CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Stéphanie Cupit-Foutou, 2023/02/07, 16h, The Gromov width of compact toric manifolds
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6877
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6877Mon, 28 Nov 2022 13:32:54 +0100Tue, 07 Feb 2023 17:00:00 +0100Tue, 07 Feb 2023 18:00:00 +0100<a target='_content' href="https://www.ruhr-uni-bochum.de/ffm/Lehrstuehle/transformationsgruppen/cupit.html">Stéphanie Cupit-Foutou</a>Ruhr-Universität BochumGeometria em LisboaYang-Hui He, 2023/02/02, 17h, Universes as Bigdata: Physics, Geometry and Machine-Learning
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6868
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6868<p>The search for the Theory of Everything has led to superstring theory, which then led physics, first to algebraic/differential geometry/topology, and then to computational geometry, and now to data science. With a concrete playground of the geometric landscape, accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades, we show how the latest techniques in machine-learning can help explore problems of interest to theoretical physics and to pure mathematics. At the core of our programme is the question: how can AI help us with mathematics?</p>Tue, 29 Nov 2022 12:57:36 +0100Thu, 02 Feb 2023 18:00:00 +0100Thu, 02 Feb 2023 19:00:00 +0100<a target='_content' href="https://www.city.ac.uk/about/people/academics/yang-hui-he">Yang-Hui He</a>City, University of LondonAbreu Faro AmphitheatreMathematics, Physics & Machine LearningYang-Hui He, 2023/02/01, 14h, The Calabi-Yau landscape: a data science approach
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6874
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6874Thu, 24 Nov 2022 08:04:15 +0100Wed, 01 Feb 2023 15:00:00 +0100Wed, 01 Feb 2023 18:00:00 +0100<a target='_content' href="https://www.city.ac.uk/about/people/academics/yang-hui-he">Yang-Hui He</a>City, University of LondonRoom P3.10, Mathematics BuildingMathematics, Physics & Machine LearningYang-Hui He, 2023/02/01, 09h 30m, The Calabi-Yau landscape: a data science approach
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6873
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6873Wed, 23 Nov 2022 21:09:23 +0100Wed, 01 Feb 2023 10:30:00 +0100Wed, 01 Feb 2023 13:30:00 +0100<a target='_content' href="https://www.city.ac.uk/about/people/academics/yang-hui-he">Yang-Hui He</a>City, University of LondonRoom P3.10, Mathematics BuildingMathematics, Physics & Machine LearningYang-Hui He, 2023/01/31, 14h, The Calabi-Yau landscape: a data science approach
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6872
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6872Wed, 23 Nov 2022 20:52:57 +0100Tue, 31 Jan 2023 15:00:00 +0100Tue, 31 Jan 2023 18:00:00 +0100<a target='_content' href="https://www.city.ac.uk/about/people/academics/yang-hui-he">Yang-Hui He</a>City, University of LondonRoom P3.10, Mathematics BuildingMathematics, Physics & Machine LearningYang-Hui He, 2023/01/31, 09h 30m, The Calabi-Yau landscape: a data science approach
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6871
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6871Wed, 23 Nov 2022 19:46:34 +0100Tue, 31 Jan 2023 10:30:00 +0100Tue, 31 Jan 2023 13:30:00 +0100<a target='_content' href="https://www.city.ac.uk/about/people/academics/yang-hui-he">Yang-Hui He</a>City, University of LondonRoom P3.10, Mathematics BuildingMathematics, Physics & Machine LearningYang-Hui He, 2023/01/30, 14h, The Calabi-Yau landscape: a data science approach
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6870
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6870<p>Motivated by physics, especially string theory and quantum field theory, we take a promenade in the landscape of Calabi-Yau geometries. This subject of Calabi-Yau varieties has been a fruitful cross-fertilization between mathematics, physics and computer science. We will take a computational algebro-geometric and data science driven perspective and focus on the explicit constructions and the various databases which have emerged over the decades. Finally, we discuss some recent developments in using neural networks and machine-learning to study such geometries.</p><p>This mini-course is aimed at beginning Ph.D. students interested in the physics and mathematics of algebraic geometry. No coding background is needed. The lectures will involve some live coding demonstrations however.</p>Thu, 24 Nov 2022 08:02:54 +0100Mon, 30 Jan 2023 15:00:00 +0100Mon, 30 Jan 2023 18:00:00 +0100<a target='_content' href="https://www.city.ac.uk/about/people/academics/yang-hui-he">Yang-Hui He</a>City, University of LondonRoom P3.10, Mathematics BuildingMathematics, Physics & Machine LearningLuis Diogo, 2022/12/20, 16h, Lagrangian tori in the cotangent bundle of the 2-sphere
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6818
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6818<p>Given a symplectic manifold, one can ask what Lagrangian submanifolds it contains. I will discuss this question for one of the simplest examples of a non-trivial symplectic manifold, namely the cotangent bundle of the 2-sphere. Specifically, I will present a result about monotone Lagrangian tori as objects in the Fukaya category. If time permits, I will also discuss the problem of classifying Lagrangian tori up to Hamiltonian isotopy. </p>Tue, 06 Dec 2022 17:10:38 +0100Tue, 20 Dec 2022 17:00:00 +0100Tue, 20 Dec 2022 18:00:00 +0100<a target='_content' href="https://sites.google.com/view/ldiogomath/home">Luis Diogo</a>Uppsala UniversityRoom P3.10, Mathematics BuildingGeometria em LisboaBruno Loureiro, 2022/12/15, 17h, Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6836
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6836<p>Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in badly-generalizing local minima. Here we investigate the cross-over between these two regimes in the high-dimensional setting, and in particular investigate the connection between the so-called mean-field/hydrodynamic regime and the seminal approach of Saad & Solla. Focusing on the case of Gaussian data, we study the interplay between the learning rate, the time scale, and the number of hidden units in the high-dimensional dynamics of stochastic gradient descent (SGD). Our work builds on a deterministic description of SGD in high-dimensions from statistical physics, which we extend and for which we provide rigorous convergence rates.</p><p>Based on: <a href="https://arxiv.org/abs/2202.00293">https://arxiv.org/abs/2202.00293</a></p><p> </p>Wed, 05 Oct 2022 15:54:34 +0200Thu, 15 Dec 2022 18:00:00 +0100Thu, 15 Dec 2022 19:00:00 +0100<a target='_content' href="https://brloureiro.github.io/">Bruno Loureiro</a>École Polytechnique Fédérale de Lausanne (EPFL)Mathematics, Physics & Machine LearningNicki Magill, 2022/12/13, 16h, Symplectic embeddings of Hirzebruch surfaces
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6831
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6831<p>The four dimensional ellipsoid embedding function of a toric symplectic manifold M measures when a symplectic ellipsoid embeds into M. It generalizes the Gromov width and ball packing numbers. In 2012, McDuff and Schlenk computed this function for a ball. The function has a delicate structure known as an infinite staircase. This implies infinitely many obstructions are needed to know when an embedding can exist. Based on work with McDuff, Pires, and Weiler, we will discuss the classification of which Hirzebruch surfaces have infinite staircases. We will focus on the part of the argument where symplectic embeddings are constructed via almost toric fibrations.</p>Wed, 30 Nov 2022 13:25:57 +0100Tue, 13 Dec 2022 17:00:00 +0100Tue, 13 Dec 2022 18:00:00 +0100<a target='_content' href="https://sites.google.com/cornell.edu/nicki-magill/">Nicki Magill</a>Cornell UniversityGeometria em LisboaZoran Petric, 2022/12/09, 12h, A diagrammatic presentation of the category 3Cob
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6883
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6883<p>The category 3Cob has closed oriented surfaces as objects and 3-dimensional cobordisms, i.e. 3-dimensional compact oriented manifolds (possibly with boundary) with canonical orientation preserving (reversing) identification of the incoming (outgoing) boundary. The composition is defined in terms of gluing. We present this category using a diagrammatic language similar to the language of standard surgery presentation of closed, orientable, connected 3-manifolds, save that besides framed links we use wedges of circles in our diagrams.</p><p>We will explain how to interpret such a diagram as an arrow of 3Cob and give an outline of the composition calculus for diagrams. This is a joint work with Jovana Nikolic and Mladen Zekic.</p>Tue, 06 Dec 2022 09:33:47 +0100Fri, 09 Dec 2022 13:00:00 +0100Fri, 09 Dec 2022 14:00:00 +0100Zoran PetricMathematical Institute SANU, Belgrade, SerbiaRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryKonstantin Eder, 2022/12/07, 17h, Super Cartan geometry and (loop) quantum supergravity
