CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Gourab Ray, 2020/11/30, 17h, Universality of dimers via imaginary geometry
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5902
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5902Sat, 19 Sep 2020 10:48:16 +0200Mon, 30 Nov 2020 18:00:00 +0100Mon, 30 Nov 2020 19:00:00 +0100<a target='_content' href="https://sites.google.com/site/gourabmathematics/home">Gourab Ray</a>University of VictoriaQM<sup>3</sup> Quantum Matter meets MathsLeonardo Macarini, 2020/11/24, 17h, New consequences of convexity beyond dynamical convexity
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5870
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5870Fri, 21 Aug 2020 13:53:08 +0200Tue, 24 Nov 2020 18:00:00 +0100Tue, 24 Nov 2020 19:00:00 +0100<a target='_content' href="https://math.tecnico.ulisboa.pt/professor.php?who=lmacar&lang=en">Leonardo Macarini</a>Instituto Superior Técnico and CAMGSDGeometria em LisboaSilvia Anjos, 2020/11/17, 17h, Stability of the symplectomorphism group of rational surfaces
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5848
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5848Fri, 31 Jul 2020 15:06:35 +0200Tue, 17 Nov 2020 18:00:00 +0100Tue, 17 Nov 2020 19:00:00 +0100<a target='_content' href="https://www.math.tecnico.ulisboa.pt/~sanjos/">Silvia Anjos</a>Instituto Superior Técnico and CAMGSDGeometria em LisboaAna Rita Pires, 2020/11/10, 17h, Many more infinite staircases in symplectic embedding functions
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5866
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5866Fri, 21 Aug 2020 10:54:25 +0200Tue, 10 Nov 2020 18:00:00 +0100Tue, 10 Nov 2020 19:00:00 +0100<a target='_content' href="https://www.maths.ed.ac.uk/~apires/">Ana Rita Pires</a>University of EdinburghGeometria em LisboaJoseph Maciejko, 2020/10/26, 17h, Hyperbolic band theory
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5897
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5897<p>The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit QED, I will present a hyperbolic generalization of Bloch theory, based on ideas from Riemann surface theory and algebraic geometry. The theory is formulated despite the non-Euclidean nature of the problem and concomitant absence of commutative translation symmetries. The general theory will be illustrated by examples of explicit computations of hyperbolic Bloch wavefunctions and bandstructures.</p>Thu, 17 Sep 2020 18:06:05 +0200Mon, 26 Oct 2020 18:00:00 +0100Mon, 26 Oct 2020 19:00:00 +0100<a target='_content' href="https://sites.ualberta.ca/~maciejko/">Joseph Maciejko</a>University of AlbertaQM<sup>3</sup> Quantum Matter meets MathsBarry Simon, 2020/10/19, 13h, Berry's Phase, $\operatorname{TKN}^2$ Integers and All That: My work on Topology in Condensed Matter Physics 1983-1993
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5869
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5869<p>I will give an overview of my work on topological methods in condensed matter physics almost 40 years ago. Include will be Homotopy and $\operatorname{TKN}^2$ integers, holonomy and Berry's phase and quarternions and Berry's phase for Fermions. If time allows, I'll discuss supersymmetry and pairs of projections.</p>Tue, 18 Aug 2020 16:21:10 +0200Mon, 19 Oct 2020 14:00:00 +0200Mon, 19 Oct 2020 15:00:00 +0200<a target='_content' href="http://math.caltech.edu/simon/simon.html">Barry Simon</a>CaltechQM<sup>3</sup> Quantum Matter meets MathsXiuxiong Chen, 2020/10/13, 17h, On the space of Kähler metrics
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5868
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5868<p>Inspired by the celebrated $C^0, C^2$ and $C^3$ a priori estimate of Calabi, Yau and others on Kähler Einstein metrics, we will present an expository report of a priori estimates on the constant scalar curvature Kähler metrics. With this estimate, we prove the Donaldson conjecture on geodesic stability and the properness conjecture on Mabuchi energy functional.</p><p>This is a joint work with Cheng JingRui.</p>Wed, 19 Aug 2020 10:07:20 +0200Tue, 13 Oct 2020 18:00:00 +0200Tue, 13 Oct 2020 19:00:00 +0200<a target='_content' href="http://www.math.stonybrook.edu/~xiu/">Xiuxiong Chen</a>Stony Brook UniversityGeometria em LisboaMasud Haque, 2020/10/12, 17h, Eigenstate Thermalization, random matrices and (non)local operators in many-body systems
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5853
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5853<p>The eigenstate thermalization hypothesis (ETH) is a cornerstone in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators (observables) is an open question. I will address this question using an analogy with random matrix theory. The starting point will be the construction of extremely non-local operators, which we call Behemoth operators. The Behemoths turn out to be building blocks for all physical operators. This construction allow us to derive scalings for both local operators and different kinds of nonlocal operators.</p>Thu, 10 Sep 2020 14:39:56 +0200Mon, 12 Oct 2020 18:00:00 +0200Mon, 12 Oct 2020 19:00:00 +0200<a target='_content' href="https://www.pks.mpg.de/~haque/">Masud Haque</a>Maynooth UniversityQM<sup>3</sup> Quantum Matter meets MathsAlexander Shapiro, 2020/10/09, 17h, Cluster realization of quantum groups and higher Teichmüller theory
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5831
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5831Thu, 17 Sep 2020 18:37:47 +0200Fri, 09 Oct 2020 18:00:00 +0200Fri, 09 Oct 2020 19:00:00 +0200<a target='_content' href="https://math.berkeley.edu/~shapiro/">Alexander Shapiro</a>University of California, BerkeleyTopological Quantum Field TheoryÉveline Legendre, 2020/10/06, 17h, Localizing the Donaldson-Futaki invariant
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5847
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5847<p>We will see how to represent the Donaldson-Futaki invariant as an intersection of equivariant closed forms. We will use it to express this invariant as the intersection on some specific subvarieties of the central fibre of the test configuration. As an application we provide a proof that for Kähler orbifolds the Donaldson-Futaki invariant is the Futaki invariant of the central fiber.</p>Sun, 13 Sep 2020 22:16:07 +0200Tue, 06 Oct 2020 18:00:00 +0200Tue, 06 Oct 2020 19:00:00 +0200<a target='_content' href="https://www.math.univ-toulouse.fr/~elegendr/">Éveline Legendre</a>Université Paul SabatierGeometria em LisboaDavide Masoero, 2020/10/02, 17h, A solution of the Riemann-Hilbert problem on the $A_2$ quiver
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5824
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5824Thu, 17 Sep 2020 18:36:40 +0200Fri, 02 Oct 2020 18:00:00 +0200Fri, 02 Oct 2020 19:00:00 +0200<a target='_content' href="http://gfm.cii.fc.ul.pt/people/dmasoero/davide-home-page/">Davide Masoero</a>Group of Mathematical Physics, University of LisbonTopological Quantum Field TheoryHans Ringstrom, 2020/10/01, 14h 30m, On highly anisotropic big bang singularities
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5894
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5894<p>In cosmology, the universe is typically modelled by spatially homogeneous and isotropic solutions to Einstein’s equations. However, for large classes of matter models, such solutions are unstable in the direction of the singularity. For this reason, it is of interest to study the anisotropic setting.</p><p>The purpose of the talk is to describe a framework for studying highly anisotropic singularities. In particular, for analysing the asymptotics of solutions to linear systems of wave equations on the corresponding backgrounds and deducing information concerning the geometry.</p><p>The talk will begin with an overview of existing results. This will serve as a background and motivation for the problem considered, but also as a justification for the assumptions defining the framework we develop.</p><p>Following this overview, the talk will conclude with a rough description of the results.</p>Mon, 14 Sep 2020 09:04:24 +0200Thu, 01 Oct 2020 15:30:00 +0200Thu, 01 Oct 2020 16:30:00 +0200Hans RingstromKTHMathematical RelativityGonçalo Oliveira, 2020/09/29, 17h, Topology and the Yang Mills functional
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5844
