CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Naichung Conan Leung, 2024/12/17, 16h, 3d mirror symmetry is mirror symmetry
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7391
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7391<p><meta charset="UTF-8" />3d mirror symmetry is a mysterious duality for certian pairs of hyperkähler manifolds, or more generally complex symplectic manifolds/stacks. In this talk, we will describe its relationships with 2d mirror symmetry. This could be regarded as a 3d analog of the paper "Mirror Symmetry is T-Duality" by Strominger, Yau and Zaslow which described 2d mirror symmetry via 1d dualities.</p>Mon, 28 Oct 2024 16:00:05 +0100Tue, 17 Dec 2024 17:00:00 +0100Tue, 17 Dec 2024 18:00:00 +0100<a target='_content' href="http://www.ims.cuhk.edu.hk/~leung/">Naichung Conan Leung</a>The Chinese University of Hong KongRoom P3.10, Mathematics Building<span lang='pt'>Geometria em Lisboa</span>Francisco Nascimento, 2024/12/03, 16h, Kinematic formulas in convex geometry
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7372
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7372Tue, 29 Oct 2024 14:03:58 +0100Tue, 03 Dec 2024 17:00:00 +0100Tue, 03 Dec 2024 18:00:00 +0100Francisco NascimentoInstituto Superior TécnicoRoom P3.10, Mathematics Building<span lang='pt'>Geometria em Lisboa</span>Dan Wang, 2024/11/19, 16h, Dependence of quantum spaces on different polarizations on toric varieties
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7342
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7342<p><meta charset="UTF-8" />A crucial problem in geometric quantization is to understand the relationship among quantum spaces associated to different polarizations. Two types of polarizations on toric varieties, Kähler and real, have been studied extensively. This talk will focus on the quantum spaces associated with mixed polarizations and explore their relationships with those associated with Kähler polarizations on toric varieties.</p>Tue, 29 Oct 2024 17:20:35 +0100Tue, 19 Nov 2024 17:00:00 +0100Tue, 19 Nov 2024 18:00:00 +0100<a target='_content' href="https://sites.google.com/view/dwang116">Dan Wang</a>CAMGSD, Instituto Superior TécnicoRoom P3.10, Mathematics Building<span lang='pt'>Geometria em Lisboa</span>Yu Shen Lin, 2024/11/12, 16h, Special Lagrangians in Calabi-Yau $3$-folds with a K3-fibration
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7390
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7390<p><meta charset="UTF-8" />Special Lagrangians form an important class of minimal submanifolds in Calabi-Yau manifolds. In this talk, we will consider the Calabi-Yau $3$-folds with a K3-fibration and the size of the K3-fibres are small. Motivated by tropical geometry, Donaldson-Scaduto conjectured that special Lagrangian collapse to ``gradient cycles" when the K3-fibres collapse. This phenomenon is similar to holomorphic curves in Calabi-Yau manifolds with collapsing special Lagrangian fibrations converging to tropical curves. Similar to the realization problem in tropical geometry, one might expect to reconstruct special Lagrangians from gradient cycles. In this talk, I will report the first theorem of this kind based on a joint work with Shih-Kai Chiu.</p>Mon, 28 Oct 2024 16:01:50 +0100Tue, 12 Nov 2024 17:00:00 +0100Tue, 12 Nov 2024 18:00:00 +0100<a target='_content' href="http://math.bu.edu/people/yslin/">Yu Shen Lin</a>Boston University<span lang='pt'>Geometria em Lisboa</span>Elli Heyes, 2024/11/11, 15h, Machine-Learning $G_2$ Geometry
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=7395
https://math.tecnico.ulisboa.pthttps://strings.math.tecnico.ulisboa.pt/seminars?action=show&id=7395<p>Kaluza-Klein reduction of 11-dimensional supergravity on $G_2$ manifolds yields a 4-dimensional effective field theory (EFT) with $N=1$ supersymmetry. $G_2$ manifolds are therefore the analog of Calabi-Yau (CY) threefolds in heterotic string theory. Since 2017 machine-learning techniques have been applied extensively to study CY manifolds but until 2024 no similar work had been carried out on $G_2$ manifolds. We first show how topological properties of these manifolds can be learnt using simple neural networks. We then discuss how one may try to learn Ricci-flat $G_2$ metrics with machine-learning.</p>Mon, 04 Nov 2024 11:28:11 +0100Mon, 11 Nov 2024 16:00:00 +0100Mon, 11 Nov 2024 17:00:00 +0100Elli HeyesDepartment of Mathematics, City, University of LondonRoom P3.10, Mathematics BuildingString TheoryZhongshan An, 2024/11/07, 14h 30m, Einstein manifolds with boundary
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7396
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7396<p>We will talk about existence of Einstein metrics on manifolds with boundary, while prescribing the induced conformal metric and mean curvature of the boundary. In dimension 3, this becomes the existence of conformal embeddings of surfaces into constant sectional curvature space forms, with prescribed mean curvature. We will show existence of such conformal emebeddings near generic Einstein background. We will also discuss the existence question in higher dimensions, where things become more subtle and a non-degenerate boundary condition is used to construct metrics with nonpositive Einstein constant.</p>Tue, 05 Nov 2024 08:59:51 +0100Thu, 07 Nov 2024 15:30:00 +0100Thu, 07 Nov 2024 16:30:00 +0100Zhongshan AnUniversity of MichiganMathematical RelativityLuca Avena, 2024/11/06, 16h, Achieving consensus on static & dynamic regular random graphs.