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6885
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6885<p>In this talk, a mathematically rigorous approach toward geometric supergravity will be discussed which, in the physical literature, is usually known as the Castellani-D'Auria-Fré approach. To this end, using tools from supergeometry, the notion of a super Cartan geometry will be introduced. Interestingly, in order to consistently incorporate the anticommutative nature of fermionic fields, the ordinary category of supermanifolds needs to be generalized in a physically consistent way leading to the notion of so-called enriched supermanifolds. We then apply this formalism to discuss a geometric formulation of (generalized) pure Anti-de Sitter supergravity with N=1,2 supersymmetry in D=4 modified by an additional Holst term. In this context, we will also talk about so-called picture changing operators (PCO) and how they can be implemented in a mathematically rigorous way. Finally, an outlook will be given for applications of this formalism to (loop) quantum supergravity and the description of quantum supersymmetric black holes.</p><p> </p>Thu, 01 Dec 2022 23:08:44 +0100Wed, 07 Dec 2022 18:00:00 +0100Wed, 07 Dec 2022 19:00:00 +0100Konstantin EderUniversity of Erlangen–NürnbergRoom P3.10, Mathematics BuildingTopological Quantum Field TheorySimone Floreani, 2022/12/07, 16h, Sub-diffusive behaviors emerging from exclusion processes
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6875
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6875<p>This talk focuses on generalizations of the exclusion process whose hydrodynamic limits are sub-diffusive equations. After recalling some known results in dimension 1, I will present in detail the partial exclusion process in random environment. This is a system of random walks where the random environment is obtained by assigning random maximal occupancies to each site of the Euclidean lattice. I will show that, when assuming that the maximal occupancies are heavy tailed and i.i.d., the hydrodynamic limit of the particle system (in any dimension greater than 1) is the fractional-kinetics equation.</p><p>This talk is based on partly ongoing projects in collaboration with A. Chiarini (Padova), F. Redig (TU Delft) and F. Sau (ISTA).</p>Mon, 05 Dec 2022 16:50:13 +0100Wed, 07 Dec 2022 17:00:00 +0100Wed, 07 Dec 2022 18:00:00 +0100<a target='_content' href="https://www.maths.ox.ac.uk/people/simone.floreani">Simone Floreani</a>University of OxfordProbability and Stochastic AnalysisSofia Tirabassi, 2022/12/06, 16h, Characterization of quasi-abelian surfaces
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6848
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6848<p>We give an effective characterization of quasi-abelian surfaces extending to the quasi-projective setting results of Enriques and Chen-Hacon. This is a joint work with M. Mendes Lopes and R. Pardini.</p>Tue, 15 Nov 2022 12:19:18 +0100Tue, 06 Dec 2022 17:00:00 +0100Tue, 06 Dec 2022 18:00:00 +0100<a target='_content' href="https://staff.math.su.se/tirabassi/">Sofia Tirabassi</a>Stockholm UniversityGeometria em LisboaElena Giorgi, 2022/12/01, 14h 30m, Physical-space estimates on black hole perturbations
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6881
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6881<p>Most works on the analysis of the wave equation on Kerr black holes rely on a combination of the vector field method and Fourier decomposition, with the notable exception of a generalized vector field method introduced by Andersson-Blue. Their method allows for commutation with second order differential operators entirely in physical-space by supplementing the Killing vector fields with the Carter operator of Kerr to obtain a local energy decay identity at the level of three derivatives of the solution for sufficiently small |a|. I this talk I will describe the main ideas of Andersson-Blue’s method and explain its advantages in two recent applications where physical space-estimates have been crucial: the linear stability of Kerr-Newman black hole to coupled gravitational-electromagnetic perturbations and our proof of the non-linear stability of the slowly rotating Kerr family with Klainerman-Szeftel.</p>Tue, 29 Nov 2022 07:12:37 +0100Thu, 01 Dec 2022 15:30:00 +0100Thu, 01 Dec 2022 16:30:00 +0100Elena GiorgiColumbia UniversityMathematical RelativityKonrad Waldorf, 2022/11/30, 17h, A representation of the string 2-group
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6849
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6849<p>The string 2-group is supposed to play the role of the spin group, but in string theory instead of quantum mechanics. Several aspects of this analogy are by now well understood. In this talk I will talk about joint work with Matthias Ludewig and Peter Kristel on a further aspect, namely the representation theory of the string 2-group. This was an open problem for a long time. Our solution combines higher-categorical topology with operator algebras, and allows a neat definition of Stolz-Teichner's "stringor bundle" as an associated 2-vector bundle.</p>Tue, 06 Dec 2022 00:29:44 +0100Wed, 30 Nov 2022 18:00:00 +0100Wed, 30 Nov 2022 19:00:00 +0100<a target='_content' href="http://math.konradwaldorf.de/www/?ref=https%3A%2F%2Fwww.google.com%2F">Konrad Waldorf</a>University of GreifswaldRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryLeandro Pimentel, 2022/11/30, 16h, Integration by Parts and the KPZ Two-Point Function
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6882
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6882<p>In this talk we will consider two models within Kardar-Parisi-Zhang (KPZ) universality class, and apply the integration by parts formula from Malliavin calculus to establish a key relation between the two-point correlation function, the polymer end-point distribution and the second derivative of the variance of the associated height function. Besides that, we will further develop an adaptation of Malliavin-Stein method that quantifies asymptotic independence with respect to the initial data. </p><p> </p><p> </p>Tue, 29 Nov 2022 10:39:51 +0100Wed, 30 Nov 2022 17:00:00 +0100Wed, 30 Nov 2022 18:00:00 +0100<a target='_content' href="http://www.im.ufrj.br/index.php/pt/pessoal/docentes/docentes/162-leandro-pinto-rodrigues-pimentel">Leandro Pimentel</a>UFRJProbability and Stochastic AnalysisJoão Pereira, 2022/11/30, 11h, Method of Moments: From Sample Complexity to Efficient Implicit Computations
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars/?action=show&id=6867
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars/?action=show&id=6867<p>The focus of this talk is the multivariate method of moments for parameter estimation. First from a theoretical standpoint, we show that in problems where the noise is high, the number of observations necessary to estimate parameters is dictated by the moments of the distribution. Second from a computational standpoint, we address the curse of dimensionality: the number of entries of higher-order moments of multivariate random variables scale exponentially with the order of the moments. For Gaussian Mixture Models (GMMs), we develop numerical methods forimplicit computations; with the empirical moment tensors. This reduces the computational and storage costs, and opens the door to the competitiveness of the method of moments as compared to expectation maximization methods. Time permitting, we connect these results to symmetric $C^P$ tensor decomposition and sketch a recent algorithm which is faster than the state-of-the-art and comes with guarantees.</p>Sun, 20 Nov 2022 15:59:57 +0100Wed, 30 Nov 2022 12:00:00 +0100Wed, 30 Nov 2022 13:00:00 +0100João PereiraInstituto de Matemática Pura e AplicadaRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsSobhan Seyfaddini, 2022/11/29, 16h, On the algebraic structure of groups of area-preserving homeomorphisms
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6794