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5844<p>The Yang-Mills functional is a physics-inspired functional for connections on vector/principal bundles. It is now almost 40 years since the, then groundbreaking, work of Atiyah and Bott extensively studying it on vector bundles over Riemann surfaces. The major outcome of this study was the relationship of its critical levels with the moduli spaces of holomorphic bundles, which allowed for results to flow in both directions of the relationship. Despite its success in that 2 dimensional setting and the 40 years that have since passed, few attempts at exploring the functional, and its critical points, in 3 dimensions were made. I will report on ongoing work with Alex Waldron and Thomas Walpuski towards a Morse theoretic approach for the Yang-Mills functional in 3 dimensional oriented Riemannian manifolds.</p><p>(joint work with Alex Waldron and Thomas Walpuski)</p>Sat, 29 Aug 2020 10:21:21 +0200Tue, 29 Sep 2020 18:00:00 +0200Tue, 29 Sep 2020 19:00:00 +0200<a target='_content' href="https://sites.google.com/view/goncalo-oliveira-math-webpage/home">Gonçalo Oliveira</a>Universidade Federal Fluminense, BrasilGeometria em LisboaTom Claeys, 2020/09/28, 17h, Deformed Airy kernel determinants: from KPZ tails to initial data for KdV
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5860
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5860<p>Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distribution in models of positive-temperature free fermions. I will explain how logarithmic derivatives of the Fredholm determinants can be expressed in terms of a $2\times 2$ Riemann-Hilbert problem.</p><p>This Riemann-Hilbert representation can be used to derive precise lower tail asymptotics for the solution of the KPZ equation with narrow wedge initial data, refining recent results by Corwin and Ghosal, and it reveals a remarkable connection with a family of unbounded solutions to the Korteweg-de Vries (KdV) equation and with an integro-differential version of the Painlevé II equation.</p>Sat, 15 Aug 2020 10:09:30 +0200Mon, 28 Sep 2020 18:00:00 +0200Mon, 28 Sep 2020 19:00:00 +0200<a target='_content' href="https://perso.uclouvain.be/tom.claeys/">Tom Claeys</a>Université Catholique de LouvainQM<sup>3</sup> Quantum Matter meets MathsAndré Henriques, 2020/09/25, 17h, Reps of relative mapping class groups via conformal nets
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5821
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5821<p>Given a surface with boundary $\Sigma$, its relative mapping class group is the quotient of $\operatorname{Diff}(\Sigma)$ by the subgroup of maps which are isotopic to the identity via an isotopy that fixes the boundary pointwise. (If $\Sigma$ has no boundary, then that's the usual mapping class group; if $\Sigma$ is a disc, then that's the group $\operatorname{Diff}(S^1)$ of diffeomorphisms of $S^1$.)</p><p>Conformal nets are one of the existing axiomatizations of chiral conformal field theory (vertex operator algebras being another one). We will show that, given an arbitrary conformal net and a surface with boundary $\Sigma$, we get a continuous projective unitary representation of the relative mapping class group (orientation reversing elements act by anti-unitaries). When the conformal net is rational and $\Sigma$ is a closed surface (i.e. $\partial \Sigma = \emptyset$), then these representations are finite dimensional and well known. When the conformal net is not rational, then we must require $\partial \Sigma \neq \emptyset$ for these representations to be defined. We will try to explain what goes wrong when $\Sigma$ is a closed surface and the conformal net is not rational.</p><p>The material presented in this talk is partially based on my paper <a href="https://arxiv.org/abs/1409.8672">arXiv:1409.8672</a> with Arthur Bartels and Chris Douglas.</p>Thu, 17 Sep 2020 18:36:23 +0200Fri, 25 Sep 2020 18:00:00 +0200Fri, 25 Sep 2020 19:00:00 +0200<a target='_content' href="https://www.maths.ox.ac.uk/people/andre.henriques">André Henriques</a>University of OxfordTopological Quantum Field TheoryYang Li, 2020/09/22, 17h, Weak SYZ conjecture for hypersurfaces in the Fermat family
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5867
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5867<p>The SYZ conjecture predicts that for polarised Calabi-Yau manifolds undergoing the large complex structure limit, there should be a special Lagrangian torus fibration. A weak version asks if this fibration can be found in the generic region. I will discuss my recent work proving this weak SYZ conjecture for the degenerating hypersurfaces in the Fermat family. Although these examples are quite special, this is the first construction of generic SYZ fibrations that works uniformly in all complex dimensions.</p>Thu, 03 Sep 2020 00:12:46 +0200Tue, 22 Sep 2020 18:00:00 +0200Tue, 22 Sep 2020 19:00:00 +0200<a target='_content' href="https://www.ias.edu/scholars/yang-li">Yang Li</a>Institute for Advanced StudyGeometria em LisboaGil Refael, 2020/09/21, 17h, Floquet higher-order topological insulators: principles and path towards realizations
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5854
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5854<p>The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, with different commutation/anticommutation relations with respect to non-spatial symmetries. In my talk I will review how these dynamical analogs of the static HOTI's emerge, and also show how a coherently excited phonon mode can be used to support non-trivial Floquet higher-order topological phases. If time allows, I will also review recent work on Floquet engineering and band flattening of twisted-bilayer graphene.</p>Mon, 14 Sep 2020 19:01:26 +0200Mon, 21 Sep 2020 18:00:00 +0200Mon, 21 Sep 2020 19:00:00 +0200<a target='_content' href="https://iqim.caltech.edu/profile/gil-refael/">Gil Refael</a>Institute for Quantum Information and MatterQM<sup>3</sup> Quantum Matter meets MathsNicolai Reshetikhin, 2020/09/18, 17h, Poisson sigma model and integrable systems
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5823
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5823Thu, 17 Sep 2020 18:36:01 +0200Fri, 18 Sep 2020 18:00:00 +0200Fri, 18 Sep 2020 19:00:00 +0200<a target='_content' href="https://math.berkeley.edu/~reshetik/">Nicolai Reshetikhin</a>University of California, BerkeleyTopological Quantum Field TheoryRobert Berman, 2020/09/15, 11h, Kähler-Einstein metrics, Archimedean Zeta functions and phase transitions
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5832
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5832<p>While the existence of a unique Kähler-Einstein metrics on a canonically polarized manifold $X$ was established already in the seventies there are very few explicit formulas available (even in the case of complex curves!). In this talk I will give a non-technical introduction to a probabilistic approach to Kähler-Einstein metrics, which, in particular, yields canonical approximations of the Kähler-Einstein metric on $X$. The approximating metrics in question are expressed as explicit period integrals and the conjectural extension to the case of a Fano variety leads to some intriguing connections with Zeta functions and the theory of phase transitions in statistical mechanics.</p>Sat, 19 Sep 2020 21:16:40 +0200Tue, 15 Sep 2020 12:00:00 +0200Tue, 15 Sep 2020 13:00:00 +0200<a target='_content' href="https://www.chalmers.se/en/staff/Pages/robertb.aspx">Robert Berman</a>Chalmers University of TechnologyGeometria em LisboaVincenzo Alba, 2020/09/14, 17h, Hydrodynamic framework for out-of-equilibrium entangled many-body systems
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5851
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5851<p>Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. For integrable models, novel hydrodynamic approaches based on a quasiparticle picture emerged as a new platform allowing for a quantitative understanding of quantum information dynamics in quantum many-body systems. Remarkably, this gives fresh insights on how thermodynamics emerges in isolated out-of-equilibrium quantum systems.</p><p>I will start by reviewing this new unifying framework. I will then discuss several applications to entanglement-related quantities, such as entanglement entropies, mutual information, logarithmic negativity. I will also show how the framework allows to study the interplay between quantum information dynamics and transport of local conserved quantities. Finally, I will derive some simple bounds on the quantum information scrambling in out-of-equilibrium systems.</p>Sun, 20 Sep 2020 08:55:20 +0200Mon, 14 Sep 2020 18:00:00 +0200Mon, 14 Sep 2020 19:00:00 +0200<a target='_content' href="https://scholar.google.com/citations?user=J5A3R7IAAAAJ&hl=it">Vincenzo Alba</a>University of AmsterdamQM<sup>3</sup> Quantum Matter meets MathsAlexis Virelizier, 2020/09/11, 17h, Homotopy Quantum Field Theories