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7384
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7384<p><meta charset="UTF-8" /></p><p>We consider the classical 2-opinion dynamics known as the voter model on finite graphs. It is well known that this interacting particle system is dual to a system of coalescing random walkers and that under so-called mean-field geometrical assumptions, as the graph size increases, the characterization of the time to reach consensus can be reduced to the study of the first meeting time of two independent random walks starting from equilibrium. </p><p>As a consequence, several recent contributions in the literature have been devoted to making this picture precise in certain graph ensembles for which the above mentioned meeting time can be explicitly studied. I will first review this type of results and then focus on the specific geometrical setting of random regular graphs, both static and dynamic (i.e. edges of the graphs are rewired at random over time), where in recent works we study precise first order behaviour of the involved observables. We will in particular show a quasi-stationary-like evolution for the discordant edges (i.e. with different opinions at their end vertices) which clarify what happens before the consensus time scale both in the static and in the dynamic graph setting. Further, in the dynamic geometrical setting we can see how consensus is affected as a function of the graph dynamics.</p><p> </p><p>Based on recent and ongoing joint works with Rangel Baldasso, Rajat Hazra, Frank den Hollander and Matteo Quattropani.</p>Tue, 22 Oct 2024 15:33:46 +0200Wed, 06 Nov 2024 17:00:00 +0100Wed, 06 Nov 2024 18:00:00 +0100Luca AvenaUniversity of FirenzeProbability and Stochastic AnalysisSaman Habibi Esfahani, 2024/11/05, 16h, On the Donaldson-Scaduto conjecture
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7386
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7386<p><meta charset="UTF-8" />This talk is based on a joint work with Yang Li. Motivated by collapsing Calabi-Yau 3-folds and G2-manifolds with Lefschetz K3 fibrations in the adiabatic setting, Donaldson and Scaduto conjectured the existence of a special Lagrangian pair-of-pants in the Calabi-Yau 3-fold $X \times \mathbb R^2$, where $X$ is either a hyperkähler K3 surface (global version) or an A2-type ALE hyperkähler 4-manifold (local version). After a brief introduction to the subject, we discuss the significance of this conjecture in the study of Calabi-Yau 3-folds and G2-manifolds, and then prove the local version of the conjecture, which in turn implies the global version for an open subset of the moduli of K3 surfaces.</p>Wed, 23 Oct 2024 13:11:51 +0200Tue, 05 Nov 2024 17:00:00 +0100Tue, 05 Nov 2024 18:00:00 +0100<a target='_content' href="https://sites.google.com/stonybrook.edu/sesfahani/home">Saman Habibi Esfahani</a>Duke University<span lang='pt'>Geometria em Lisboa</span>Steven Senger, 2024/10/31, 13h 30m, Dot product problems in the fractal setting and barriers to current methods
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7379
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7379<p>We begin with a simply stated problem in discrete geometry: at least how many distinct dot products must be determined by a large finite set of points in the plane? This is related to some well-studied problems of Erdos about distances. The distance problems have celebrated variants in the fractal setting, such as the Falconer distance problem, which have seen significant progress in recent years. However, the analogous problems for dot products in the fractal setting have not moved past the most fundamental results. We discuss the barriers to current methods, in hopes of motivating new approaches to overcome these barriers.</p>Thu, 17 Oct 2024 09:33:49 +0200Thu, 31 Oct 2024 14:30:00 +0100Thu, 31 Oct 2024 15:30:00 +0100<a target='_content' href="https://math.missouristate.edu/profile-display.aspx?p=StevenSenger">Steven Senger</a>Missouri State UniversityRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsMatteo Quattropani, 2024/10/30, 16h, Cutoff at the entropic time for Repeated Block Averages
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7383
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7383<p><meta charset="UTF-8" /></p><p>The Averaging process (a.k.a. repeated averages) is a redistribution model over the vertex set of a graph. Given a graph G, the process starts with a non-negative mass associated to each vertex. At each discrete time an edge is sampled uniformly at random, and the masses at the two extremes of the edge are equally redistributed on these two vertices. Clearly, as time grows to infinity, the state of the system will converge (in some sense) to a flat configuration in which all the vertices have the same mass. Despite the simplicity of its formulation, even in the case of seemingly straightforward geometries—such as the complete graph or the 1-d torus— the analysis of the mixing behavior of this process can be handled only by means of non trivial probabilistic and functional analytic techniques. In the talk I will focus on the (mean-field) hypergraph case, in which edges are replaced by a more general notion of “blocks”. I will discuss the speed of convergence to equilibrium as a function of the blocks size, providing sharp conditions for the emergence of the cutoff phenomenon, i.e., a dynamical phase transition in which equilibrium is reached abruptly on a given time scale.</p><p>The talk is based on joint works with Pietro Caputo (Roma) and Federico Sau (Trieste).</p>Tue, 22 Oct 2024 15:34:53 +0200Wed, 30 Oct 2024 17:00:00 +0100Wed, 30 Oct 2024 18:00:00 +0100Matteo QuattropaniUniversity of Roma (Tor Vergata)Probability and Stochastic AnalysisÖdül Tetik, 2024/10/30, 10h, Yoga with twisted stratifications
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7378
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7378<p>Linked spaces, originally motivated by applications to TQFTs, simultaneously simplify and generalise stratified spaces. I will briefly introduce the concept and the accompanying exit-path quasi-category construction. To exhibit the nontriviality of the generalisation, I will then consider some fundamental categories (as in "fundamental groupoid") of linked spaces and realise, from a "twist" of the complement of the trefoil knot with a point defect, a two-object category where the hom-set is the modular group PSL(2,Z) and argue that there is no stratified space with this fundamental category.</p>Sun, 03 Nov 2024 22:54:14 +0100Wed, 30 Oct 2024 11:00:00 +0100Wed, 30 Oct 2024 12:00:00 +0100<a target='_content' href="https://o-tetik.github.io/">Ödül Tetik</a>University of ViennaTopological Quantum Field TheoryIzabella Stuhl, 2024/10/23, 17h, Lattice hard-core Gibbs measures
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7385
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7385<p>Dense-packing problems on two and three dimensional lattices will be discussed, and their role will be shown in the analysis of the phase diagram of the hard-core model. Namely, high-density pure phases/extreme Gibbs distributions of the model are generated by certain ground states - in accordance with the Pirogov-Sinai theory - which are dense-packings for this model in the high-density regime.</p>Wed, 23 Oct 2024 03:38:25 +0200Wed, 23 Oct 2024 18:00:00 +0200Wed, 23 Oct 2024 19:00:00 +0200Izabella StuhlPennsylvania State UniversityProbability and Stochastic AnalysisHenrik Winther, 2024/10/18, 16h 15m, The Gap Phenomenon for Automorphisms of Parabolic Geometries
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7361