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6794<p>In an influential article from the 1970s, Albert Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the $n$-ball is simple for $n\geq 3$, asked if the same statement holds in dimension $2$. In a joint work with Cristofaro-Gardiner and Humilière, we proved that the group of compactly supported area-preserving homeomorphisms of the $2$-disc is not simple. This answers Fathi's question and settles what is known as "the simplicity conjecture" in the affirmative.</p><p>In fact, Fathi posed a more general question about all compact surfaces: is the group of "Hamiltonian homeomorphisms" (which I will define) simple? In my talk, I will review recent joint work with Cristofaro-Gardiner, Humilière, Mak and Smith answering this more general question of Fathi. The talk will be for the most part elementary and will only briefly touch on Floer homology which is a crucial ingredient of the solution.</p>Wed, 30 Nov 2022 08:57:23 +0100Tue, 29 Nov 2022 17:00:00 +0100Tue, 29 Nov 2022 18:00:00 +0100<a target='_content' href="https://webusers.imj-prg.fr/~sobhan.seyfaddini/Recherche.html">Sobhan Seyfaddini</a>Institut de Mathématiques de Jussieu - Paris Rive GaucheGeometria em LisboaMarkus Reichstein, 2022/11/24, 17h, Integrating Machine Learning with System Modelling and Observations for a better understanding of the Earth System
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6819
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6819<p>The Earth is a complex dynamic networked system. Machine learning, i.e. derivation of computational models from data, has already made important contributions to predict and understand components of the Earth system, specifically in climate, remote sensing and environmental sciences. For instance, classifications of land cover types, prediction of land-atmosphere and ocean-atmosphere exchange, or detection of extreme events have greatly benefited from these approaches. Such data-driven information has already changed how Earth system models are evaluated and further developed. However, many studies have not yet sufficiently addressed and exploited dynamic aspects of systems, such as memory effects for prediction and effects of spatial context, e.g. for classification and change detection. In particular new developments in deep learning offer great potential to overcome these limitations. Yet, a key challenge and opportunity is to integrate (physical-biological) system modeling approaches with machine learning into hybrid modeling approaches, which combines physical consistency and machine learning versatility. A couple of examples are given with focus on the terrestrial biosphere, where the combination of system-based and machine-learning-based modelling helps our understanding of aspects of the Earth system.</p>Fri, 25 Nov 2022 22:31:32 +0100Thu, 24 Nov 2022 18:00:00 +0100Thu, 24 Nov 2022 19:00:00 +0100<a target='_content' href="https://futureearth.org/contacts/markus-reichstein/">Markus Reichstein</a>MPI for BiogeochemistryMathematics, Physics & Machine LearningThomas Mountford, 2022/11/23, 16h, Greedy cleaning of Poisson dust on French railway
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6860
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6860<p>We consider a system of N half lines issuing from the origin, on which there is a Poisson process of dust particles initially. We have N^ \alpha workers who clean dust particles according to a greedy algorithm; they move to the closest dust particle and remove it and then wait an exponential time before chosing a new particle. We consider for which values of alpha one can have half lines where two or more workers go to infinity. The talk uses only elementary probability arguments and well known properties of Poisson processes. It should be accessible to all.<br />Joint with Sergey Foss and Takis Konstantopoulous</p>Tue, 22 Nov 2022 13:17:35 +0100Wed, 23 Nov 2022 17:00:00 +0100Wed, 23 Nov 2022 18:00:00 +0100Thomas MountfordÉcole Polytechnique Fédérale de LausanneProbability and Stochastic AnalysisJoão Pimentel Nunes, 2022/11/22, 16h, The geometric interpretation of the Peter-Weyl theorem
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6805
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6805<p>Let $K$ be a compact Lie group. I will review the construction of Mabuchi geodesic families of $K\times K$–invariant Kähler structures on $T^\ast K$, via Hamiltonian flows in imaginary time generated by a strictly convex invariant function on $\operatorname{Lie}K$, and the corresponding geometric quantization. At infinite geodesic time, one obtains a rich mixed polarization of $T^\ast K$, the Kirwin-Wu polarization, which is then continuously connected to the vertical polarization of $T^\ast K$. The geometric quantization of $T^\ast K$ along this family of polarizations is described by a generalized coherent state transform that, as geodesic time goes to infinity, describes the convergence of holomorphic sections to distributional sections supported on Bohr-Sommerfeld cycles. These are in correspondence with coadjoint orbits $O_{\lambda+\rho}$. One then obtains a concrete (quantum) geometric interpretation of the Peter-Weyl theorem, where terms in the non-abelian Fourier series are directly related to geometric cycles in $T^\ast K$. The role of a singular torus action in this construction will also be emphasized. This is joint work with T. Baier, J. Hilgert, O. Kaya and J. Mourão.</p>Wed, 23 Nov 2022 10:09:15 +0100Tue, 22 Nov 2022 17:00:00 +0100Tue, 22 Nov 2022 18:00:00 +0100<a target='_content' href="https://www.math.tecnico.ulisboa.pt/~jpnunes/">João Pimentel Nunes</a>Instituto Superior Técnico, Universidade de LisboaRoom P3.10, Mathematics BuildingGeometria em LisboaTom Goldstein, 2022/11/17, 17h, Building (and breaking) neural networks that think fast and slow
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6839
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6839<p>Most neural networks are built to solve simple pattern matching tasks, a process that is often known as “fast” thinking. In this talk, I’ll use adversarial methods to explore the robustness of neural networks. I’ll also discuss whether vulnerabilities of AI systems that have been observed in academic labs can pose real security threats to industrial systems. Then, I’ll present methods for constructing neural networks that exhibit “slow” thinking abilities akin to human logical reasoning. Rather than learning simple pattern matching rules, these networks have the ability to synthesize algorithmic reasoning processes and solve difficult discrete search and planning problems that cannot be solved by conventional AI systems. Interestingly, these reasoning systems naturally exhibit error correction and robustness properties that make them more difficult to break than their fast thinking counterparts.</p>Fri, 18 Nov 2022 00:07:26 +0100Thu, 17 Nov 2022 18:00:00 +0100Thu, 17 Nov 2022 19:00:00 +0100<a target='_content' href="https://www.cs.umd.edu/~tomg/">Tom Goldstein</a>University of MarylandMathematics, Physics & Machine LearningGiuseppe Negro, 2022/11/17, 13h 30m, Explicit solutions to the cubic wave equation
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6853
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6853<p>We construct a two-parameter family of solutions to the focusing cubic wave equation in $\mathbb{R}^{1+3}$. Depending on the values of the parameters, these solutions either scatter to linear ones, blow-up in finite time, or exhibit a new type of unstable behaviour that acts as a threshold between the other two. We further prove that the blow-up behaviour is stable and we characterize the threshold behaviour precisely, both pointwise and in Sobolev sense.</p><p>Joint work with Thomas Duyckaerts (Sorbonne Paris Nord).</p>Sat, 19 Nov 2022 13:32:44 +0100Thu, 17 Nov 2022 14:30:00 +0100Thu, 17 Nov 2022 15:30:00 +0100<a target='_content' href="https://sites.google.com/view/gnegro/home">Giuseppe Negro</a>CAMGSD, Instituto Superior TécnicoRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsFiona Torzewska, 2022/11/16, 17h, Topological quantum field theories and homotopy cobordisms
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6861
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6861<p>I will begin by explaining the construction of a category $\operatorname{CofCos}$, whose objects are topological spaces and whose morphisms are cofibrant cospans. Here the identity cospan is chosen to be of the form $X\to X\times [0,1] \rightarrow X$, in contrast with the usual identity in the bicategory $\operatorname{Cosp}(V)$ of cospans over a category $V$. The category $\operatorname{CofCos}$ has a subcategory $\operatorname{HomCob}$ in which all spaces are homotopically $1$-finitely generated. There exist functors into $\operatorname{HomCob}$ from a number of categorical constructions which are potentially of use for modelling particle trajectories in topological phases of matter: embedded cobordism categories and motion groupoids for example. Thus, functors from $\operatorname{HomCob}$ into $\operatorname{Vect}$ give representations of the aforementioned categories.</p><p>I will also construct a family of functors $Z_G : \operatorname{HomCob} \to \operatorname{Vect}$, one for each finite group $G$, showing that topological quantum field theories previously constructed by Yetter, and an untwisted version of Dijkgraaf-Witten, generalise to functors from $\operatorname{HomCob}$. I will construct this functor in such a way that it is clear the images are finite dimensional vector spaces, and the functor is explicitly calculable.</p>Fri, 02 Dec 2022 09:10:26 +0100Wed, 16 Nov 2022 18:00:00 +0100Wed, 16 Nov 2022 19:00:00 +0100<a target='_content' href="https://fionatorzewska.github.io/">Fiona Torzewska</a>University of LeedsRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryMatias del Hoyo, 2022/11/15, 16h, Completeness of metrics and linearization of Lie groupoids