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5813
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5813<p>Homotopy quantum field theories (HQFTs) generalize topological quantum field theories (TQFTs) by replacing manifolds by maps from manifolds to a fixed target space $X$. For example, any cohomology class in $H^3(X)$ defines a 3-dimensional HQFT with target $X$. If $X$ is aspherical, that is $X = K(G, 1)$ for some group $G$, then this cohomological HQFT is related to the Dijkgraaf-Witten invariant and is computed as a Turaev-Viro state sum via the category of $G$-graded vector spaces. More generally, the state sum Turaev-Viro TQFT and the surgery Reshetikhin-Turaev TQFT extend to HQFTs (using graded fusion categories) which are related via the graded categorical center.</p><p>This is joint work with V. Turaev.</p>Sun, 13 Sep 2020 20:49:47 +0200Fri, 11 Sep 2020 18:00:00 +0200Fri, 11 Sep 2020 19:00:00 +0200<a target='_content' href="http://math.univ-lille1.fr/~virelizi/">Alexis Virelizier</a>Université de LilleTopological Quantum Field TheoryNick Sheridan, 2020/09/08, 17h, Lagrangian cobordism and Chow groups
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5865
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5865<p>Homological mirror symmetry predicts an equivalence of categories, between the Fukaya category of one space and the derived category of another. We can “decategorify” by taking the Grothendieck group of these categories, to get an isomorphism of abelian groups. The first of these abelian groups is related, by work of Biran-Cornea, to the Lagrangian cobordism group; the second is related, via the Chern character, to the Chow group. I will define the Lagrangian cobordism and Chow groups (which is much easier than defining the categories). Then I will describe joint work with Ivan Smith in which we try to compare them directly, and find some interesting analogies.</p>Mon, 14 Sep 2020 19:09:55 +0200Tue, 08 Sep 2020 18:00:00 +0200Tue, 08 Sep 2020 19:00:00 +0200<a target='_content' href="https://www.maths.ed.ac.uk/~nsherida/">Nick Sheridan</a>University of EdinburghGeometria em LisboaSvetlana Jitomirskaya, 2020/09/07, 17h, Anderson localization and local eigenvalue statistics
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5852
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5852<p>Poisson local statistics of eigenvalues is widely accepted as a necessary signature of Anderson localization, but so far has been rigorously established only for random systems. We will argue that this paradigm is wrong, and the reality is a lot more complex and interesting, by presenting both rigorous results for the Harper and Maryland models and numerics for other quasiperiodic and similar models with localization. We will also discuss a conjecture on what the distribution is in the general ergodic situation.</p>Sun, 13 Sep 2020 22:30:55 +0200Mon, 07 Sep 2020 18:00:00 +0200Mon, 07 Sep 2020 19:00:00 +0200<a target='_content' href="https://www.math.uci.edu/~szhitomi/">Svetlana Jitomirskaya</a>University of California, IrvineQM<sup>3</sup> Quantum Matter meets MathsMarco Morandotti, 2020/09/04, 11h, Spatially inhomogeneous evolutionary games
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5890
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5890<p>We study an interaction model of a large population of players based on an evolutionary game, which describes the dynamical process of how the distribution of strategies changes in time according to their individual success.</p><p>We assume that the population of players is distributed over a state space and that they are each endowed with probability distributions of pure strategies, which they draw at random to evolve their states. Simultaneously, the mixed strategies evolve according to a replicator dynamics, modeling the success of pure strategies according to a payoff functional.</p><p>We establish existence, uniqueness, and stability of Lagrangian and Eulerian solutions of this dynamical game by using methods of ODE and optimal transport on Banach spaces.</p><p>We apply the general theoretical framework to perform the mean-field analysis of a multi-population agent-based model, where a particle dynamics derived by a nonlocal velocity and a Markov-type jump process for the labels are coupled.</p><p>An alternate Lagrangian approximation scheme at discrete times is also proposed.</p><p>This research is from joint works with S. Almi, L. Ambrosio, M. Fornasier, G. Savaré, and F. Solombrino.</p>Thu, 03 Sep 2020 09:18:15 +0200Fri, 04 Sep 2020 12:00:00 +0200Fri, 04 Sep 2020 13:00:00 +0200<a target='_content' href="http://marcomorandotti.weebly.com/">Marco Morandotti</a>Politecnico di TorinoLisbon WADE — Webinar in Analysis and Differential EquationsMark Gross, 2020/07/28, 17h, Intrinsic Mirror Symmetry
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5830
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5830<p>I will talk about joint work with Bernd Siebert, proposing a general mirror construction for log Calabi-Yau pairs, i.e., a pair $(X,D)$ with $D$ a “maximally degenerate” boundary divisor and $K_X+D=0$, and for maximally unipotent degenerations of Calabi–Yau manifolds. We accomplish this by constructing the coordinate ring or homogeneous coordinate ring respectively in the two cases, using certain kinds of Gromov-Witten invariants we call “punctured invariants”, developed jointly with Abramovich and Chen.</p>Tue, 28 Jul 2020 23:29:52 +0200Tue, 28 Jul 2020 18:00:00 +0200Tue, 28 Jul 2020 19:00:00 +0200<a target='_content' href="https://www.dpmms.cam.ac.uk/person/mg475">Mark Gross</a>Department of Pure Mathematics and Mathematical Statistics, University of CambridgeGeometria em LisboaRaquel Queiroz, 2020/07/27, 17h, Boundary Obstructed Topological Phases
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5834
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5834<p>Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. Here, we introduce a new notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, given a symmetric boundary termination we say two bulk Hamiltonians belong to distinct boundary obstructed topological phases (BOTPs) if they can be deformed to each other on a system with periodic boundaries, but cannot be deformed to each other in the open system without closing the gap at at least one high symmetry surface. BOTPs are not topological phases of matter in the standard sense since they are adiabatically deformable to each other on a torus but, similar to SPTs, they are associated with boundary signatures in open systems such as surface states or fractional corner charges. In contrast to SPTs, these boundary signatures are not anomalous and can be removed by symmetrically adding lower dimensional SPTs on the boundary, but they are stable as long as the spectral gap at high-symmetry edges/surfaces remains open. We show that the double-mirror quadrupole model of [Science, 357(6346), 2018] is a prototypical example of such phases, and present a detailed analysis of several aspects of boundary obstructions in this model. In addition, we introduce several three-dimensional models having boundary obstructions, which are characterized either by surface states or fractional corner charges. We also provide a general framework to study boundary obstructions in free-fermion systems in terms of Wannier band representations (WBR), an extension of the recently-developed band representation formalism to Wannier bands. WBRs capture the notion of topological obstructions in the Wannier bands which can then be used to study topological obstructions in the boundary spectrum by means of the correspondence between the Wannier and boundary spectra. This establishes a form of bulk-boundary correspondence for BOTPs by relating the bulk band representation to the boundary topology.</p>Mon, 10 Aug 2020 10:10:54 +0200Mon, 27 Jul 2020 18:00:00 +0200Mon, 27 Jul 2020 19:00:00 +0200<a target='_content' href="https://www.weizmann.ac.il/physics/raquel-queiroz">Raquel Queiroz</a>Weizmann Institute of ScienceQM<sup>3</sup> Quantum Matter meets MathsEzra Getzler, 2020/07/24, 17h, Gluing local gauge conditions in BV quantum field theory
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5807
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5807<p>In supersymmetric sigma models, there is frequently no global choice of Lagrangian submanifold for BV quantization. I will take the superparticle, a toy version of the Green Schwarz superstring, as my example, and show how to extend the light-cone gauge to the physically relevant part of phase space. This involves extending a formula of Mikhalkov and A. Schwarz that generalizes the prescription of Batalin and Vilkovisky for the construction of the functional integral.</p><p>This is joint work with S. Pohorence.</p>Sun, 26 Jul 2020 08:31:35 +0200Fri, 24 Jul 2020 18:00:00 +0200Fri, 24 Jul 2020 19:00:00 +0200<a target='_content' href="https://sites.northwestern.edu/getzler/">Ezra Getzler</a>Northwestern UniversityTopological Quantum Field TheoryColin Guillarmou, 2020/07/21, 17h, On the marked length spectrum and geodesic stretch in negative curvature