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7361<p>We consider and resolve the gap problem for global automorphisms of complex or real parabolic geometries. Concretely, the automorphism group of a parabolic geometry of type $(G, P)$ is largest for the flat model $G/P$. The symmetry dimension is maximal in this case and is equal to $\operatorname{dim} G$. We prove that the next realizable, so-called submaximal dimension of the automorphism group of a $(G, P)$ type geometry is the dimension of a (specific) maximal parabolic subgroup in $G$. We also discuss maximal and submaximal dimensions of the automorphism group of compact models and provide several examples. Joint work with B. Kruglikov.</p>Tue, 15 Oct 2024 07:45:56 +0200Fri, 18 Oct 2024 17:15:00 +0200Fri, 18 Oct 2024 18:00:00 +0200Henrik WintherArtic University of NorwayRoom 3.08, Building 6, Gualtar Campus, University of MinhoGEMS — Geometry MeetingsDario Di Pinto, 2024/10/18, 15h, Geometry and topology of anti-quasi-Sasakian manifolds
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7358
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7358<p>In the present talk I will introduce a new class of almost contact metric manifolds, called anti-quasi-Sasakian (aqS for short). They are non-normal almost contact metric manifolds $(M, φ, ξ, η, g)$, locally fibering along the 1-dimensional foliation generated by $ξ$ onto Kähler manifolds endowed with a closed 2-form of type $(2,0)$. Various examples of anti-quasi-Sasakian manifolds will be provided, including compact nilmanifolds, $\mathbb{S}^1$-bundles and manifolds admitting a $\operatorname{Sp}(n) × \{1\}$-reduction of the structural group of the frame bundle. Then, I will discuss some geometric obstructions to the existence of aqS structures, mainly related to curvature and topological properties. In particular, I will focus on compact manifolds endowed with aqS structures of maximal rank, showing that they cannot be homogeneous and they must satisfy some restrictions on the Betti numbers. This is based on joint works with Giulia Dileo (Bari) and Ivan Yudin (Coimbra).</p>Tue, 01 Oct 2024 08:04:00 +0200Fri, 18 Oct 2024 16:00:00 +0200Fri, 18 Oct 2024 16:45:00 +0200Dario Di PintoUniversidade de CoimbraRoom 3.08, Building 6, Gualtar Campus, University of MinhoGEMS — Geometry MeetingsPedro M. Silva, 2024/10/18, 14h, Projective structures and the geometry of the conformal limit
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7360
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7360<p>The classical non-abelian Hodge correspondence is a gauge-theoretic construction that has allowed for the use of complex geometric methods in the study of representations of the fundamental group of a closed surface. The conformal limit was introduced by Gaiotto as a parameterized variation of this classical correspondence. In this talk, we will explore how, in the case of representations into $\operatorname{SL}(2,\mathbb{C})$, this limit is related to complex projective structures. We will also use this relation to further our geometric understanding of the limiting process. This is joint work with Peter B. Gothen.</p>Thu, 17 Oct 2024 17:10:11 +0200Fri, 18 Oct 2024 15:00:00 +0200Fri, 18 Oct 2024 15:45:00 +0200Pedro M. SilvaUniversidade de LisboaRoom 3.08, Building 6, Gualtar Campus, University of MinhoGEMS — Geometry MeetingsJesús Oliver, 2024/10/18, 11h 30m, A vector field method for semilinear wave equations on FLRW spacetimes
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7380
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7380<p>The Friedman-Lemaître-Robertson-Walker (FLRW) spacetime is often called the <em>Standard Model</em> of modern cosmology. In this talk we discuss small data global existence of solutions to a family of nonlinear wave equations propagating on a fixed FLRW spacetime. The initial value problem here takes the form \begin{equation} \label{semiwave}\begin{cases}-\partial_t^2\phi-n\dot a({a}^{-1}\partial_t\phi) +a^{-2} \Delta \phi = \mathcal{N}(\partial\phi) , \\ \phi(t_0,x)=\phi_0(x), \quad\partial_t\phi(t_0,x)=\phi_1(x),<br />\end{cases}\end{equation} where $n\gt 2$, $t_0\gt 1$, and $\mathcal{N}$ is a nonlinear function depending (at most) quadratically on derivatives of $\phi$. We consider cosmologies undergoing an accelerated expansion in the direction of positive time \[ a(t)\gt 0 , \qquad \dot a(t)\gt 0, \quad {\text{ and }} \int_{t_0}^{\infty} \frac{1}{a(s)} ds\lt \infty.\] By pairing weighted energy estimates with favorable structure on $\mathcal{N}$, we show how one can establish global wellposedness and sharp decay for solutions to a suitable class of equations of the form \eqref{semiwave}. We also discuss how this method can be extended to the case of nonaccelerated expanding FLRW spacetimes.</p>Wed, 16 Oct 2024 10:46:34 +0200Fri, 18 Oct 2024 12:30:00 +0200Fri, 18 Oct 2024 13:30:00 +0200Jesús OliverCalifornia State University, East BayRoom P4.35, Mathematics BuildingMathematical RelativityViviana del Barco, 2024/10/18, 11h 30m, $G_2$-instantons on nilpotent Lie groups
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7359
https://math.tecnico.ulisboa.pthttps://gems.math.tecnico.ulisboa.pt/seminars?action=show&id=7359<p>In this talk we will discuss recent advancements on $G_2$-instantons on 7-dimensional 2-step nilpotent Lie groups endowed with a left-invariant coclosed $G_2$-structures. I will present necessary and sufficient conditions for the characteristic connection of the $G_2$-structure to be an instanton, in terms of the torsion of the $G_2$-structure, the torsion of the connection and the Lie group structure. These conditions allow to show that the metrics corresponding to the $G_2$-instantons define a naturally reductive structure on the simply connected 2-step nilpotent Lie group with left-invariant Riemannian metric. This is a joint work with Andrew Clarke and Andrés Moreno.</p>Thu, 19 Sep 2024 14:10:05 +0200Fri, 18 Oct 2024 12:30:00 +0200Fri, 18 Oct 2024 13:15:00 +0200Viviana del BarcoUniversidade Estadual de CampinasRoom 3.08, Building 6, Gualtar Campus, University of MinhoGEMS — Geometry MeetingsAldo Pratelli, 2024/10/17, 13h 30m, Small minimal clusters in Riemannian (or Finsler) manifolds
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7374
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7374<p>Since a Riemannian manifold is locally similar to the Euclidean space, it is easy to see that isoperimetric sets of small volume in such a manifold are very close to balls, and in particular they are connected. Much less is known for the case of minimal clusters. In this talk, we will describe the general situation and we will present a recent result showing that also small minimal clusters are connected if the ambient space is a compact Riemannian manifold. In addition, we will discuss also the situation for Finsler manifolds, showing that a small minimal m-cluster can have at most m connected components. While it might seem reasonable that also in this case small minimal clusters are connected, we will present an example showing that this is not true. We will conclude by listing some open problems. (Most of the presented results are based on joint works with D. Carazzato and S. Nardulli).</p><p> </p>Fri, 11 Oct 2024 06:13:05 +0200Thu, 17 Oct 2024 14:30:00 +0200Thu, 17 Oct 2024 15:30:00 +0200<a target='_content' href="http://pagine.dm.unipi.it/pratelli/">Aldo Pratelli</a>Università di PisaRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsAlan Hammond, 2024/10/16, 17h, The Trail Of Lost Pennies: random turn games governed by stakes
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7381