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6798
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6798<p>Every smooth fiber bundle admits a complete Ehresmann connection. I will talk about the story of this theorem and its relation with Riemannian submersions. Then, after discussing some foundations of Riemannian geometry of Lie groupoids and stacks, I will present a generalization of the theorem into this framework, which somehow answers an open problem on linearization. Talk based on collaborations with my former student M. de Melo.</p>Tue, 15 Nov 2022 17:31:00 +0100Tue, 15 Nov 2022 17:00:00 +0100Tue, 15 Nov 2022 18:00:00 +0100<a target='_content' href="https://sites.google.com/view/mldelhoyo/">Matias del Hoyo</a>Universidade Federal FluminenseRoom P3.10, Mathematics BuildingGeometria em LisboaJoão Sacramento, 2022/11/10, 17h, The least-control principle for learning at equilibrium
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6840
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6840<p>A large number of models of interest in both neuroscience and machine learning can be expressed as dynamical systems at equilibrium. This class of systems includes deep neural networks, equilibrium recurrent neural networks, and meta-learning. In this talk I will present a new principle for learning equilibria with a temporally - and spatially - local rule. Our principle casts learning as a least-control problem, where we first introduce an optimal controller to lead the system towards a solution state, and then define learning as reducing the amount of control needed to reach such a state. We show that incorporating learning signals within a dynamics as an optimal control enables transmitting activity-dependent credit assignment information, avoids storing intermediate states in memory, and does not rely on infinitesimal learning signals. In practice, our principle leads to strong performance matching that of leading gradient-based learning methods when applied to an array of benchmarking experiments. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.</p>Thu, 10 Nov 2022 21:27:54 +0100Thu, 10 Nov 2022 18:00:00 +0100Thu, 10 Nov 2022 19:00:00 +0100<a target='_content' href="http://www.joaosacramento.com/">João Sacramento</a>ETH ZürichMathematics, Physics & Machine LearningSarah Petersen, 2022/11/10, 16h 30m, The $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=6843
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=6843<p>This talk describes an extension of Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation for introducing these methods is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain for $C_2$-equivariant Eilenberg-MacLane spaces associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ gives a $C_2$-equivariant analogue of the classical computation due to Serre at the prime 2. We also investigate a twisted bar spectral sequence computing the homology of these equivariant Eilenberg-MacLane spaces.</p>Thu, 10 Nov 2022 07:26:16 +0100Thu, 10 Nov 2022 17:30:00 +0100Thu, 10 Nov 2022 18:30:00 +0100<a target='_content' href="https://sites.google.com/view/sarahpetersen/home">Sarah Petersen</a>MPIM BonnRoom P3.10, Mathematics BuildingAlgebraVincenzo Bianca, 2022/11/10, 14h 30m, Diffusion processes in heterogeneous media
https://math.tecnico.ulisboa.pthttps://pde.math.tecnico.ulisboa.pt/seminars?action=show&id=6858
https://math.tecnico.ulisboa.pthttps://pde.math.tecnico.ulisboa.pt/seminars?action=show&id=6858<p>We discuss a transmission problem driven by the $p$-Laplace operator, equipped with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis. First, it lacks representation formulas. Also, its ellipticity may collapse as the gradient vanishes. Our arguments circumvent those difficulties and lead to new regularity estimates. First, we prove local boundedness for the solutions. Then we establish an integral estimate for the gradient in $BMO$ spaces. The latter implies solutions have a borderline Hölder modulus of continuity.</p>Mon, 07 Nov 2022 22:48:06 +0100Thu, 10 Nov 2022 15:30:00 +0100Thu, 10 Nov 2022 16:30:00 +0100Vincenzo BiancaUniversidade de CoimbraRoom P3.10, Mathematics BuildingPartial Differential EquationsDamião Araújo, 2022/11/10, 13h 30m, On highly degenerate Alt-Phillips problems
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6857
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6857<p>In this talk, we study regularity properties for nonvariational singular elliptic equations ruled by highly degenerate second order operators. We obtain optimal $C^{1,\alpha}$ regularity along the free boundary. We also show existence of solutions, nondegeneracy properties and fine geometric estimates for the free boundary. This is a joint work with Ginaldo Sá - UFPB.</p>Sat, 19 Nov 2022 13:31:32 +0100Thu, 10 Nov 2022 14:30:00 +0100Thu, 10 Nov 2022 15:30:00 +0100Damião AraújoUniversidade Federal da ParaíbaRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsNicolas Lanchier, 2022/11/09, 17h, Consensus and discordance in the Axelrod model for the dynamics of cultures
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6859
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6859<p>The Axelrod model is a spatial stochastic model for the dynamics of cultures which includes two important social components: homophily, the tendency of individuals to interact more frequently with individuals who are more similar, and social influence, the tendency of individuals to become more similar when they interact. Each individual is characterized by a collection of opinions about different issues, and pairs of neighbors interact at a rate equal to the number of issues for which they agree, which results in the interacting pair agreeing on one more issue. This model has been extensively studied during the past 20 years based on numerical simulations and heuristic arguments while there is a lack of analytical results. This talk gives rigorous fluctuation and fixation results for the one-dimensional system that sometimes confirm and sometimes refute some of the conjectures formulated by applied scientists.</p>Tue, 08 Nov 2022 11:58:39 +0100Wed, 09 Nov 2022 18:00:00 +0100Wed, 09 Nov 2022 19:00:00 +0100Nicolas LanchierArizona State UniversityProbability and Stochastic AnalysisSimon Jubert, 2022/11/08, 16h, A Yau-Tian-Donaldson correspondence on a class of toric fibration
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6829
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6829<p>The Yau-Tian-Donaldson (YTD) conjecture predicts that the existence of an extremal metric (in the sense of Calabi) in a given Kähler class of Kähler manifold is equivalent to a certain algebro-geometric notion of stability of this class. In this talk, we will discuss the resolution of this conjecture for a certain class of toric fibrations, called semisimple principal toric fibrations. After an introduction to the Calabi Problem for general Kähler manifolds, we will focus on the toric setting. Then we will see how to reduce the Calabi problem on the total space of a semisimple principal toric fibration to a weighted constant scalar curvature Kähler problem on the toric fibers. If the time allows, I will give elements of proof.</p>Mon, 14 Nov 2022 09:42:13 +0100Tue, 08 Nov 2022 17:00:00 +0100Tue, 08 Nov 2022 18:00:00 +0100Simon JubertUniversité du Québec à MontréalGeometria em LisboaMonica Kang, 2022/11/07, 17h, Nonperturbative gravity corrections to bulk reconstruction
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6822
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6822<p>I will first motivate the benefits on taking the algebraic approach to understand AdS/CFT and how an algebra of local operators of QFT has knowledge of a spacetime region. Utilizing both operator algebras and quantum information theory, I will explain a new framework for understanding nonperturbative gravitational aspects of bulk reconstruction with a finite or infinite-dimensional boundary Hilbert space. This will be understood as approximate recovery containing gravitational errors, and the bulk reconstruction in this context will be understood using the privacy/correctability correspondence.</p>Wed, 09 Nov 2022 09:13:02 +0100Mon, 07 Nov 2022 18:00:00 +0100Mon, 07 Nov 2022 19:00:00 +0100Monica KangCalifornia Institute of TechnologyString TheoryFrederico Fiuza, 2022/11/03, 17h, Accelerating the understanding of nonlinear dynamical systems using machine learning
