gravity Conjecture and BPS Particles
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6389
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6389<p>Motivated by the Weak Gravity Conjecture, we uncover an intricate interplay between black holes, BPS particle counting, and Calabi-Yau geometry in five dimensions. In particular, we point out that extremal BPS black holes exist only in certain directions in the charge lattice, and we argue that these directions fill out a cone that is dual to the cone of effective divisors of the Calabi-Yau threefold. The tower and sublattice versions of the Weak Gravity Conjecture require an infinite tower of BPS particles in these directions, and therefore imply purely geometric conjectures requiring the existence of infinite towers of holomorphic curves in every direction within the dual of the cone of effective divisors. We verify these geometric conjectures in a number of examples by computing Gopakumar-Vafa invariants.</p>Thu, 14 Oct 2021 11:32:09 +0100Mon, 04 Oct 2021 16:15:00 +0100Mon, 04 Oct 2021 17:15:00 +0100Ben HeidenreichUniversity of Massachusetts, AmherstString TheoryVolkan Cevher, 2021/09/30, 17h, Optimization Challenges in Adversarial Machine Learning
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6350
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6350<p>Thanks to neural networks (NNs), faster computation, and massive datasets, machine learning (ML) is under increasing pressure to provide automated solutions to even harder real-world tasks beyond human performance with ever faster response times due to potentially huge technological and societal benefits. Unsurprisingly, the NN learning formulations present a fundamental challenge to the back-end learning algorithms despite their scalability, in particular due to the existence of traps in the non-convex optimization landscape, such as saddle points, that can prevent algorithms from obtaining “good” solutions.</p><p>In this talk, we describe our recent research that has demonstrated that the non-convex optimization dogma is false by showing that scalable stochastic optimization algorithms can avoid traps and rapidly obtain locally optimal solutions. Coupled with the progress in representation learning, such as over-parameterized neural networks, such local solutions can be globally optimal.</p><p>Unfortunately, this talk will also demonstrate that the central min-max optimization problems in ML, such as generative adversarial networks (GANs), robust reinforcement learning (RL), and distributionally robust ML, contain spurious attractors that do not include any stationary points of the original learning formulation. Indeed, we will describe how algorithms are subject to a grander challenge, including unavoidable convergence failures, which could explain the stagnation in their progress despite the impressive earlier demonstrations.</p>Fri, 01 Oct 2021 08:00:36 +0100Thu, 30 Sep 2021 17:00:00 +0100Thu, 30 Sep 2021 18:00:00 +0100<a target='_content' href="https://people.epfl.ch/volkan.cevher?lang=en">Volkan Cevher</a>Laboratory for Information and Inference Systems – LIONS, EPFLMathematics, Physics & Machine LearningRafael D. Benguria, 2021/09/30, 14h, Gagliardo-Nirenberg-Sobolev Inequalities and their counterparts on bounded domains
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6340
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6340<p>The Gagliardo-Nirenberg-Sobolev (GNS) inequalities have played a major role in applied mathematics and mathematical physics in more than half a century. In this talk I will present several new results concerning the counterparts of the GNS inequalities on bounded domains. Of course concentration of the minimizers of the GNS inequalities is a main tool in the proof of existence of minimizers on bounded domains. Naturally concentration occurs in the interior for Dirichlet boundary conditions and on the boundary for Neumann boundary conditions. In the Neumann case this leaves a set of interesting open problems depending on the characteristic of the boundary. This is in part joint work with Cristobal Vallejos (Penn State U.) and Hanne Van Den Bosch (U. de Chile) and in part with Soledad Benguria (U. Wisconsin, Madison).</p>Fri, 01 Oct 2021 07:24:53 +0100Thu, 30 Sep 2021 14:00:00 +0100Thu, 30 Sep 2021 15:00:00 +0100<a target='_content' href="http://www.fis.puc.cl/~rbenguri/">Rafael D. Benguria</a>Universidad Católica de ChileLisbon WADE — Webinar in Analysis and Differential EquationsStanislav Volkov, 2021/09/29, 17h, About discrete Bak-Sneppen model
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6422
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6422<p> </p><p>The discrete version of the famous Bak-Sneppen model (https://en.wikipedia.org/wiki/Bak-Sneppen_model) is a Markov chain on the space of {0,1} sequences of length n with periodic boundary conditions, which runs as follows. Fix some 00.54. This result is indeed correct, however, its proof is not. I shall present the rigorous proof of the Barbay and Kenyon's result, as well as some better bounds for the critical p.</p><p> </p><p> </p>Tue, 28 Sep 2021 15:54:39 +0100Wed, 29 Sep 2021 17:00:00 +0100Wed, 29 Sep 2021 18:00:00 +0100<a target='_content' href="https://www.maths.lth.se/matstat/staff/s.volkov/">Stanislav Volkov</a>Lund UniversityProbability and Stochastic AnalysisBarbara Fantechi, 2021/09/28, 16h 30m, Smoothability of non normal stable Gorenstein Godeaux surfaces