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5828
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5828<p>I will review a couple of recent of results proved with T. Lefeuvre and G. Knieper on the local rigidity of the marked length spectrum of negatively curved metrics.</p>Sat, 25 Jul 2020 10:22:51 +0200Tue, 21 Jul 2020 18:00:00 +0200Tue, 21 Jul 2020 19:00:00 +0200<a target='_content' href="https://www.imo.universite-paris-saclay.fr/~guillarmou/">Colin Guillarmou</a>Laboratoire de Mathématiques d'Orsay, Université Paris-SudGeometria em LisboaChristophe Garban, 2020/07/20, 17h, A new point of view on topological phase transitions
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5829
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5829<p>Topological phase transitions were discovered by Berezinskii-Kosterlitz-Thouless in the 70's. They describe intriguing phase transitions for classical spins systems such as the plane rotator model (or $XY$ model). I will start by reviewing how this phase transition arises in cases such as:</p><ul><li>the $XY$ model (spins on $\mathbb{Z}^2$ with values in the unit circle)</li><li>the integer-valued Gaussian Free Field (or $\mathbb{Z}$-ferromagnet)</li><li>Abelian Yang-Mills on $\mathbb{Z}^4$</li></ul><p>I will then connect topological phase transitions to a<b> statistical reconstruction problem</b> concerning the Gaussian Free Field and will show that the feasibility of the reconstruction undergoes a KT transition.</p><p>This is a joint work with Avelio Sepúlveda (Lyon) and the talk will be based mostly on the preprint: <a href="https://arxiv.org/abs/2002.12284" rel="noreferrer" target="_blank">https://arxiv.org/abs/2002.12284</a></p>Sat, 25 Jul 2020 10:10:50 +0200Mon, 20 Jul 2020 18:00:00 +0200Mon, 20 Jul 2020 19:00:00 +0200<a target='_content' href="http://math.univ-lyon1.fr/~garban/">Christophe Garban</a>Université Lyon 1QM<sup>3</sup> Quantum Matter meets MathsPedro Boavida de Brito, 2020/07/17, 17h, Galois symmetries of knot spaces
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5818
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5818<p>I’ll describe how the absolute Galois group of the rationals acts on a space which is closely related to the space of all knots. The path components of this space form a finitely generated abelian group which is, conjecturally, a universal receptacle for integral finite-type knot invariants. The added Galois symmetry allows us to extract new information about its homotopy and homology beyond characteristic zero. I will then discuss some work in progress concerning higher-dimensional variants.</p><p>This is joint work with Geoffroy Horel.</p>Tue, 21 Jul 2020 19:38:15 +0200Fri, 17 Jul 2020 18:00:00 +0200Fri, 17 Jul 2020 19:00:00 +0200Pedro Boavida de BritoInstituto Superior Técnico and CAMGSDTopological Quantum Field TheoryTian-Jun Li, 2020/07/14, 17h, Symplectic rational $G$-surfaces and the plane Cremona group
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5808
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5808<p>We give characterizations of a finite group $G$ acting symplectically on a rational surface ($\mathbb{CP}^2$ blown up at two or more points). In particular, we obtain a symplectic version of the dichotomy of $G$-conic bundles versus $G$-del Pezzo surfaces for the corresponding $G$-rational surfaces, analogous to the one in algebraic geometry. The connection with the symplectic mapping class group will be mentioned.</p><p>This is a joint work with Weimin Chen and Weiwei Wu (and partly with Jun Li).</p>Thu, 16 Jul 2020 08:07:29 +0200Tue, 14 Jul 2020 18:00:00 +0200Tue, 14 Jul 2020 19:00:00 +0200<a target='_content' href="https://math.umn.edu/directory/tian-jun-li">Tian-Jun Li</a>University of MinnesotaGeometria em LisboaPavel Exner, 2020/07/14, 16h, Vertex coupling and spectra of periodic quantum graphs
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5827
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5827<p>The talk focuses on the influence of the vertex coupling on spectral properties of periodic quantum graphs. Specifically, two questions will be addressed. The first concerns the number of open spectral gaps; it is shown that graphs with a nontrivial $\delta$ coupling can have finite but nonzero number of them. Secondly, motivated by recent attempts to model the anomalous Hall effect, we investigate a class of vertex couplings that violate the time reversal invariance. For the simplest coupling of this type we show that its high-energy properties depend on the parity of the lattice vertices, and discuss various consequences of this property.</p>Wed, 15 Jul 2020 08:45:58 +0200Tue, 14 Jul 2020 17:00:00 +0200Tue, 14 Jul 2020 18:00:00 +0200<a target='_content' href="http://gemma.ujf.cas.cz/~exner/">Pavel Exner</a>Doppler Institute for Mathematical Physics and Applied Mathematics, PragueRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsGiandomenico Palumbo, 2020/07/13, 17h, Four-dimensional semimetals with tensor monopoles: from surface states to topological responses
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5810
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5810<p>Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. A prominent example is provided by the chiral magnetic effect in three-dimensional Weyl semimetals, which stems from the chiral anomaly. Here, we reveal a distinct quantum effect, coined <em>parity magnetic effect</em>, which is induced by the parity anomaly in a four-dimensional topological semimetal. Upon preserving time-reversal symmetry, the spectrum of our model is doubly degenerate and the nodal (Dirac) points behave like $\mathbb{Z}_2$ monopoles. When time-reversal symmetry is broken, while preserving the sublattice (chiral) symmetry, our system supports spin-3/2 quasiparticles and the corresponding Dirac-like cones host tensor monopoles characterized by a $\mathbb{Z}$ number, the Dixmier-Douady invariant. In both cases, the semimetal exhibits topologically protected Fermi arcs on its boundary. Besides its theoretical implications in both condensed matter and quantum field theory, the peculiar 4D magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.</p>Mon, 13 Jul 2020 22:55:31 +0200Mon, 13 Jul 2020 18:00:00 +0200Mon, 13 Jul 2020 19:00:00 +0200<a target='_content' href="https://www.ulb.be/fr/giandomenico-palumbo">Giandomenico Palumbo</a>Université Libre de BruxellesQM<sup>3</sup> Quantum Matter meets MathsRicardo Campos, 2020/07/10, 17h, The homotopy type of associative and commutative algebras
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5816
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5816<p>Given a topological space, how much of its homotopy type is captured by its algebra of singular cochains? The experienced rational homotopy theorist will argue that one should consider instead a commutative algebra of forms. This raises the more algebraic question</p><blockquote><p>Given a dg commutative algebra, how much of its homotopy type (quasi-isomorphism type) is contained in its associative part?</p></blockquote><p>Despite its elementary formulation, this question turns out to be surprisingly subtle and has important consequences.</p><p>In this talk, I will show how one can use operadic deformation theory to give an affirmative answer in characteristic zero.</p><p>We will also see how the Koszul duality between Lie algebras and commutative algebras allows us to use similar arguments to deduce that under good conditions Lie algebras are determined by the (associative algebra structure of) their universal enveloping algebras.</p><p>Joint with Dan Petersen, Daniel Robert-Nicoud and Felix Wierstra and based on <a href="https://arxiv.org/abs/1904.03585">arXiv:1904.03585</a>.</p>Sat, 11 Jul 2020 17:40:14 +0200Fri, 10 Jul 2020 18:00:00 +0200Fri, 10 Jul 2020 19:00:00 +0200<a target='_content' href="https://imag.umontpellier.fr/~campos/">Ricardo Campos</a>CNRS - University of MontpellierTopological Quantum Field TheoryElvira Zappale, 2020/07/09, 16h, Optimal design problems
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5826