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6816
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6816<p>The description of nonlinear, multi-scale dynamics is a common challenge in a wide range of physical systems and research fields — from weather forecast to controlled nuclear fusion. The development of reduced models that balance between accuracy and complexity is critical to advancing theoretical comprehension and enabling holistic computational descriptions of these problems. I will discuss how techniques from statistical and machine learning are offering new ways of inferring reduced physics models from the increasingly abundant data of nonlinear dynamics produced by experiments, observations, and simulations. In particular, I will focus on how sparse regression techniques can be used to infer interpretable plasma physics models (in the form of nonlinear partial differential equations) directly from the data of first-principles fully-kinetic simulations. The potential of this approach is demonstrated by recovering the fundamental hierarchy of plasma physics models based solely on particle-based simulation data of complex plasma dynamics. I will discuss how this data-driven methodology provides a promising tool to accelerate the development of reduced theoretical models of nonlinear dynamical systems and to design computationally efficient algorithms for multi-scale simulations.</p>Fri, 04 Nov 2022 08:01:07 +0100Thu, 03 Nov 2022 18:00:00 +0100Thu, 03 Nov 2022 19:00:00 +0100<a target='_content' href="https://kipac.stanford.edu/people/frederico-fiuza">Frederico Fiuza</a>SLACMathematics, Physics & Machine LearningJosé Natário, 2022/11/03, 14h 30m, Relativistic elasticity and compactness bounds
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6852
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6852<p>After reviewing the basics of relativistic elasticity theory, I will introduce a general framework to study spherically symmetric self-gravitating elastic bodies systematically within general relativity, and apply it to investigate compactness bounds in this context.</p>Wed, 02 Nov 2022 11:01:10 +0100Thu, 03 Nov 2022 15:30:00 +0100Thu, 03 Nov 2022 16:30:00 +0100José NatárioInstituto Superior TécnicoMathematical RelativityEllen Saada, 2022/11/02, 17h, Ergodicity of some dynamics of DNA sequences
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6846
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6846<p>In this joint work with M. Falconnet and N. Gantert, we define interacting particle systems on configurations of the integer lattice (with values in some finite alphabet) by the superimposition of two dynamics: a substitution process with finite range rates, and a circular permutation mechanism (called “cut-and-paste”) with possibly unbounded range.</p><p>The model is motivated by the dynamics of DNA sequences: we consider an ergodic model for substitutions, the RN+YpR model, introduced by Berard et al. in 2008, as well as three particular cases. We investigate whether they remain ergodic with the additional cut-and-paste mechanism, which models insertions and deletions of nucleotides. Using either duality or attractiveness techniques, we provide various sets of sufficient conditions, concerning only the substitution rates, for ergodicity of the superimposed process.</p>Tue, 01 Nov 2022 10:00:21 +0100Wed, 02 Nov 2022 18:00:00 +0100Wed, 02 Nov 2022 19:00:00 +0100<a target='_content' href="https://helios2.mi.parisdescartes.fr/~esaada/">Ellen Saada</a>Université de ParisProbability and Stochastic AnalysisTimothy Hollowood, 2022/10/31, 15h, Is Hawking’s Black Hole Information Loss Paradox Solved?
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6828
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6828<p>Recent developments involving replica wormholes, the generalized entropy, quantum extremal surfaces, holographic map, etc, have shown what is missing in Hawking’s original calculation. We can now see how to perform semi-classical calculations that are entirely consistent with unitary: information is not lost. The state of the Hawking radiation has subtle correlations that build up as a black hole evaporates and ensure that the final state is pure. The interpretation of the results for the picture of a black hole with a smooth internal geometry before the singularity is reached is less clear. I will review these developments and present a simple microscopic model which can be used to illustrate the issues involved. The recent observation that the holographic map, the map between the semi-classical and microscopic states, is non-isometric plays a key role. Contrary to some suggestions, manipulation of the radiation far from the black hole cannot affect its interior in a non-local way. The picture seems entirely consistent with microscopic constructions like fuzzballs in string theory.</p>Tue, 01 Nov 2022 13:18:09 +0100Mon, 31 Oct 2022 16:00:00 +0100Mon, 31 Oct 2022 17:00:00 +0100Timothy HollowoodSwansea UniversityString TheoryRobert Nowak, 2022/10/27, 17h, The Neural Balance Theorem and its Consequences
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6820
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6820<p>Rectified Linear Units (ReLUs) are the most common activation function in deep neural networks. Weight decay is the most prevalent form of regularization used in deep learning. Together ReLUs and weight decay lead to an interesting effect known as “Neural Balance”: the norms of the input and output weights of each ReLU are automatically equalized at a global minima of the training objective. Neural Balance has a number of important consequences ranging from characterizations of the function spaces naturally associated to neural networks, their immunity to the curse of dimensionality, and to new and more effective architectures and training strategies.</p><p>This talk is based on joint work with Rahul Parhi and Liu Yang.</p>Fri, 28 Oct 2022 13:01:35 +0200Thu, 27 Oct 2022 18:00:00 +0200Thu, 27 Oct 2022 19:00:00 +0200<a target='_content' href="https://nowak.ece.wisc.edu/">Robert Nowak</a>University of Wisconsin-MadisonMathematics, Physics & Machine LearningDominik Schmid, 2022/10/26, 17h, Mixing times for the TASEP on the circle
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6842
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6842<p> </p><p>The exclusion process is one of the best-studied examples of an interacting particle system. In this talk, we consider simple exclusion processes on finite graphs. We give an overview over some recent results on the mixing time of the totally asymmetric simple exclusion process (TASEP). In particular, we provide bounds on the mixing time of the TASEP on the circle, using a connection to periodic last passage percolation. This talk is based on joint work with Allan Sly.</p><p> </p><p> </p>Mon, 17 Oct 2022 20:14:18 +0200Wed, 26 Oct 2022 18:00:00 +0200Wed, 26 Oct 2022 19:00:00 +0200<a target='_content' href="https://sites.google.com/view/dominik-schmid">Dominik Schmid</a>Bonn UniversityProbability and Stochastic AnalysisMarko Vojinovic, 2022/10/26, 17h, Insights into the Standard Model and quantum gravity from higher gauge theory
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6844
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6844<p>Higher category theory can be employed to generalize the notion of symmetry, by passing from a gauge group to the notion of a gauge n-group. The n-groups are designed to generalize notions of connection and parallel transport, from curves to manifolds of dimension higher than one. They also give rise to a class of topological actions called nBF actions. One can then employ a 3-group as a gauge symmetry and the corresponding 3BF action, to describe the full Einstein-Cartan theory of gravity coupled to Standard Model fields. Such an action is naturally adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter.</p><p>Once constructed, the properties of the model open up the possibility of a nontrivial unification of all fields. A 3-group naturally contains additional novel gauge groups which specify the spectrum of fermions and scalars present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. The presence and the properties of new gauge groups have the potential to explain fermion families, and other structure in the matter spectrum of the Standard Model.</p>Fri, 02 Dec 2022 20:41:55 +0100Wed, 26 Oct 2022 18:00:00 +0200Wed, 26 Oct 2022 19:00:00 +0200<a target='_content' href="http://www.markovojinovic.com/professional/">Marko Vojinovic</a>University of BelgradeRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryGaëtan Cane, 2022/10/19, 17h, Superdiffusion transition for a noisy harmonic chain subject to a magnetic field