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7381<p>In 1987, Harris and Vickers [HV87] proposed a model of a race in which two firms invest resources, each trying to be the first to secure a patent. They called the model tug of war. A counter moves randomly left or right on an integer interval, with the odds of a rightward move at each turn determined by the resources expended by each of the firms at the turn. The game ends when the counter reaches one or another end of the interval, the patent thus accorded to one or another firm. In 2009, Peres, Schramm, Sheffield and Wilson [PSSW09] independently introduced a similar game, which they also named tug of war. Two players also push a counter on a board, with a trivial rule for turn victor selection, via the toss of a fair coin; but also with a much richer geometric setting: by considering the game played in the limit of small step size in a domain in Euclidean space, the value of the game was found to be infinity harmonic, namely to satisfy an infinity version of the usual Laplace equation. These two works, HV87 and PSSW09, have unleashed two big but thus far non-interacting waves of attention, from economists and mathematicians respectively. In this talk, we will discuss the Trail of Lost Pennies, which is a tug-of-war game played on the integers in which the resources that each player expends during the game are deducted from her terminal receipt. The solution of this game is remarkably sensitive to the relative incentives of the two players, with a change in incentive of order $10^{-4}$ being sufficient to fundamentally alter outcomes. Overall we will indicate how stake-governed tug-of-war may weave the two strands of research in economics and mathematics, with the geometrically richer mathematical setting being allied to the resource-based rules for turn victor that is characteristic of the economics research strand.</p>Tue, 15 Oct 2024 12:12:25 +0200Wed, 16 Oct 2024 18:00:00 +0200Wed, 16 Oct 2024 19:00:00 +0200Alan HammondUC BerkeleyProbability and Stochastic AnalysisWilliam Stewart, 2024/10/16, 10h, Domain walls and oplax natural transformations
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7357
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7357<p>I will review the notion of a topological (or gapped) domain wall between topological quantum field theories and illustrate an equivalence between domain walls and oplax natural transformations. I will show how this provides a reformulation of Lurie's cobordism hypothesis with singularities.</p>Sat, 19 Oct 2024 11:23:53 +0200Wed, 16 Oct 2024 11:00:00 +0200Wed, 16 Oct 2024 12:00:00 +0200<a target='_content' href="https://www.wbstewart.com/bio">William Stewart</a>Technical University of MunichTopological Quantum Field TheoryGabriel Nahum, 2024/10/09, 17h, Generalized Porous Media Model
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7377
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7377<p>In this talk, I am going to present a generalization of the Porous Media Model (PMM) analogue of the Bernstein polynomial basis, in the context of gradient models. The PMM is a symmetric nearest-neighbour process associated with the Porous Media Equation, and the corresponding dynamics are kinetically constrained, in the sense that particles diffuse in the lattice under a set of conditions on local configurations. While in the PMM, the occupation values of two neighbouring sites are exchanged only if there are "enough" groups of particles around them, our generalized model describes a system where, at very low densities, there is no interaction, while at high densities, there is no space for movement. I am going to present the construction of the model and its main properties, and, if time permits, discuss its extension in a long-range interaction context.</p>Tue, 08 Oct 2024 13:06:02 +0200Wed, 09 Oct 2024 18:00:00 +0200Wed, 09 Oct 2024 19:00:00 +0200Gabriel NahumINRIA LyonProbability and Stochastic AnalysisPeter Kristel, 2024/10/09, 10h, 2-vector bundles
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7353
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7353<p>I will introduce the notion of 2-vector bundles, which are a categorified version of vector bundles. This notion is based on the idea that the bicategory of 2-vector spaces is the bicategory of algebras, bimodules, and intertwiners. I will recall the definition of that bicategory, which leads into the definition of 2-vector bundles. As time permits, I will discuss connections to string geometry, and extended TQFT, and classifying results. This is all based on work with Matthias Ludewig and Konrad Waldorf.</p>Sat, 19 Oct 2024 11:21:25 +0200Wed, 09 Oct 2024 11:00:00 +0200Wed, 09 Oct 2024 12:00:00 +0200<a target='_content' href="http://peterkristel.com/">Peter Kristel</a>Hausdorff Center for MathematicsTopological Quantum Field TheoryOscar Reula, 2024/10/04, 14h 30m, Relativistic Dissipative Fluids
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7369
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7369<p> </p><p>In general relativity we don't have any preferred time function, so we can not have infinite propagation speeds. Thus, parabolic systems like the Navier-Stokes equations are not possible. To overcome this several proposals for admissible theories have been put forward in the past. Notably, the first ones were ill posed, namely a small variation on the initial data produced huge differences on the solutions. Fortunately new proposals have arisen which are well posed. Here we discuss one of them. In particular we shall concentrate on one describing conformally invariant fluids, the limit when the particle's mass is much smaller than their thermal speeds. In this case the universe of possible theories collapses to a four parameter family, only one of them related to the propagation speeds of the system. This case is well posed. We shall further discuss some simulations exploring these free parameter variations and some efforts to construct algorithms to automatically generate computer codes for solving them.</p>Tue, 01 Oct 2024 13:24:38 +0200Fri, 04 Oct 2024 15:30:00 +0200Fri, 04 Oct 2024 16:30:00 +0200Oscar ReulaUniversidad Nacional de CórdobaSeminar room (2.8.3), Physics BuildingMathematical RelativityCarsten Gundlach, 2024/10/03, 15h, The interplay of mathematics and numerics in understanding naked singularity formation in critical collapse
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7368
https://math.tecnico.ulisboa.pthttps://mr.math.tecnico.ulisboa.pt/seminars?action=show&id=7368<p>I will give an overview of numerical evidence that codimension one-sets of smooth initial data for matter coupled to GR form naked singularities – from scalar fields and fluids in spherical symmetry, where the evidence is strong, to vacuum GR, where the evidence is still confusing, but at least now beginning to be agreed by independent codes. Can one hope to prove some form of this naked singularity conjecture? In the last ten years or so, there has been considerable mathematical progress on the existence and stability of smooth self-similar blowup solutions in dispersive PDEs, and on naked singularity formation in GR. I will highlight some of these papers that particularly interest me as steps on the way to a future proof of naked singularity formation from codimension-one smooth initial data.</p>Mon, 30 Sep 2024 10:24:25 +0200Thu, 03 Oct 2024 16:00:00 +0200Thu, 03 Oct 2024 17:00:00 +0200Carsten GundlachUniversity of SouthamptonMathematical RelativityDaniel Kious, 2024/10/02, 17h, Sharp threshold for the ballisticity of the random walk on the exclusion process