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5826<p>I will present several integral representation results for certain functionals arising in the context of optimal design and damage models, in presence of a perimeter penalization term. I will consider several frameworks, and I will also discuss the case with non-standard growth conditions.</p>Tue, 14 Jul 2020 10:24:35 +0200Thu, 09 Jul 2020 17:00:00 +0200Thu, 09 Jul 2020 18:00:00 +0200<a target='_content' href="https://docenti.unisa.it/005311/home">Elvira Zappale</a>Università Degli Studi di SalernoRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsManuel Asorey, 2020/07/08, 11h, Bulk-Edge dualities in Topological Matter
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5811
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5811<p>Novel bulk-edge dualities have recently emerged in topological materials from the observation of some phenomenological correspondences. The similarity of these dualities with string theory dualities is very appealing and has boosted a quite significant number of cross field studies.</p><p>We analyze the bulk-edge dualities in the integer quantum Hall effect, where due to the simpler nature of planar systems the duality can be analyzed by powerful analytic techniques. The results show that the correspondence is less robust than expected. In particular, it is highly dependent of the type of boundary conditions of the topological material. We introduce a formal proof of the equivalence of bulk and edge approaches to the quantization of Hall conductivity for metallic plates with local boundary conditions. However, the proof does not work for non-local boundary conditions, like the Atiyah-Patodi-Singer boundary conditions, due to the appearance of gaps between the bulk and edge states.</p>Fri, 10 Jul 2020 14:14:12 +0200Wed, 08 Jul 2020 12:00:00 +0200Wed, 08 Jul 2020 13:00:00 +0200<a target='_content' href="https://loop.frontiersin.org/people/95946/overview">Manuel Asorey</a>University of ZaragozaQM<sup>3</sup> Quantum Matter meets MathsRahul Pandharipande, 2020/07/07, 17h, Abel-Jacobi maps and the moduli of differentials
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5820
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5820<p>The moduli of $(C,f)$ where $C$ is a curve and $f$ is a rational function leads to the well-developed theory of Hurwitz spaces. The study of the moduli of $(C,\omega)$ where $C$ is a curve and $\omega$ is a meromorphic differential is a younger subject. I will discuss recent developments in the study of the moduli spaces of holomorphic/meromorphic differentials on curves. Many of the basic questions about cycle classes and integrals have now been solved (through the work of many people) — but there are also several interesting open directions.</p>Fri, 10 Jul 2020 20:47:23 +0200Tue, 07 Jul 2020 18:00:00 +0200Tue, 07 Jul 2020 19:00:00 +0200<a target='_content' href="https://people.math.ethz.ch/~rahul/">Rahul Pandharipande</a>ETH ZürichGeometria em LisboaTom Sutherland, 2020/07/03, 17h, Mirror symmetry for Painlevé surfaces
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5825
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5825<p>This talk will survey aspects of mirror symmetry for ten families of non-compact hyperkähler manifolds on which the dynamics of one of the Painlevé equations is naturally defined. They each have a pair of natural realisations: one as the complement of a singular fibre of a rational elliptic surface and another as the complement of a triangle of lines in a (singular) cubic surface. The two realisations relate closely to a space of stability conditions and a cluster variety of a quiver respectively, providing a perspective on SYZ mirror symmetry for these manifolds. I will discuss joint work in progress with Helge Ruddat studying the canonical basis of theta functions on these cubic surfaces.</p>Tue, 07 Jul 2020 19:15:37 +0200Fri, 03 Jul 2020 18:00:00 +0200Fri, 03 Jul 2020 19:00:00 +0200<a target='_content' href="https://webpages.ciencias.ulisboa.pt/~tasutherland/index.html">Tom Sutherland</a>Group of Mathematical Physics, University of LisbonTopological Quantum Field TheoryTara Holm, 2020/06/30, 17h, Symplectic embeddings and infinite staircases
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5764
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5764<p>McDuff and Schlenk determined when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional ball. They found that if the ellipsoid is close to round, the answer is given by an infinite staircase determined by Fibonacci numbers, while if the ellipsoid is sufficiently stretched, all obstructions vanish except for the volume obstruction. Infinite staircases have also been found when embedding ellipsoids into polydisks (Frenkel-Muller, Usher) and into the ellipsoid $E(2,3)$ (Cristofaro-Gardiner-Kleinman). We will describe a general approach to the question of when embedding ellipsoids into a toric target has an infinite staircase, where we provide the first obstruction to the existence of a staircase. We use this obstruction to explore infinite staircases for toric symplectic manifolds, identifying three new infinite staircases, and culminating in the conjecture that these are the only toric examples. We will describe further work-in-progress on ellipsoid embedding functions with more general targets. I will not assume any prior acquaintance with infinite staircases and will motivate the talk with plentiful examples and pictures. This talk is based on a number of collaborations with Dan Cristofaro-Gardiner, Alessia Mandini, and Ana Rita Pires; Maria Bertozzi, Emily Maw, Dusa McDuff, Grace Mwakyoma, Ana Rita Pires, Morgan Weiler; and Nicki Magill.</p>Sat, 04 Jul 2020 10:47:29 +0200Tue, 30 Jun 2020 18:00:00 +0200Tue, 30 Jun 2020 19:00:00 +0200<a target='_content' href="https://math.cornell.edu/tara-holm">Tara Holm</a>Cornell UniversityGeometria em LisboaBarbara Brandolini, 2020/06/30, 16h, Sharp lower bounds for Neumann eigenvalues
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5822
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5822<p>We will discuss lower bounds for the first non-trivial Neumann eigenvalue $\mu_1(\Omega)$ of the $p$-Laplace operator ($p \gt 1$) in a Lipschitz, bounded domain $\Omega$ in $\mathbb{R}^n$. In 1960 Payne and Weinberger proved that, when $\Omega$ is convex and $p = 2$, then \begin{equation}\label{eq:1}\mu_1(\Omega) \geq \frac{\pi^2}{d(\Omega)^2},\end{equation} where $d(\Omega)$ is the diameter of $\Omega$. The above estimate is asymptotically sharp, since $\mu_1(\Omega)d(\Omega)^2$ tends to $\pi^2$ for a parallelepiped all but one of whose dimensions shrink to $0$. On the other hand, it does not hold true in general for non-convex sets. In this talk we will focus on the non-convex setting. We will consider an arbitrary Lipschitz, bounded domain $\Omega$ in $\mathbb{R}^n$ and we will show a sharp lower bound for $\mu_1(\Omega)$ which, differently from \eqref{eq:1}, involves the best isoperimetric constant relative to $\Omega$ and is sharp, at least when $p = n = 2$, as the isoperimetric constant relative to $\Omega$ goes to $0$. Moreover, in a suitable class of convex planar domains, our estimate will turn out to be better than \eqref{eq:1}.</p><p>Furthermore, we will see that, when $p = n = 2$ and $\Omega$ consists of the points on one side of a smooth curve $\gamma$, within a suitable distance $\delta$ from it, then $\mu_1(\Omega)$ can be sharply estimated from below in terms of the length of $\gamma$, the $L^\infty$ norm of its curvature and $\delta$.</p>Wed, 01 Jul 2020 10:26:06 +0200Tue, 30 Jun 2020 17:00:00 +0200Tue, 30 Jun 2020 18:00:00 +0200<a target='_content' href="https://www.docenti.unina.it/barbara.brandolini">Barbara Brandolini</a>Università Degli Studi di Napoli Federico IILisbon WADE — Webinar in Analysis and Differential EquationsRaffaele Resta, 2020/06/29, 17h, The insulating state of matter: a geometrical theory
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5762
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5762<p>The insulating versus conducting behavior of condensed matter is commonly addressed in terms of electronic excitations and/or conductivity. At variance with such wisdom, W. Kohn hinted in 1964 that the insulating state of matter reflects a peculiar organization of the electrons in their ground state, and does not require an energy gap.</p><p>Kohn’s <em>theory of the insulating state</em> got a fresh restart in 1999; at the root of these developments is the modern theory of polarization, developed in the early 1990s, and based on a geometrical concept (Berry phase). Since insulators and metals polarize in a qualitatively different way, quantum geometry also discriminates insulators from conductors. A common geometrical “marker”, based on the quantum metric, caracterizes all insulators (band insulators, Anderson insulators, Mott insulators, quantum Hall insulators...); such marker diverges in conductors.</p>Tue, 30 Jun 2020 13:19:08 +0200Mon, 29 Jun 2020 18:00:00 +0200Mon, 29 Jun 2020 19:00:00 +0200<a target='_content' href="http://www-dft.ts.infn.it/~resta/">Raffaele Resta</a>Instituto Officina dei Materiali, CNR, Trieste, ItalyRoom P3.10, Mathematics BuildingQM<sup>3</sup> Quantum Matter meets MathsAldo Cotrone, 2020/06/29, 15h, Complexity in the presence of a boundary