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6841
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6841<p> </p><p>Understanding the diffusive or superdiffusive behavior of the energy in classical physical systems is challenging because of the non-linearity of the interactions between the particles. A way to reduce the difficulty is to replace the nonlinearity by a stochastic noise. In this presentation I will consider a noisy harmonic chain subjected to a magnetic field. We will see that according to the intensity of the magnetic field, the superdiffusive nature of the system changes. </p><p> </p><p> </p>Tue, 18 Oct 2022 14:11:10 +0200Wed, 19 Oct 2022 18:00:00 +0200Wed, 19 Oct 2022 19:00:00 +0200Gaëtan CaneUniversité d'OrléansProbability and Stochastic AnalysisMiguel Moreira, 2022/10/18, 16h, Virasoro constraints in sheaf theory
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6815
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6815<p>Virasoro constraints for Gromov-Witten invariants have a rich history tied to the very beginning of the subject, but recently there have been many developments on the sheaf side. In this talk I will survey those developments and talk about joint work with A. Bojko and W. Lim where we propose a general conjecture of Virasoro constraints for moduli spaces of sheaves and formulate it using the vertex algebra that D. Joyce recently introduced to study wall-crossing. Using Joyce's framework we can show compatibility between wall-crossing and the constraints, which we then use to prove that they hold for moduli of stable sheaves on curves and surfaces with $h^{0,1}=h^{0,2}=0$. In the talk I will give a rough overview of the vertex algebra story and focus on the ideas behind the proof in the case of curves.</p>Wed, 19 Oct 2022 14:46:41 +0200Tue, 18 Oct 2022 17:00:00 +0200Tue, 18 Oct 2022 18:00:00 +0200<a target='_content' href="https://people.math.ethz.ch/~mimoreira/">Miguel Moreira</a>ETH ZurichGeometria em LisboaJosé Miguel Urbano, 2022/10/14, 16h, Semi-Supervised Learning and the $\infty$-Laplacian
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6835
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6835<p>Motivated by a recent application in Semi-Supervised Learning (SSL), the minicourse is a brief introduction to the analysis of infinity-harmonic functions. We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions and its several drawbacks, leading to the notion of AMLE (Absolutely Minimising Lipschitz Extension). We then explore the equivalence between being absolutely minimising Lipschitz, enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense.</p>Thu, 13 Oct 2022 20:35:06 +0200Fri, 14 Oct 2022 17:00:00 +0200Fri, 14 Oct 2022 18:00:00 +0200<a target='_content' href="https://cemse.kaust.edu.sa/people/person/miguel-urbano">José Miguel Urbano</a>KAUSTAmphitheatre Fa2, ISTMathematics, Physics & Machine LearningJosé Miguel Urbano, 2022/10/14, 14h 30m, Semi-Supervised Learning and the $\infty$-Laplacian
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6834
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6834<p>Motivated by a recent application in Semi-Supervised Learning (SSL), the minicourse is a brief introduction to the analysis of infinity-harmonic functions. We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions and its several drawbacks, leading to the notion of AMLE (Absolutely Minimising Lipschitz Extension). We then explore the equivalence between being absolutely minimising Lipschitz, enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense.</p>Mon, 31 Oct 2022 17:58:02 +0100Fri, 14 Oct 2022 15:30:00 +0200Fri, 14 Oct 2022 16:30:00 +0200<a target='_content' href="https://cemse.kaust.edu.sa/people/person/miguel-urbano">José Miguel Urbano</a>KAUSTAmphitheatre Fa2, ISTMathematics, Physics & Machine LearningDiogo Gomes, 2022/10/14, 11h, From Calculus of Variations to Reinforcement Learning
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6833
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6833<p>This course begins with a brief introduction to classical calculus of variations and its applications to classical problems such as geodesic trajectories and the brachistochrone problem. Then, we examine Hamilton-Jacobi equations, the role of convexity and the classical verification theorem. Next, we illustrate the lack of classical solutions and motivate the definition of viscosity solutions. The course ends with a brief description of the reinforcement learning problem and its connection with Hamilton-Jacobi equations.</p>Mon, 31 Oct 2022 17:57:34 +0100Fri, 14 Oct 2022 12:00:00 +0200Fri, 14 Oct 2022 13:00:00 +0200<a target='_content' href="https://www.kaust.edu.sa/en/study/faculty/diogo-gomes">Diogo Gomes</a>KAUSTAmphitheatre Fa2, ISTMathematics, Physics & Machine LearningDiogo Gomes, 2022/10/14, 09h 30m, From Calculus of Variations to Reinforcement Learning
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6832
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6832<p>This course begins with a brief introduction to classical calculus of variations and its applications to classical problems such as geodesic trajectories and the brachistochrone problem. Then, we examine Hamilton-Jacobi equations, the role of convexity and the classical verification theorem. Next, we illustrate the lack of classical solutions and motivate the definition of viscosity solutions. The course ends with a brief description of the reinforcement learning problem and its connection with Hamilton-Jacobi equations.</p>Mon, 31 Oct 2022 17:55:38 +0100Fri, 14 Oct 2022 10:30:00 +0200Fri, 14 Oct 2022 11:30:00 +0200<a target='_content' href="https://www.kaust.edu.sa/en/study/faculty/diogo-gomes">Diogo Gomes</a>KAUSTAmphitheatre Fa2, ISTMathematics, Physics & Machine LearningAntonella Grassi, 2022/10/11, 16h, A family of threefolds with several unusual features
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6808
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6808<p>I will discuss some of the unusual properties, in geometry and physics, of a family of Calabi-Yau threefolds fibered by elliptic curves. I will compare it to a construction by Elkies and a classical results of Burkhardt. This leads to some open questions.</p>Mon, 28 Nov 2022 09:57:42 +0100Tue, 11 Oct 2022 17:00:00 +0200Tue, 11 Oct 2022 18:00:00 +0200<a target='_content' href="https://www.unibo.it/sitoweb/antonella.grassi3/cv-en">Antonella Grassi</a>Università di BolognaGeometria em LisboaJie-qiang Wu, 2022/10/10, 11h, Algebra of diffeomorphism invariant observables in Jackiw-Teitelboim gravity
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6821
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=6821<p>Diffeomorphism symmetry is an intrinsic difficulty in gravitational theory, which appears in almost all of the questions in gravity. As is well known, the diffeomorphism symmetries in gravity should be interpreted as gauge symmetries, so only diffeomorphism invariant operators are physically interesting. However, because of the non-linear effect of gravitational theory, the results for diffeomorphism invariant operators are very limited.</p><p>In this work, we focus on the Jackiw-Teitelboim gravity in classical limit, and use Peierls bracket (which is a linear response like computation of observables’ bracket) to compute the algebra of a large class of diffeomorphism invariant observables. With this algebra, we can reproduce some recent results in Jackiw-Teitelboim gravity including: traversable wormhole, scrambling effect, and $SL(2)$ charges. We can also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the “typical state” version of the firewall paradox.</p><p>In the talk, I will first give a brief introduction of Peierls bracket, and then use the Peierls bracket to study the brackets between diffeomorphism invariant observables in Jackiw-Teitelboim gravity. I will then give two applications of this algebra: reproducing the scrambling effect, and studying the energy change after creating an excitation in the bulk.</p><p>Work based on <a href="https://arxiv.org/pdf/2108.04841.pdf">https://arxiv.org/pdf/2108.04841.pdf</a></p>Tue, 01 Nov 2022 13:22:12 +0100Mon, 10 Oct 2022 12:00:00 +0200Mon, 10 Oct 2022 13:00:00 +0200Jie-qiang WuITP BeijingString TheoryMarcus Khuri, 2022/10/06, 14h 30m, Level Set Methods in Mathematical GR
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6830