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7366
https://math.tecnico.ulisboa.pt/seminars/ps?action=show&id=7366<p>In this talk, I will overview works on random walks in dynamical random environments. I will recall a result obtained in collaboration with Hilario and Teixeira and then I will focus on a work with Conchon--Kerjan and Rodriguez. Our main interest is to investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, with density in [0,1]. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole. We prove that the speed of the walk, seen as a function of the density, exists for all density but at most one, and that it is strictly monotonic. We will explain how this can be seen as a sharpness result and provide an outline of the proof, whose general strategy is inspired by techniques developed for studying the sharpness of strongly-correlated percolation models.</p>Thu, 26 Sep 2024 21:22:43 +0200Wed, 02 Oct 2024 18:00:00 +0200Wed, 02 Oct 2024 19:00:00 +0200Daniel KiousUniversity of BathProbability and Stochastic AnalysisJoão Pedro Ramos, 2024/10/02, 14h, Time-frequency representations and optimal concentration inequalities
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7355
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7355<p>A fundamental question in mathematical analysis, with consequences to fields such as partial differential equations, mathematical physics, signal processing and many others, is that of simultaneous time-frequency concentration of signals. More specifically: given a set $Ω = I × J ⊂ \mathbb{R}^2$, how much information can be inferred about $f$ from its measurements on $I$, and measurements of its Fourier transform on $J$?</p><p>As classically known, the Uncertainty Principle prevents sharp localization, but one may hope to obtain suitably `almost-localized' signals if the underlying sets $Ω$ considered are large enough. The topic of how much of such a localization is achievable has been extensively studied by several authors, such as I. Daubechies, Y. Meyer, D. Donoho, C. Fefferman and many others, leading to the development of the theory of Wavelets and that of the Short-time Fourier transform.</p><p>In this talk, we shall highlight recent developments on concentration results for time-frequency representations, with emphasis on the cases of the Short-time Fourier and Wavelet transforms. Our main goal will be to understand the Nicola-Tilli theorem on sharp concentration for the Gabor transform, its recent stability version, and other generalizations thereof, with a focus on open problems and possible future directions.</p>Wed, 02 Oct 2024 06:58:21 +0200Wed, 02 Oct 2024 15:00:00 +0200Wed, 02 Oct 2024 16:00:00 +0200<a target='_content' href="https://sites.google.com/view/gionnoramos/">João Pedro Ramos</a>École Polytechnique Fédérale de LausanneRoom 6.2.33, Faculty of Sciences of the Universidade de LisboaLisbon WADE — Webinar in Analysis and Differential EquationsDario Di Pinto, 2024/10/01, 16h, Geometry and topology of anti-quasi-Sasakian manifolds
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7356
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7356<p>In the present talk I will introduce a new class of almost contact metric manifolds, called <em>anti-quasi-Sasakian </em>(<em>aqS</em> for short). They are non-normal almost contact metric manifolds $(M,φ,ξ,η,g)$, locally fibering along the 1-dimensional foliation generated by $ξ$ onto <meta charset="UTF-8" />Kähler manifolds endowed with a closed 2-form of type (2,0). Various examples of anti-quasi-Sasakian manifolds will be provided, including compact nilmanifolds, $\mathbb{S}^1$-bundles and manifolds admitting a $\operatorname{Sp}(n)\times \{1\}$-reduction of the structural group of the frame bundle. Then, I will discuss some geometric obstructions to the existence of <em>aqS</em> structures, mainly related to curvature and topological properties. In particular, I will focus on compact manifolds endowed with <em>aqS</em> structures of maximal rank, showing that they cannot be homogeneous and they must satisfy some restrictions on the Betti numbers.</p><p>This is based on joint works with Giulia Dileo (Bari) and Ivan Yudin (Coimbra).</p><h4>References</h4><ol><li>D. Di Pinto, <em>On anti-quasi-Sasakian manifolds of maximal rank</em> J. Geom. Phys. <strong>200 </strong>(2024), Paper no. 105174, 10 pp.</li><li>D. Di Pinto, G. Dileo, <em>Anti-quasi-Sasakian manifolds</em>, Ann. Global Anal. Geom. <strong>64</strong> (1), Article no. 5 (2023), 35 pp.</li></ol>Fri, 04 Oct 2024 13:36:54 +0200Tue, 01 Oct 2024 17:00:00 +0200Tue, 01 Oct 2024 18:00:00 +0200<a target='_content' href="https://cmuc.mat.uc.pt/rdonweb/person/ppgeral.do?idpessoa=1425">Dario Di Pinto</a>CMUC, Universidade de CoimbraRoom P3.10, Mathematics Building<span lang='pt'>Geometria em Lisboa</span>Makson Santos, 2024/09/26, 13h 30m, Regularity theory for fully nonlinear nonlocal equations
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7354
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7354<p>In this talk, we investigate the regularity properties of solutions to a class of fully nonlinear nonlocal equations, both elliptic and degenerate. For the elliptic case, we establish optimal regularity results for equations with a right-hand side in $L^p$, where the regularity space depends on the value of $p$. In the degenerate case, we prove the existence of at least one viscosity solution belonging to the class $C_{loc}^{1, \alpha}$ for some constant $\alpha \in (0,1)$. Additionally, when the order of the operator is sufficiently close to 2, we derive regularity estimates in Hölder spaces for the gradient of any viscosity solution.</p>Thu, 19 Sep 2024 13:24:22 +0200Thu, 26 Sep 2024 14:30:00 +0200Thu, 26 Sep 2024 15:30:00 +0200<a target='_content' href="https://sites.google.com/view/makson-santos">Makson Santos</a>CEMS.UL / CMAFcIORoom 6.2.33, Faculty of Sciences of the Universidade de LisboaLisbon WADE — Webinar in Analysis and Differential EquationsSinai Robins, 2024/09/26, 10h, Introduction to Fourier methods for polytopes and cones
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7352
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7352<p>This short course is an introduction to the nascent field of Fourier analysis on polytopes and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the field.</p><p>Of the many applications of these techniques, we will focus on the following, as time permits:</p><ol><li>The Fourier transform of a polytope, given its vertex description</li><li>Minkowski and Siegel's theorems in the geometry of numbers</li><li>Tilings and multi-tilings of Euclidean space by translations of a polytope</li><li>Discrete volumes of polytopes (Ehrhart theory)</li><li>The Fourier transform of a polytope, given its hyperplane description. Here we iterate the divergence theorem.</li></ol><p>We assume familiarity with linear algebra, calculus and infinite series. Throughout, we introduce the topics gently, by giving examples and exercises.</p>Tue, 10 Sep 2024 15:11:41 +0200Thu, 26 Sep 2024 11:00:00 +0200Thu, 26 Sep 2024 12:30:00 +0200<a target='_content' href="https://sites.google.com/site/sinairobins">Sinai Robins</a>IME, Universidade de São PauloRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsSinai Robins, 2024/09/25, 10h 30m, Introduction to Fourier methods for polytopes and cones
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7351