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5780
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5780<p>After a brief introduction to the concept of Computational Complexity, I will show how to calculate it in several theories with boundaries in two dimensions. In particular, I will consider a free boson discretized on a lattice with Dirichlet boundary conditions, and "Boundary CFTs" with a holographic dual. I will identify certain contributions in the results for the Complexity which are characteristic of the presence of boundaries. Moreover, the results in the two most popular holographic prescriptions, the so-called "CV" and "CA" prescriptions, are qualitatively different. Thus, one can obtain information on the fitness of the holographic prescriptions in describing faithfully the Complexity of the dual states.</p>Tue, 28 Jul 2020 16:51:37 +0200Mon, 29 Jun 2020 16:00:00 +0200Mon, 29 Jun 2020 17:00:00 +0200Aldo CotroneUniversity of FlorenceString TheoryMarko Stošić, 2020/06/26, 17h, Rational and algebraic links and knots-quivers correspondence
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5795
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5795<p>I will start with a brief overview of knots-quivers correspondence, where colored HOMFLY-PT (or BPS) invariants of the knot are expressed as motivic Donaldson-Thomas invariants of a corresponding quiver.</p><p>This deep conjectural relationship already had some surprising applications.</p><p>In this talk I will focus on showing that the knots-quivers correspondence holds for rational links, as well as much larger class of arborescent links (algebraic links in the sense of Conway). This is done by extending the correspondence to tangles, and showing that the set of tangles satisfying tangles-quivers correspondence is closed under the tangle addition operation.</p><p>This talk is based on joint work with Paul Wedrich.</p>Sat, 27 Jun 2020 16:37:44 +0200Fri, 26 Jun 2020 18:00:00 +0200Fri, 26 Jun 2020 19:00:00 +0200<a target='_content' href="https://math.tecnico.ulisboa.pt/professor?who=mstosic">Marko Stošić</a>Instituto Superior Técnico and CAMGSDTopological Quantum Field TheoryMário Silveirinha, 2020/06/24, 11h, Topological theory of non-Hermitian photonic systems
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5767
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5767<p>Recently, topological materials and topological effects have elicited a great interest in the photonics community [<a href="#LJS">1</a>]. While condensed-matter phenomena are traditionally described by Hermitian operators, the same is not true in the context of macroscopic electrodynamics where a dissipative response is the rule, not the exception. In this talk, I will discuss how to determine the topological phases of dissipative (non-Hermitian) photonic structures from first principles using a gauge-independent Green function [<a href="#Silv">2</a>, <a href="#PS">3</a>]. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the system Green function over a line parallel to the imaginary-frequency axis. The approach introduces in a natural way the "band-gaps" of non-Hermitian systems as the strips of the complex-frequency plane wherein the system Green function is analytical. I apply the developed theory to nonreciprocal electromagnetic continua and photonic crystals, with lossy and or gainy elements. Furthermore, I discuss the validity of the bulk-edge correspondence in the non-Hermitian case.</p><ol><li id="LJS">L. Lu, J. D. Joannopoulos, M. Soljačić, <em>Topological photonics</em>, Nat. Photonics, 8, 821, (2014).</li><li id="Silv">M. G. Silveirinha, <em>Topological theory of non-Hermitian photonic systems</em>, Phys. Rev. B, 99, 125155, 2019.</li><li id="PS">F. R. Prudêncio, M. G. Silveirinha, <a href="https://arxiv.org/abs/2003.01539"><em>First Principles Calculation of Topological Invariants of non-Hermitian Photonic Crystal</em>s</a>.</li></ol>Fri, 26 Jun 2020 23:30:19 +0200Wed, 24 Jun 2020 12:00:00 +0200Wed, 24 Jun 2020 13:00:00 +0200<a target='_content' href="http://web.tecnico.ulisboa.pt/mario.silveirinha/">Mário Silveirinha</a>Instituto Superior TécnicoQM<sup>3</sup> Quantum Matter meets MathsMario Garcia-Fernandez, 2020/06/23, 17h, Gauge theory for string algebroids
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5766
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5766<p>In this talk I will overview recent joint work with Roberto Rubio and Carl Tipler in <a href="https://arxiv.org/abs/2004.11399">arXiv:2004.11399</a>. We introduce a moment map picture for string algebroids, a special class of holomorphic Courant algebroids introduced in <a href="https://arxiv.org/abs/1807.10329">arXiv:1807.10329</a>. An interesting feature of our construction is that the Hamiltonian gauge action is described by means of Morita equivalences, as suggested by higher gauge theory. The zero locus of the moment map is given by the solutions of the Calabi system, a coupled system of equations which provides a unifying framework for the classical Calabi problem and the Hull-Strominger system. Our main results are concerned with the geometry of the moduli space of solutions. Assuming a technical condition, we prove that the moduli space carries a pseudo-Kähler metric with Kähler potential given by the <em>dilaton functional</em>, a topological formula for the metric, and an infinitesimal Donaldson-Uhlenbeck-Yau type theorem. Finally, we relate our topological formula to a physical prediction for the gravitino mass in order to obtain a new conjectural obstruction for the Hull-Strominger system.</p>Wed, 24 Jun 2020 10:03:18 +0200Tue, 23 Jun 2020 18:00:00 +0200Tue, 23 Jun 2020 19:00:00 +0200<a target='_content' href="https://sites.google.com/site/mariogarciafern/home">Mario Garcia-Fernandez</a>ICMAT and Universidad Autónoma de MadridGeometria em LisboaTatsuya Miura, 2020/06/23, 11h, On the isoperimetric inequality and surface diffusion flow for multiply winding curves
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5814
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5814<p>In this talk we discuss dynamical stability of multiply covered circles under the surface diffusion flow. To this end we first establish a general form of the isoperimetric inequality for immersed closed curves under rotational symmetry, which would be of independent interest. We then apply it to obtaining a certain class of rotationally symmetric initial curves from which solutions to the surface diffusion flow exist globally-in-time and converge to multiply covered circles. This talk is based on a joint work with Shinya Okabe at Tohoku University.</p>Wed, 24 Jun 2020 12:44:28 +0200Tue, 23 Jun 2020 12:00:00 +0200Tue, 23 Jun 2020 13:00:00 +0200<a target='_content' href="https://sites.google.com/view/tatsuya-miura">Tatsuya Miura</a>Tokyo Institute of TechnologyLisbon WADE — Webinar in Analysis and Differential EquationsDmitri Bykov, 2020/06/22, 15h, Flag manifold sigma-models and Ricci flow
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5815
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5815<p>I will review various results related to flag manifold sigma-models, with emphasis on their integrability properties. On simpler examples, such as the $\operatorname{\mathbb{CP}}^n$-model, I will demonstrate that the trigonometrically-deformed geometries are solutions to the Ricci flow equations.</p>Tue, 28 Jul 2020 16:52:54 +0200Mon, 22 Jun 2020 16:00:00 +0200Mon, 22 Jun 2020 17:00:00 +0200Dmitri BykovSteklov Mathematical Institute MoscowString TheoryMikhail Khovanov, 2020/06/19, 17h, Introduction to foam evaluation
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5790
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5790<p>Foam evaluation was discovered by Louis-Hardrien Robert and Emmanuel Wagner slightly over three years ago. It's a remarkable formula assigning a symmetric function to a foam, that is, to a decorated 2-dimensional CW-complex embedded in three-space. We'll explain their formula in the 3-color case in the context of unoriented foams and discuss its relation to Kronheimer-Mrowka homology of graphs and the four-color theorem.</p>Sun, 21 Jun 2020 19:02:52 +0200Fri, 19 Jun 2020 18:00:00 +0200Fri, 19 Jun 2020 19:00:00 +0200<a target='_content' href="https://www.math.columbia.edu/~khovanov/">Mikhail Khovanov</a>Columbia UniversityTopological Quantum Field TheoryLucas Sá, 2020/06/17, 11h, Random matrix theory of dissipative quantum chaos