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6830<p>We will review recent developments concerning the use of level set techniques associated with solutions to elliptic equations, in particular spacetime harmonic functions, and their application to positive mass theorems and comparison geometry.</p>Tue, 04 Oct 2022 08:34:58 +0200Thu, 06 Oct 2022 15:30:00 +0200Thu, 06 Oct 2022 16:30:00 +0200Marcus KhuriStony Brook UniversityMathematical RelativityKohei Hayashi, 2022/10/05, 17h, Derivation of the KPZ equation from microscopic systems in a high temperature regime
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6827
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6827<p>The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation with universality, and it has been derived from several microscopic models through scaling limits. When the temperature of a system tends to infinity, we can often extract a heat diffusion part with some residual perturbation by a Taylor expansion argument, which decomposition is crucial for the derivation. We will show through some particular models that we can thereby obtain the KPZ equation as a limit in a robust way. </p>Wed, 28 Sep 2022 16:15:45 +0200Wed, 05 Oct 2022 18:00:00 +0200Wed, 05 Oct 2022 19:00:00 +0200Kohei HayashiUniversity of Tokyo, JapanProbability and Stochastic AnalysisGustavo Granja, 2022/10/04, 16h, Topology of almost complex structures
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6810
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6810<p>I will report on joint work in progress with Aleksandar Milivojevic (MPIM Bonn) on the elementary topology of the space of almost complex structures on a manifold. First I will describe a certain natural parametrization and associated stratification of the space of linear complex structures on a vector space and give a lower bound for the number of complex k-planes jointly preserved by two linear complex structures. Then I will focus on dimension 6 and prove a formula for the homological intersection of two orthogonal almost complex structures on a Riemannian 6-manifold when these are regarded as sections of the twistor space.</p>Wed, 05 Oct 2022 10:08:41 +0200Tue, 04 Oct 2022 17:00:00 +0200Tue, 04 Oct 2022 18:00:00 +0200<a target='_content' href="https://www.math.tecnico.ulisboa.pt/~ggranja/">Gustavo Granja</a>Instituto Superior Técnico - Universidade de LisboaRoom P3.10, Mathematics BuildingGeometria em LisboaLeandro Chiarini, 2022/09/30, 14h, Stochastic homogenisation of Gaussian fields
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars/?action=show&id=6825
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars/?action=show&id=6825<p>In this talk, we discuss the convergence of a sequence of random fields that generalise the Gaussian Free Field and bi-Laplacian field. Such fields are defined in terms of non-homogeneous elliptic operators which will be sampled at random. Under standard assumptions of stochastic homogenisation, we identify the limit fields as the usual GFF and bi-Laplacian fields up to a multiplicative constant. This is a joint work with W. Ruszel.</p>Tue, 27 Sep 2022 15:53:15 +0200Fri, 30 Sep 2022 15:00:00 +0200Fri, 30 Sep 2022 16:00:00 +0200Leandro ChiariniUniversidade de UtrechtRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsPetar Veličković, 2022/09/29, 17h, Geometric Deep Learning: Grids, Graphs, Groups, Geodesics and Gauges
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6632
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6632<p>The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach — such as computer vision, playing Go, or protein folding — are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation.</p><p>While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This talk is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications.</p><p>Such a 'geometric unification' endeavour in the spirit of Felix Klein's Erlangen Program serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.</p>Sun, 02 Oct 2022 14:31:20 +0200Thu, 29 Sep 2022 18:00:00 +0200Thu, 29 Sep 2022 19:00:00 +0200<a target='_content' href="https://petar-v.com/">Petar Veličković</a>DeepMind and University of CambridgeMathematics, Physics & Machine LearningClaudio Landim, 2022/09/28, 17h, Metastability from the point of view of large deviations
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6826
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6826<p>Consider a sequence of continuous-time Markov chains $X^n_t$ evolving on a fixed finite state space $V$. Let $I_n$ be its level two large deviations rate functiona. Under a general hypothesis on the jump rates, we derive an expansion for $I_n$: we show that $I_n$ can be written as$ I^0 + \sum_{1\ le p\le q} (\theta^p_n)^{-1} I^p$ In this formula, $\theta^p_n$ are the time-scales at which a meta-stable behavior is observed and I^p the level two large deviations rate function of the Markov chain which describes the evolution of the chain $X^n_t$ in the time-scale $\theta^p_n$.</p>Wed, 28 Sep 2022 16:11:09 +0200Wed, 28 Sep 2022 18:00:00 +0200Wed, 28 Sep 2022 19:00:00 +0200Claudio LandimIMPA-BrasilProbability and Stochastic AnalysisLino Amorim, 2022/09/27, 16h, From categories to Gromov-Witten invariants
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6814
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6814<p>Kontsevich suggested that enumerative predictions of Mirror Symmetry should follow directly from Homological Mirror Symmetry. This requires a natural construction of analogues of Gromov-Witten invariants associated to any A-infinity Calabi-Yau category, with some extra choices. I will explain what these choices are and survey two approaches to this construction, one in genus zero and another (conjectural) in all genera.</p>Wed, 05 Oct 2022 13:26:15 +0200Tue, 27 Sep 2022 17:00:00 +0200Tue, 27 Sep 2022 18:00:00 +0200<a target='_content' href="https://www.math.ksu.edu/~lamorim/">Lino Amorim</a>Kansas State UniversityRoom P3.10, Mathematics BuildingGeometria em LisboaChristophe Poquet, 2022/09/21, 17h, Slow-fast dynamics and periodic behaviour in mean-field systems
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6813
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6813<p>We will study a model of noisy units in mean field interaction, which is described in the large population limit by a non linear PDE. Relying on a slow/fast approach we will show the emergence of noise induced periodic behaviors. We will focus in particular on the case when each unit evolves according to the FiztHugh Nagumo model.</p>Tue, 13 Sep 2022 08:59:40 +0200Wed, 21 Sep 2022 18:00:00 +0200Wed, 21 Sep 2022 19:00:00 +0200<a target='_content' href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjq-8WRppH6AhVWXfEDHTaKAnQQFnoECAsQAQ&url=http%3A%2F%2Fmath.univ-lyon1.fr%2F~poquet%2F&usg=AOvVaw1YaoFqfYdnRbGVAzvMpogn">Christophe Poquet</a>ICJ Université Lyon 1Probability and Stochastic AnalysisPavel Safronov, 2022/09/21, 17h, Skein modules and 4d TQFTs
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6812
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6812<div>It is well-known that the quantum Chern–Simons theory (as formalized by Reshetikhin and Turaev) has a framing anomaly: to have a functorial dependence on cobordisms, they have to be equipped with an extra tangential structure besides the orientation. Following Walker and Freed–Teleman, one can view the anomaly of the Chern–Simons theory as an invertible 4d TQFT, the Crane–Yetter theory. While the Chern–Simons theory makes sense only when q, the quantum parameter, is a root of unity, the anomaly theory make sense for any q. I will describe the behavior of this 4d TQFT for generic q and, in particular, a description of its spaces of states on closed 3-manifolds. This is based on joint work with Sam Gunningham and David Jordan.</div>Mon, 03 Oct 2022 15:35:36 +0200Wed, 21 Sep 2022 18:00:00 +0200Wed, 21 Sep 2022 19:00:00 +0200Pavel SafronovUniversity of EdinburghTopological Quantum Field TheoryAlexander Givental, 2022/09/16, 16h, K-theoretic Gromov-Witten invariants and their adelic characterization
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6707
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=6707<p>Gromov-Witten invariants of a given Kahler target space are defined as suitable intersection numbers in moduli spaces of stable maps of complex curves into the target space. Their K-theoretic analogues are defined as holomorphic Euler characteristics of suitable vector bundles over these moduli spaces.</p><p>We will describe how the Kawasaki-Riemann-Roch theorem expressing holomorphic Euler characteristics in cohomological terms leads to the adelic formulas for generating functions encoding K-theoretic Gromov-Witten invariants.</p>Tue, 20 Sep 2022 15:35:34 +0200Fri, 16 Sep 2022 17:00:00 +0200Fri, 16 Sep 2022 18:00:00 +0200<a target='_content' href="https://math.berkeley.edu/~giventh/">Alexander Givental</a>University of BerkeleyRoom P3.10, Mathematics BuildingGeometria em LisboaMarina Logares, 2022/09/14, 17h, Hitchin systems