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7351<p>This short course is an introduction to the nascent field of Fourier analysis on polytopes and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the field.</p><p>Of the many applications of these techniques, we will focus on the following, as time permits:</p><ol><li>The Fourier transform of a polytope, given its vertex description</li><li>Minkowski and Siegel's theorems in the geometry of numbers</li><li>Tilings and multi-tilings of Euclidean space by translations of a polytope</li><li>Discrete volumes of polytopes (Ehrhart theory)</li><li>The Fourier transform of a polytope, given its hyperplane description. Here we iterate the divergence theorem.</li></ol><p>We assume familiarity with linear algebra, calculus and infinite series. Throughout, we introduce the topics gently, by giving examples and exercises.</p>Tue, 10 Sep 2024 15:13:20 +0200Wed, 25 Sep 2024 11:30:00 +0200Wed, 25 Sep 2024 13:00:00 +0200<a target='_content' href="https://sites.google.com/site/sinairobins">Sinai Robins</a>IME, Universidade de São PauloRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsSinai Robins, 2024/09/24, 10h 30m, Introduction to Fourier methods for polytopes and cones
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7350
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7350<p>This short course is an introduction to the nascent field of Fourier analysis on polytopes and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the field.</p><p>Of the many applications of these techniques, we will focus on the following, as time permits:</p><ol><li>The Fourier transform of a polytope, given its vertex description</li><li>Minkowski and Siegel's theorems in the geometry of numbers</li><li>Tilings and multi-tilings of Euclidean space by translations of a polytope</li><li>Discrete volumes of polytopes (Ehrhart theory)</li><li>The Fourier transform of a polytope, given its hyperplane description. Here we iterate the divergence theorem.</li></ol><p>We assume familiarity with linear algebra, calculus and infinite series. Throughout, we introduce the topics gently, by giving examples and exercises.</p>Tue, 10 Sep 2024 15:14:40 +0200Tue, 24 Sep 2024 11:30:00 +0200Tue, 24 Sep 2024 13:00:00 +0200<a target='_content' href="https://sites.google.com/site/sinairobins">Sinai Robins</a>IME, Universidade de São PauloRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsSinai Robins, 2024/09/23, 10h 30m, Introduction to Fourier methods for polytopes and cones
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7349
https://math.tecnico.ulisboa.pthttps://samgsd.math.tecnico.ulisboa.pt/seminars?action=show&id=7349<p>This short course is an introduction to the nascent field of Fourier analysis on polytopes and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the field.</p><p>Of the many applications of these techniques, we will focus on the following, as time permits:</p><ol><li>The Fourier transform of a polytope, given its vertex description</li><li>Minkowski and Siegel's theorems in the geometry of numbers</li><li>Tilings and multi-tilings of Euclidean space by translations of a polytope</li><li>Discrete volumes of polytopes (Ehrhart theory)</li><li>The Fourier transform of a polytope, given its hyperplane description. Here we iterate the divergence theorem.</li></ol><p>We assume familiarity with linear algebra, calculus and infinite series. Throughout, we introduce the topics gently, by giving examples and exercises.</p>Tue, 10 Sep 2024 15:15:08 +0200Mon, 23 Sep 2024 11:30:00 +0200Mon, 23 Sep 2024 13:00:00 +0200<a target='_content' href="https://sites.google.com/site/sinairobins">Sinai Robins</a>IME, Universidade de São PauloRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsSalvador López Martínez, 2024/09/19, 13h 30m, Dark soliton solutions to the Nonlinear Schrödinger Equation
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7348
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7348<p>Solitons are relevant structures in nonlinear physics that appear in several contexts such as nonlinear optics and Bose-Einstein condensation. They are localized waves which travel without changing shape, even after eventual collisions between them. Specifically, dark solitons represent traveling local minima of the density (in contrast to local maxima for the bright ones).</p><p>In the talk, I will discuss some analytical results on the existence and properties of dark soliton solutions to the Nonlinear Schrödinger Equation, which is the most usual model for describing Bose-Einstein condensation and light propagation in optical fibers. I will focus on the more recent advances concerning the nonlocal version of the NSE, which is intended to capture nonlocal physical interactions. I will finish by presenting some open problems.</p>Thu, 19 Sep 2024 15:16:49 +0200Thu, 19 Sep 2024 14:30:00 +0200Thu, 19 Sep 2024 15:30:00 +0200<a target='_content' href="https://portalcientifico.uam.es/es/ipublic/researcher/331485">Salvador López Martínez</a>Universidad Autónoma de MadridRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsThang Le, 2024/09/18, 17h, Algebraic structures of skein algebras
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7346
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7346<p>We will survey some results of stated $SL_n$ skein algebras and show how to use them to study the ordinary skein algebras of surfaces. We will discuss the integrality of the skein algebra, the injectivity of the cutting homomorphism, and the structure of the skein algebras of the bigon and the triangle. The talk is based on joint work with F. Costantino, J. Korinman, A. Sikora, and T. Yu.</p>Tue, 24 Sep 2024 13:35:17 +0200Wed, 18 Sep 2024 18:00:00 +0200Wed, 18 Sep 2024 19:00:00 +0200<a target='_content' href="https://letu.math.gatech.edu/">Thang Le</a>Georgia Institute of TechnologyTopological Quantum Field TheoryChris Elliott, 2024/09/11, 16h, Topological twists of superconformal field theory
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7345
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7345<p>In quantum field theory, "twisting" is a procedure for producing new theories from old, where the new theories have particularly nice symmetry properties (for example, topological quantum field theories). The twisting construction involves the choice of a nilpotent element of a super Lie algebra that acts on the theory. I will discuss joint work with Owen Gwilliam and Matteo Lotito on twisting for theories with an action of a superconformal algebra and the appearance of interesting algebraic structures such as vertex algebras and $E_n$ algebras.</p>Sat, 14 Sep 2024 10:05:18 +0200Wed, 11 Sep 2024 17:00:00 +0200Wed, 11 Sep 2024 18:00:00 +0200<a target='_content' href="https://chrisjelliott.github.io/">Chris Elliott</a>Amherst CollegeTopological Quantum Field TheoryRaphaël Rouquier, 2024/09/04, 17h, 2-Representation theory of gl(1|1)
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7344
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7344<p>2-Representations of simple Lie algebras are expected to lead to 4-dimensional TQFTs, as envisioned by Crane and Frenkel. The tensor product of 2-representations introduces homotopical phenomena which disappear when considering instead the case of the super Lie algebra gl(1|1). I will discuss how to construct parts of the structure of a braided monoidal 2-category associated to gl(1|1), and how this compares with the known 4-dimensional Heegaard–Floer TQFT.</p>Sat, 14 Sep 2024 10:03:04 +0200Wed, 04 Sep 2024 18:00:00 +0200Wed, 04 Sep 2024 19:00:00 +0200<a target='_content' href="https://www.math.ucla.edu/~rouquier/">Raphaël Rouquier</a>University of California, Los AngelesTopological Quantum Field TheoryColleen Delaney, 2024/08/28, 17h, An efficient* classical algorithm for some quantum invariants of 3-manifolds