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5819
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5819<p>Describing complex interacting quantum systems is a daunting task. One very fruitful approach to this problem, developed for unitary dynamics, is to represent the Hamiltonian of a system by a large random matrix. This eventually led to the development of the field of quantum chaos. Arguably, one of its most spectacular achievements was the identification of universal signatures of chaos in quantum systems, characterizing the correlations of their energy levels. In this talk, we will focus on the recent application of (non-Hermitian) random matrix theory to open quantum systems, where dissipation and decoherence coexist with unitary dynamics. First, we will discuss a class of stochastic Lindbladians with random Hamiltonian and independent random dissipation channels (jump operators), as a model for the generator of complicated nonunitary dynamics. We will then explain what difficulties arise when combining dissipation with quantum chaos, and how to overcome them. In particular, we discuss a new non-Hermitian random matrix ensemble with eigenvalues on the torus and how it connects to our recent proposal of using complex spacing ratios as a signature of dissipative quantum chaos.</p>Wed, 17 Jun 2020 22:35:14 +0200Wed, 17 Jun 2020 12:00:00 +0200Wed, 17 Jun 2020 13:00:00 +0200Lucas SáInstituto Superior Técnico and CEFEMAQM<sup>3</sup> Quantum Matter meets MathsAlessia Mandini, 2020/06/16, 17h, Quasi-parabolic Higgs bundles and null hyperpolygon spaces
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5763
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5763<p>Hyperpolygons spaces are a family of hyperkähler manifolds, that can be obtained from coadjoint orbits by hyperkähler reduction. Jointly with L. Godinho, we showed that these space are isomorphic to certain families of parabolic Higgs bundles, when a suitable condition between the parabolic weights and the spectra of the coadjoint orbits is satisfied.</p><p>In analogy to this construction, we introduce two moduli spaces: the moduli spaces of quasi-parabolic $\operatorname{SL}(2,\mathbb{C})$-Higgs bundles over $\mathbb{CP}^1$ on one hand and the null hyperpolygon spaces on the other, and establish an isomorphism between them.</p><p>Finally we describe the fixed loci of natural involutions defined on these spaces and relate them to the moduli space of null hyperpolygons in the Minkowski $3$-space.</p><p>This is based in joint works with Leonor Godinho.</p>Thu, 25 Jun 2020 11:59:54 +0200Tue, 16 Jun 2020 18:00:00 +0200Tue, 16 Jun 2020 19:00:00 +0200<a target='_content' href="http://www.professores.uff.br/alessiamandini/">Alessia Mandini</a>IST and Universidade Federal FluminenseGeometria em LisboaRiccardo Adami, 2020/06/16, 16h, Ground states of the Nonlinear Schroedinger Equation on Graphs: an overview
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5812
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5812<p>Driven by physical and technological applications, during the last five years the study of nonlinear evolution on branched structures (graphs, networks) has undergone a fast development. We review on the main achievements and on the open problems. This is a joint project with several people, among which Simone Dovetta, Enrico Serra, Lorenzo Tentarelli, and Paolo Tilli.</p>Tue, 16 Jun 2020 22:04:31 +0200Tue, 16 Jun 2020 17:00:00 +0200Tue, 16 Jun 2020 18:00:00 +0200<a target='_content' href="https://didattica.polito.it/pls/portal30/sviluppo.scheda_pers_swas.show?m=30120">Riccardo Adami</a>Politecnico di TorinoRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsAntti Kupiainen, 2020/06/12, 17h, Integrability of Liouville Conformal Field Theory
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5805
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5805<p>A. Polyakov introduced Liouville Conformal Field theory (LCFT) in 1981 as a way to put a natural measure on the set of Riemannian metrics over a two dimensional manifold. Ever since, the work of Polyakov has echoed in various branches of physics and mathematics, ranging from string theory to probability theory and geometry.</p><p>In the context of 2D quantum gravity models, Polyakov’s approach is conjecturally equivalent to the scaling limit of Random Planar Maps and through the Alday-Gaiotto-Tachikava correspondence LCFT is conjecturally related to certain 4D Yang-Mills theories. Through the work of Dorn, Otto, Zamolodchikov and Zamolodchikov and Teschner LCFT is believed to be to a certain extent integrable.</p><p>I will review a probabilistic construction of LCFT developed together with David, Rhodes and Vargas and recent proofs of the integrability of LCFT:</p><ul><li>The proof in a joint work with Rhodes and Vargas of the DOZZ formula (<a href="https://arxiv.org/abs/1707.08785">Annals of Mathematics, 81-166,191 (2020)</a>)</li><li>The proof in a joint work with Guillarmou, Rhodes and Vargas of the bootstrap conjecture for LCFT (<a href="https://arxiv.org/abs/2005.11530">arXiv:2005.11530</a>).</li></ul>Thu, 25 Jun 2020 11:59:16 +0200Fri, 12 Jun 2020 18:00:00 +0200Fri, 12 Jun 2020 19:00:00 +0200<a target='_content' href="https://researchportal.helsinki.fi/en/persons/antti-kupiainen">Antti Kupiainen</a>University of HelsinkiTopological Quantum Field TheoryZlatko Papic, 2020/06/10, 11h, Quantum many-body scars: a new form of weak ergodicity breaking in constrained quantum systems
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5749
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5749<p>Recent experiments on large chains of Rydberg atoms [<a href="#b1">1</a>] have demonstrated the possibility of realising one-dimensional, kinetically constrained quantum systems. It was found that such systems exhibit surprising signatures of non-ergodic dynamics, such as robust periodic revivals in global quenches from certain initial states. This weak form of ergodicity breaking has been interpreted as a manifestation of "quantum many-body scars" [<a href="#b2">2</a>], i.e., the many-body analogue of unstable classical periodic orbits of a single particle in a chaotic stadium billiard. Scarred many-body eigenstates have been shown to exhibit a range of unusual properties which violate the Eigenstate Thermalisation Hypothesis, such as equidistant energy separation, anomalous expectation values of local observables and subthermal entanglement entropy. I will demonstrate that these properties can be understood using a tractable model based on a single particle hopping on the Hilbert space graph, which formally captures the idea that scarred eigenstates form a representation of a large $\operatorname{SU}(2)$ spin that is embedded in a thermalising many-body system. I will show that this picture allows to construct a more general family of scarred models where the fundamental degree of freedom is a quantum clock [<a href="#b3">3</a>]. These results suggest that scarred many-body bands give rise to a new universality class of constrained quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.</p><ol><li><a href="https://www.nature.com/articles/nature24622" id="b1" name="b1">H. Bernien et al., Nature 551, 579 (2017).</a></li><li><a href="https://www.nature.com/articles/s41567-018-0137-5" id="b2" name="b2">C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, Z. Papic, Nat. Phys. 14, 745 (2018).</a></li><li><a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.030601" id="b3" name="b3">Kieran Bull, Ivar Martin, and Z. Papic, Phys. Rev. Lett. 123, 030601 (2019).</a></li></ol>Mon, 15 Jun 2020 10:12:10 +0200Wed, 10 Jun 2020 12:00:00 +0200Wed, 10 Jun 2020 13:00:00 +0200<a target='_content' href="https://theory.leeds.ac.uk/zlatko-papic/">Zlatko Papic</a>University of LeedsQM<sup>3</sup> Quantum Matter meets MathsKai Cieliebak, 2020/06/09, 17h, Partial orders on contactomorphism groups and their Lie algebras
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5798
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5798<p>Eliashberg, Kim and Polterovich constructed nontrivial partial orders on contactomorphism groups of certain contact manifolds. After recalling their results, the subject of this talk will be the remnants of these partial orders on the orbits of the coadjoint action on their Lie algebras.</p>Mon, 15 Jun 2020 20:47:58 +0200Tue, 09 Jun 2020 18:00:00 +0200Tue, 09 Jun 2020 19:00:00 +0200<a target='_content' href="https://www.uni-augsburg.de/en/fakultaet/mntf/math/prof/geom/cieliebak/">Kai Cieliebak</a>Augsburg UniversityGeometria em LisboaLucio Boccardo, 2020/06/09, 16h, Recent developments on Dirichlet problems with singular convection/drift terms