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6370
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6370<p>This is joint work with Marco Franciosi and Rita Pardini.</p><p>Godeaux surfaces, with $K^2=1$ and $p_g=q=0$, are the (complex projective) surfaces of general type with the smallest possible invariants. A complete classification, i.e. an understanding of their moduli space, has been an open problem for many decades.</p><p>The KSBA (after Kollár, Sheperd-Barron and Alexeev) compactification of the moduli includes so called stable surfaces. Franciosi, Pardini and Rollenske classified all such surfaces in the boundary which are Gorenstein (i.e., not too singular).</p><p>We prove that most of these surfaces corresponds to a point in the moduli which is nonsingular of the expected dimension 8. We expect that the methods used (which include classical and recent infinitesimal deformation theory, as well as algebraic stacks and the cotangent complex) can be applied to all cases, and to more general moduli as well.</p><p>The talk is aimed at a non specialist mathematical audience, and will focus on the less technical aspects of the paper.</p>Fri, 01 Oct 2021 09:02:45 +0100Tue, 28 Sep 2021 16:30:00 +0100Tue, 28 Sep 2021 17:30:00 +0100<a target='_content' href="http://barbarafantechi.com">Barbara Fantechi</a>SISSAGeometria em LisboaJoão Faria Martins, 2021/09/24, 17h, Quinn Finite Total Homotopy TQFT as a once-extended TQFT
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6407
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6407<p>Quinn Finite Total Homotopy TQFT is a TQFT that works in any dimension and that depends on the choice of a homotopy finite space $B$ (e.g. $B$ can be the classifying space of a finite group or of a finite 2-group). I will report on ongoing joint work with Tim Porter on once-extended versions of Quinn Finite total homotopy TQFT, and I will show how to compute them for the case when $B$ is the classifying space of a finite strict omega-groupoid (represented by a crossed complex).</p><p> </p>Tue, 28 Sep 2021 10:15:42 +0100Fri, 24 Sep 2021 17:00:00 +0100Fri, 24 Sep 2021 18:00:00 +0100<a target='_content' href="http://www1.maths.leeds.ac.uk/~pmtjfa/index.html">João Faria Martins</a>University of Leeds, UKTopological Quantum Field TheoryLeong Chuan Kwek, 2021/09/23, 10h, Machine Learning and Quantum Technology
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6346
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6346<p>The rise of machine learning in recent times has remarkably transformed science and society. The goal of machine learning is to get computers to act without being explicitly programmed. Machine learning with deep reinforcement learning (RL) was recently recognized as a powerful tool to engineer dynamics in quantum system. Also, recently there has been some interest to exploit and leverage the limited available quantum resources for performing classically challenging tasks with noisy intermediate-scale quantum (NISQ) computers. Here, we discuss some of our recent work on the applications of machine learning to quantum systems.</p>Thu, 23 Sep 2021 22:42:04 +0100Thu, 23 Sep 2021 10:00:00 +0100Thu, 23 Sep 2021 11:00:00 +0100<a target='_content' href="https://nie.edu.sg/profile/kwek-leong-chuan">Leong Chuan Kwek</a>Nanyang Technological University, SingaporeMathematics, Physics & Machine LearningReza Gheissari, 2021/09/22, 17h, Cutoff for the Glauber dynamics of the discrete Gaussian free field.
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6415
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6415<p>The Gaussian free field (GFF) is a canonical model of random surfaces in probability theory, generalizing the Brownian bridge to higher dimensions. It arises naturally as the stationary solution to the stochastic heat equation with additive noise (SHE), and together the SHE and GFF are expected to be the universal scaling limit of the dynamics and equilibrium of many random surface models arising in lattice statistical physics. We study the mixing time (time to converge to stationarity, when started out of equilibrium) for the central pre-limiting object, the discrete Gaussian free field (DGFF) evolving under the Glauber dynamics. In joint work with S. Ganguly, we establish that for every dimension d larger than one , on a box of side-length n in Zd, the Glauber dynamics for the DGFF exhibits cutoff at time (d/\pi^2) n^2 \log n with an O(n^2) window. Our proof relies on an "exact" representation of the DGFF dynamics in terms of random walk trajectories with space-dependent jump times, which we expect to be of independent interest.</p>Mon, 27 Sep 2021 18:40:14 +0100Wed, 22 Sep 2021 17:00:00 +0100Wed, 22 Sep 2021 18:00:00 +0100<a target='_content' href="https://www.stat.berkeley.edu/~gheissari/">Reza Gheissari</a>UC BerkeleyProbability and Stochastic Analysis