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7343
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7343<p>We will share some recent results that are instructive for approaching the classification of 3d TQFTs and topological order by computational complexity. We show that the Turaev-Viro-Barrett-Westbury state sum TQFT invariants of 3-manifolds that arise from Tambara-Yamagami fusion categories can actually be computed in polynomial time on a classical computer, provided that there is a bound on the first Betti number. On the other hand, if we don’t insist on a bound on the first Betti number, then the invariants should be NP-hard to compute. This talk is based on joint work with Clément Maria and Eric Samperton.</p>Tue, 03 Sep 2024 19:18:36 +0200Wed, 28 Aug 2024 18:00:00 +0200Wed, 28 Aug 2024 19:00:00 +0200Colleen DelaneyPurdue UniversityTopological Quantum Field TheoryTashi Walde, 2024/08/21, 17h, Assembly of constructible factorization algebras
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7340
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7340<p>The theory of factorization algebras, and particularly that of constructible factorization algebras, is expected to be very well behaved. For example, it has long been “known” that the assignment taking a stratified manifold to its category of constructible factorization algebras satisfies gluing, i.e., is itself a sheaf. Unfortunately, this and other related facts about factorization algebras have long been “folklore knowledge”, but with no proofs available.</p><p>In this talk I will report on recent work with Eilind Karlsson and Claudia I. Scheimbauer, where we close some of these gaps in the literature, including the aforementioned gluing result.</p>Thu, 29 Aug 2024 10:29:52 +0200Wed, 21 Aug 2024 18:00:00 +0200Wed, 21 Aug 2024 19:00:00 +0200<a target='_content' href="https://www.math.cit.tum.de/en/algebra/personen/walde/">Tashi Walde</a>Technical University of MunichTopological Quantum Field TheoryClark Barwick, 2024/08/14, 17h, Factorization algebras in quite a lot of generality
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7312
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7312<p>In the last decade there has been a flurry of interest in <em>arithmetic quantum field theories</em>. Since the 1960s, researchers have identified an analogy between various objects of arithmetic geometry and low-dimensional manifolds. For example, Spec of a number ring “looks like” an open 3-manifold, and primes therein “are” embedded knots. This story has become known as <em>arithmetic topology</em>. The idea of arithmetic QFT is to enrich that analogy by importing tools from physics, just as with low-dimensional topology. One even dreams of using these tools to study number-theoretic questions (the behavior of L-functions, Langlands dualities, etc.).</p><p>But the objects of arithmetic geometry are not manifolds. The tools of topology and differential geometry do not work directly in arithmetic. So it’s unclear how to translate physical concepts to arithmetic settings.</p><p>To this end, we introduce a minimalist framework for factorization algebras, where the role of the spacetime manifold can be played by a geometric object of a very general sort. In retrospect, the main idea amounts to a categorification of Borcherds’ approach to vertex algebras.</p>Tue, 20 Aug 2024 10:53:33 +0200Wed, 14 Aug 2024 18:00:00 +0200Wed, 14 Aug 2024 19:00:00 +0200<a target='_content' href="https://www.maths.ed.ac.uk/~cbarwick/">Clark Barwick</a>University of EdinburghTopological Quantum Field TheoryDavid Ayala, 2024/08/07, 17h, Factorization homology of higher categories
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7329
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7329<p>The “alpha” version of factorization homology pairs framed <em>n</em>-manifolds with $E_n$-algebras. This construction generalizes the classical homology of a manifold, yields novel results concerning configuration spaces of points in a manifold, and supplies a sort of state-sum model for sigma-models (i.e., mapping spaces) to (<em>n</em>-1)-connected targets. This “alpha” version of factorization homology novelly extends Poincaré duality, shedding light on deformation theory and dualities among field theories. Being defined using homotopical mathematical foundations, “alpha” factorization homology is manifestly functorial and continuous in all arguments, notably in moduli of manifolds and embeddings between them, and it satisfies a local-to-global expression that is inherently homotopical in nature.</p><p>Now, $E_n$-algebras can be characterized as $(∞,n)$-categories equipped with an (<em>n</em>-1)-connected functor from a point. The (full) “beta” version of factorization homology pairs framed <em>n</em>-manifolds with pointed $(∞,n)$-categories with adjoints. Applying 0th homology, or $π_0$, recovers a version of the string net construction on surfaces, as well as skein modules of 3-manifolds. In some sense, the inherently homotopical nature of (full) “beta” factorization homology affords otherwise unforeseen continuity in all arguments, and local-to-global expressions.</p><p>In this talk, I will outline a definition of “beta” factorization homology, focusing on low-dimensions and on suitably reduced $(∞,n)$-categories (specifically, braided monoidal categories). I will outline some examples, and demonstrate some features of factorization homology. Some of this material is established in the literature, some a work in progress, and some conjectural — the status of each assertion will be made clear. I will be especially interested in targeting this talk to those present, and so will welcome comments and questions.</p>Mon, 12 Aug 2024 22:22:11 +0200Wed, 07 Aug 2024 18:00:00 +0200Wed, 07 Aug 2024 19:00:00 +0200<a target='_content' href="https://math.montana.edu/dayala/">David Ayala</a>Montana State UniversityTopological Quantum Field TheoryJackson Van Dyke, 2024/07/31, 17h, Geometric quantization, fusion categories, and Rozansky–Witten theory
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7335
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7335<p>I will begin by reviewing geometric and deformation quantization of a symplectic vector space. The goal will be to explain an analogy between these objects and Rozansky–Witten theory (along with a certain four-dimensional TQFT). This analogy will factor through an analogy concerning three-dimensional TQFTs generated by pointed fusion categories. Throughout, there will be an emphasis on equivariance and anomalies.</p><p> </p>Mon, 05 Aug 2024 14:26:04 +0200Wed, 31 Jul 2024 18:00:00 +0200Wed, 31 Jul 2024 19:00:00 +0200<a target='_content' href="https://jacksontvandyke.com/">Jackson Van Dyke</a>Technical University of MunichTopological Quantum Field TheoryAnton Kapustin, 2024/07/24, 17h, Topological invariants of gapped states and cosheaves on sites
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7311
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7311<p>Recently, an approach to constructing topological invariants of gapped ground-states of lattice systems has been developed in our joint work with N. Sopenko. It applies to arbitrary gapped states of infinite-volume lattice spin systems with rapidly decaying interactions and employs C*-algebraic techniques. In this talk, I will explain an interpretation of these invariants as obstructions to gauging, i.e. to promoting a symmetry to a local symmetry. The key observation is that locality on a lattice is an asymptotic notion sensitive only to the large-scale geometry of the support set. Following Kashiwara and Schapira, one can encode locality using a natural Grothendieck topology on a category of semilinear subsets of Eucludean space. Infinitesimal symmetries of a gapped state form a cosheaf over the corresponding site, and the topological invariants are encoded in its Cech complex.</p>Sun, 04 Aug 2024 11:54:47 +0200Wed, 24 Jul 2024 18:00:00 +0200Wed, 24 Jul 2024 19:00:00 +0200<a target='_content' href="http://theory.caltech.edu/~kapustin/">Anton Kapustin</a>CaltechTopological Quantum Field TheoryMonica Vazirani, 2024/07/17, 17h, Skeins on tori