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6811
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=6811<p>Hitchin systems are in the core of the intersection between integrable systems and gauge theories. These are algebraic completely integrable systems defined by moduli spaces of (decorated) Higgs bundles. In this talk I shall describe several Hitchin systems. This is based on past and ongoing work with Biswas, Martens, Peón-Nieto and Szabó.</p>Thu, 22 Sep 2022 00:32:53 +0200Wed, 14 Sep 2022 18:00:00 +0200Wed, 14 Sep 2022 19:00:00 +0200Marina LogaresComplutense University of MadridTopological Quantum Field TheoryWei-Kuo Chen, 2022/09/14, 17h, Computational perspective of local magnetization in the Sherrington-Kirkpatrick model
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6809
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6809<p> </p><p>Spin glasses are disordered spin systems originally introduced to explain some unusual magnetic behavior of certain alloys. Although their formulations are typically easy to state, many of them enjoy several profound mathematical and physical principles that are extremely challenging to prove. In this talk, I will focus on the Sherrington-Kirkpatrick model and consider its local magnetization in the computational perspective. While it has been well-understood that this quantity satisfies so-called cavity method and Thouless-Anders-Palmer equations in the literature, I will explain how they give rise to novel iterative algorithms and are helpful in simulating the local magnetization in the high temperature regime. Based on a joint work with Si Tang.</p><p> </p><p> </p>Tue, 13 Sep 2022 08:57:04 +0200Wed, 14 Sep 2022 18:00:00 +0200Wed, 14 Sep 2022 19:00:00 +0200<a target='_content' href="https://sites.google.com/view/wkchen/home">Wei-Kuo Chen</a>University of MinnesotaProbability and Stochastic AnalysisJonathan Bennett, 2022/09/13, 14h, The nonlinear Brascamp-Lieb inequality and applications
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6806
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=6806<p>The Brascamp-Lieb inequality is a broad generalisation of many well-known multilinear inequalities in analysis, including the multilinear Hölder, Loomis-Whitney and sharp Young convolution inequalities. There is by now a rich theory surrounding this classical inequality, along with applications in convex geometry, harmonic analysis, partial differential equations, number theory and beyond. In this talk we present a certain nonlinear variant of the Brascamp-Lieb inequality, placing particular emphasis on some of its applications. Most of this is joint work with Stefan Buschenhenke, Neal Bez, Michael Cowling and Taryn Flock.</p>Mon, 05 Sep 2022 21:48:58 +0200Tue, 13 Sep 2022 15:00:00 +0200Tue, 13 Sep 2022 16:00:00 +0200<a target='_content' href="https://www.birmingham.ac.uk/staff/profiles/maths/bennett-jonathan.aspx">Jonathan Bennett</a>University of BirminghamRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsInês Hipólito, 2022/09/08, 17h, The Free Energy Principle in the Edge of Chaos
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6629
https://math.tecnico.ulisboa.pthttps://mpml.tecnico.ulisboa.pt/seminars?action=show&id=6629<p>Living beings do an extraordinary thing. By being alive they are resisting the second law of thermodynamics. This law stipulates that open, living systems tend to dissipation by the increase of entropy or chaos. From minimal cognitive organisms like plants to more complex organisms equipped with nervous systems, all living systems adjust and adapt to their environments, thereby resisting the second law. Impressively, while all animals cognitively enact and survive their local environments, more complex systems do so also by actively constructing their local environments, thereby not only defying the second law, but also (evolution) selective properties. Because all living beings defy the second law by adjusting and engaging with the environment, a prominent question is how do living organisms persist while engaging in adaptive exchanges with their complex environments? In this talk I will offer an overview of how the Free Energy Principle (FEP) offers a principled solution to this problem. The FEP prescribes that living systems maintain themselves by remaining in non-equilibrium steady states by restricting themselves to a limited number of states; it has been widely applied to explain neurocognitive function and embodied action, develop artificial intelligence and inspire psychopathology models.</p>Mon, 24 Oct 2022 08:47:01 +0200Thu, 08 Sep 2022 18:00:00 +0200Thu, 08 Sep 2022 19:00:00 +0200<a target='_content' href="http://www.ineshipolito.org/">Inês Hipólito</a>Humboldt-UniversitätMathematics, Physics & Machine LearningAlisa Knizel, 2022/09/07, 17h, Stationary measure for the open KPZ equation:
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6801
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6801<p>The Kardar-Parisi-Zhang (KPZ) equation is the stochastic partial differential equation that models interface growth. In the talk I will present the construction of a stationary measure for the KPZ equation on a bounded interval with general inhomogeneous Neumann boundary conditions. Along the way, we will encounter classical orthogonal polynomials, the asymmetric simple exclusion process, and precise asymptotics of q-Gamma functions. This construction is a joint work with Ivan Corwin.</p>Fri, 19 Aug 2022 11:51:30 +0200Wed, 07 Sep 2022 18:00:00 +0200Wed, 07 Sep 2022 19:00:00 +0200<a target='_content' href="https://sites.google.com/view/alisaknizel/home">Alisa Knizel</a>University of ChicagoProbability and Stochastic AnalysisBadri Krishnan, 2022/09/01, 14h 30m, A quasi-local view of black hole mergers
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6803
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt?action=show&id=6803<p>In this talk I will summarize recent progress and open mathematical problems in understanding black hole mergers quasi-locally, i.e. by using marginally trapped surfaces instead of event horizons.</p>Mon, 29 Aug 2022 15:26:37 +0200Thu, 01 Sep 2022 15:30:00 +0200Thu, 01 Sep 2022 16:30:00 +0200Badri KrishnanRadboud UniversityMathematical RelativityEric Cator, 2022/08/31, 17h, PNG model on the circle
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6804
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6804<p>We will introduce a periodic version of the Polynuclear growth model (PNG) and show that it is a solvable model. We can give stationary measures for the model at a fixed time and for the distribution of the space-time paths, which in this model are up-down paths that form rings. This is joint work with Pablo Ferrari (UBA). </p>Wed, 31 Aug 2022 15:08:34 +0200Wed, 31 Aug 2022 18:00:00 +0200Wed, 31 Aug 2022 19:00:00 +0200<a target='_content' href="https://www.ru.nl/en/people/cator-e">Eric Cator</a>Radboud UniversiteitProbability and Stochastic AnalysisPietro Caputo, 2022/08/24, 17h, Rapid mixing of Gibbs samplers: Coupling, Spectral Independence, and Entropy Factorizations
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6802
https://math.tecnico.ulisboa.pthttps://math.tecnico.ulisboa.pt/seminars/ps/?action=show&id=6802<p>We discuss some recent developments in the analysis of convergence to stationarity for the Gibbs sampler of general spin systems on arbitrary graphs. These are based on two recently introduced concepts: Spectral Independence and Block Factorization of Entropy. We show that the existence of a contractive coupling for a local Markov chain implies that the system is spectrally independent, and that if a system is spectrally independent then its entropy functional satisfies a general block factorization. As a corollary, we obtain new optimal bounds on the mixing time of a large class of sampling algorithms for the ferromagnetic Ising/Potts models in the so-called tree-uniqueness regime, including non-local chains such as the Swendsen-Wang dynamics. The methods apply to systems with hard constraints such as proper colorings and the hard core gas. We also discuss the entropy factorization for the uniform distribution over permutations and its role in the proof of a conjectured bound on the permanent of arbitrary matrices. Based on some recent joint works with Alexandre Bristiel, Antonio Blanca, Zongchen Chen, Daniel Parisi, Alistair Sinclair, Daniel Stefankovic, and Eric Vigoda.</p>Fri, 19 Aug 2022 11:55:20 +0200Wed, 24 Aug 2022 18:00:00 +0200Wed, 24 Aug 2022 19:00:00 +0200<a target='_content' href="http://www.mat.uniroma3.it/users/caputo/">Pietro Caputo</a>University Roma TreProbability and Stochastic Analysis