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7327
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7327<p>We study skeins on the 2-torus and 3-torus via the representation theory of the double affine Hecke algebra of type A and its connection to quantum D-modules. As an application we can compute the dimension of the generic $\operatorname{SL}_N$- and $\operatorname{GL}_N$-skein module of the 3-torus for arbitrary $N$. This is joint work with Sam Gunningham and David Jordan.</p>Sun, 04 Aug 2024 11:54:47 +0200Wed, 17 Jul 2024 18:00:00 +0200Wed, 17 Jul 2024 19:00:00 +0200Monica VaziraniUniversity of California, DavisTopological Quantum Field TheoryDiogo Oliveira e Silva, 2024/07/16, 16h, Sharp extension inequalities on finite fields
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7210
https://math.tecnico.ulisboa.pthttps://geolis.math.tecnico.ulisboa.pt/seminars?action=show&id=7210<p>Sharp restriction theory and the finite field extension problem have both received much attention in the last two decades, but so far they have not intersected. In this talk, we discuss our first results on sharp restriction theory on finite fields. Even though our methods for dealing with paraboloids and cones borrow some inspiration from their euclidean counterparts, new phenomena arise which are related to the underlying arithmetic and discrete structures. The talk is based on recent joint work with Cristian González-Riquelme (<a href="https://arxiv.org/abs/2405.16647">https://arxiv.org/abs/2405.16647</a>)</p>Sun, 04 Aug 2024 11:54:47 +0200Tue, 16 Jul 2024 17:00:00 +0200Tue, 16 Jul 2024 18:00:00 +0200<a target='_content' href="https://www.math.tecnico.ulisboa.pt/~oliveiraesilva/index.html">Diogo Oliveira e Silva</a>Instituto Superior TécnicoRoom P3.10, Mathematics Building<span lang='pt'>Geometria em Lisboa</span>Minghao Wang, 2024/07/10, 15h, Feynman graph integrals from topological-holomorphic theories and their applications
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7244
https://math.tecnico.ulisboa.pthttps://tqft.math.tecnico.ulisboa.pt/seminars?action=show&id=7244<p>Feynman graph integrals of topological field theories have been proved to be ultraviolet finite by Axelrod and Singer, and Kontsevich independently. This result leads to many applications including universal finite type knot invariants and the formality of $E_n$ operads. In this talk, I will extend the finiteness results (and some anomaly cancellation results) to Feynman graph integrals of topological-holomorphic theories on flat spaces. The main technique for the proof is compactification of the moduli space of metric graphs. As a result, we can construct many factorization algebras from quantum topological-holomorphic theories. In the special case of 4d Chern–Simons theory, the factorization algebra structure encodes the Yang–Baxter equation. If time permits, I will sketch how to extend these results to Feynman graph integrals on Kähler manifolds. Part of this work is joint with Brian Williams.</p><p>Reference: <a href="https://arxiv.org/abs/2401.08113">https://arxiv.org/abs/2401.08113</a></p><p> </p>Sun, 04 Aug 2024 11:54:47 +0200Wed, 10 Jul 2024 16:00:00 +0200Wed, 10 Jul 2024 17:00:00 +0200<a target='_content' href="https://www.bu.edu/math/profile/minghao-wang/">Minghao Wang</a>Boston UniversityTopological Quantum Field TheoryAndreia Chapouto, 2024/07/10, 14h 30m, Deep- and shallow-water limits of statistical equilibria for the intermediate long wave equation
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7310
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7310<p>The intermediate long wave equation (ILW) models the internal wave propagation of the interface in a stratified fluid of finite depth, providing a natural connection between two famous water-wave equations: the Benjamin-Ono equation (= the deep-water regime) and the Korteweg-de Vries equation (= the shallow-water regime).</p><p>I will discuss how to exploit the completely integrable nature of the equation to establish the statistical convergence of ILW to both BO and KdV, namely, the convergence of the higher order conservation laws for ILW and of their associated invariant measures. Here, we observe a stark contrast between the two regimes, with distinct modes of convergence as well as a novel 2-to-1 collapse of the invariant ILW dynamics to the corresponding invariant KdV dynamics.</p>Sun, 04 Aug 2024 11:54:47 +0200Wed, 10 Jul 2024 15:30:00 +0200Wed, 10 Jul 2024 16:30:00 +0200<a target='_content' href="https://www.maths.ed.ac.uk/~achapouto/">Andreia Chapouto</a>University of EdinburghRoom P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsBenedetta Pellacci, 2024/07/10, 13h 30m, Singular analysis in spectral optimization problems arising in logistic models: New achievements
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7268
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt/seminars?action=show&id=7268<p>We will discuss some recent results concerning weighted eigenvalue problems in bounded Lipschitz domains, under Neumann boundary conditions.</p><p>The optimization of the distribution of resources leads to minimize a principal eigenvalue with respect to the sign-changing weight. Important qualitative properties of the positivity set of the optimal weight, such as being connected, as well as its location, are still not known in general.</p><p>We will present some new achievements in the asymptotical study regarding these properties.</p><p>Joint works with Dario Mazzoleni (Università di Pavia), Lorenzo Ferreri (Scuola Normale Superiore di Pisa) and Gianmaria Verzini (Politecnico di Milano).</p>Sun, 04 Aug 2024 11:54:47 +0200Wed, 10 Jul 2024 14:30:00 +0200Wed, 10 Jul 2024 15:30:00 +0200<a target='_content' href="https://www.researchgate.net/profile/Benedetta-Pellacci">Benedetta Pellacci</a>Università degli Studi della Campania <em>Luigi Vanvitelli</em>Room P3.10, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsMarco Robalo, 2024/07/10, 10h, Introduction to Matrix Factorizations and mirror symmetry
https://math.tecnico.ulisboa.pthttps://slg.math.tecnico.ulisboa.pt/seminars/?action=show&id=7288
https://math.tecnico.ulisboa.pthttps://slg.math.tecnico.ulisboa.pt/seminars/?action=show&id=7288Sun, 04 Aug 2024 11:54:47 +0200Wed, 10 Jul 2024 11:00:00 +0200Wed, 10 Jul 2024 12:00:00 +0200<a target='_content' href="https://marco-robalo.perso.math.cnrs.fr">Marco Robalo</a>Institut de Mathématiques de Jussieu-Paris Rive GaucheRoom P3.10, Mathematics BuildingSummer Lectures in GeometryMarco Robalo, 2024/07/08, 10h, Introduction to shifted symplectic geometry via examples (cont.)
https://math.tecnico.ulisboa.pthttps://slg.math.tecnico.ulisboa.pt/seminars/?action=show&id=7287
https://math.tecnico.ulisboa.pthttps://slg.math.tecnico.ulisboa.pt/seminars/?action=show&id=7287Sun, 04 Aug 2024 11:54:47 +0200Mon, 08 Jul 2024 11:00:00 +0200Mon, 08 Jul 2024 12:00:00 +0200<a target='_content' href="https://marco-robalo.perso.math.cnrs.fr">Marco Robalo</a>Institut de Mathématiques de Jussieu-Paris Rive GaucheRoom P3.10, Mathematics BuildingSummer Lectures in Geometry