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5797
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5797<p>In the talk we discuss two Dirichlet problems ("formally" in duality)\begin{align}\label{(CP)}\tag{CP}u\in W_0^{1,q}(\Omega): \; &\operatorname{div}(M(x)\nabla {u})+a(x)\,{u}=-\operatorname{div}({u}\,E(x)) +f(x);<br />\\ \label{(DP)}\tag{DP}\psi\in W_0^{1,q}(\Omega): & - \operatorname{div}(M(x)\nabla \psi)+a(x)\,\psi= E(x)\cdot\nabla \psi +g(x)\end{align}where $\Omega$ is a bounded open set in $\mathbb{R}^N$, $M(x)$ ia bounded elliptic matrix, $f$, $g$ are functions belonging to $L^m(\Omega)$, $m\geq1$, $E\in(L^N(\Omega))^N$, $0\lt \alpha_0\leq a(x)\in L^1(\Omega)$.</p><p>In the first part we briefly <strong>recall</strong> some recent results:</p><ul><li>existence and summability properties of weak solutions ($q=2$), if $m\geq\frac{2N}{ N+1}$;</li><li>Calderon-Zygmund theory ($q=m^*$, infinite energy solutions), if $1\lt m \lt \frac{2N}{ N+1}$;<m<\frac{2n}{ n=""></m<\frac{2n}{></li><li>uniqueness;</li><li>the case $|E|\leq\frac{A}{|x|}$, where $E\not\in(L^N(\Omega))^N$;</li><li>the case $E\in(L^2(\Omega))^N$.</li></ul><p>Then we <strong>show</strong>:</p><ul><li>a new (simpler) existence proof, thanks to the presence of the zero order term, for \eqref{(CP)};</li><li>a straight duality proof for \eqref{(DP)};</li><li>continuous dependence of the solutions with respect to the weak convergence of the coefficients;</li><li>regularizing effect of dominated coefficients ($|f|\leq Q\,a(x)$ or $|g|\leq Q\,a(x)$, $Q\gt 0$);</li><li>"weak" maximum principle: if $f(x)\geq0$ [$g(x)\geq0$] and, of course, not =0 a.e., then $u(x)\geq0$ [$\psi(x)\geq0$] and the set where $u$ [$\psi$] is zero has zero measure (at most).</li></ul><p><strong>Work in progress:</strong> obstacle problem; nonlinear principal part.<br /><strong>Open problem:</strong> "strong" maximum principle.</p>Mon, 15 Jun 2020 09:47:43 +0200Tue, 09 Jun 2020 17:00:00 +0200Tue, 09 Jun 2020 18:00:00 +0200Lucio BoccardoUniversità di Roma La SapienzaRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsCharles Marteau, 2020/06/08, 15h, New boundary conditions for $AdS_2$
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5804
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5804<p>We describe new boundary conditions for $AdS_2$ in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to $\operatorname{Diff}(S^1) \times C^{\infty}(S^1)$, whose breaking to $\operatorname{SL}(2, \mathbb{R}) \times U(1)$ controls the near-$AdS_2$ dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory. It can be interpreted as the coadjoint action of the warped Virasoro group. We show that this theory is holographically dual to the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.</p>Mon, 08 Jun 2020 21:03:58 +0200Mon, 08 Jun 2020 16:00:00 +0200Mon, 08 Jun 2020 17:00:00 +0200Charles MarteauInstitut Polytechnique de ParisString TheoryJohn Huerta, 2020/06/05, 17h, Bundle Gerbes on Supermanifolds
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5794
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5794<p>Bundle gerbes are a generalization of line bundles that play an important role in constructing WZW models with boundary. With an eye to applications for WZW models with superspace target, we describe the classification of bundle gerbes on supermanifolds, and sketch a proof of their existence for large families of super Lie groups.</p>Tue, 16 Jun 2020 07:46:18 +0200Fri, 05 Jun 2020 18:00:00 +0200Fri, 05 Jun 2020 19:00:00 +0200John HuertaInstituto Superior Técnico and CAMGSDTopological Quantum Field TheoryJohanna Erdmenger, 2020/06/03, 11h, Turbulent hydrodynamics in strongly correlated Kagome metals
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5755
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5755<p>A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids are not amenable to the perturbative methods of Fermi liquid theory, but can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene, which possesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes of their band structure provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in stoichiometric Scandium (Sc) Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction and hence reflects the strength of the correlations, is enhanced by a factor of about 3.2 as compared to graphene, due to orbital hybridization. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put, for the first time, the turbulent flow regime described by holography within the reach of experiments.</p>Mon, 15 Jun 2020 10:15:36 +0200Wed, 03 Jun 2020 12:00:00 +0200Wed, 03 Jun 2020 13:00:00 +0200<a target='_content' href="https://www.physik.uni-wuerzburg.de/en/tp3/people/chairholder/prof-dr-johanna-erdmenger/">Johanna Erdmenger</a>University of WürzburgQM<sup>3</sup> Quantum Matter meets MathsSteve Zelditch, 2020/06/02, 17h, Probabilistic aspects of toric Kahler geometry
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5757
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5757<p>Let $(M, \omega, L)$ be a polarized toric Kahler manifold with polytope $P$. Associated to this data is a family $\mu_k^x$ of probability measures on $P$ parametrized by $x \in P.$ They generalize the multi-nomial measures on the simplex, where $M = \mathbb{CP}^n$ and $\omega$ is the Fubini-Study measure. As is well-known, these measures satisfy a law of large numbers, a central limit theorem, a large deviations principle and entropy asymptotics. The measure of maximal entropy in this family corresponds to the center of mass $x$ of $P$. All of these results generalize to any toric Kahler manifold, except the center of mass result, which holds for Fano toric Kahler-Einstein manifolds.</p><p>Joint work with Peng Zhou and Pierre Flurin.</p>Mon, 15 Jun 2020 20:49:18 +0200Tue, 02 Jun 2020 18:00:00 +0200Tue, 02 Jun 2020 19:00:00 +0200<a target='_content' href="https://sites.math.northwestern.edu/~zelditch/">Steve Zelditch</a>Northwestern UniversityGeometria em LisboaMaria Colombo, 2020/06/02, 16h, Nonunique characteristic curves of Sobolev vector fields
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5786
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5786<p>Given a vector field in $\mathbb{R}^d$, the classical Cauchy-Lipschitz theorem shows existence and uniqueness of its flow provided the vector field is sufficiently smooth; this, in turn, translates in existence and uniqueness results for the transport equation. In 1989, Di Perna and Lions proved that Sobolev regularity for vector fields, with bounded divergence and a growth assumption, is sufficient to establish existence, uniqueness and stability of a generalized notion of flow, consisting of a suitable selection among the trajectories of the associated ODE. A long-standing open question is whether the uniqueness of the regular Lagrangian flow is a corollary of the uniqueness of the trajectory of the ODE for a.e. initial datum. In this talk we give an overview of the topic and we provide a negative answer to this question. To show this result we exploit the connection with the transport equation, based on Ambrosio’s superposition principle, and a new ill-posedness result for positive solutions of the continuity equation.</p>Mon, 15 Jun 2020 09:49:04 +0200Tue, 02 Jun 2020 17:00:00 +0200Tue, 02 Jun 2020 18:00:00 +0200<a target='_content' href="https://www.epfl.ch/labs/amcv/amcv/prof-maria-colombo/">Maria Colombo</a>École Polytechnique Fédérale de LausanneRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsSilvia Nagy, 2020/06/01, 15h, Perturbative gravity via BRST Yang-Mills<sup>2</sup>
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5803
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5803<p>I will present a formulation of gravity as a double copy of gauge theories in the context of the Becchi-Rouet-Stora-Tyutin (BRST) formalism. I will show how this gives an algorithm for consistently mapping gauge choices from Yang-Mills to gravity. Moreover, it resolves the issue of the dilaton degree of freedom arising in the double copy, thus allowing for the consistent construction of solutions in General Relativity. I will describe the perturbative construction at higher orders. I will also give a formulation of the BRST double copy in a spherical background.</p>Tue, 02 Jun 2020 10:24:33 +0200Mon, 01 Jun 2020 16:00:00 +0200Mon, 01 Jun 2020 17:00:00 +0200Silvia NagyUniversity of NottinghamString TheoryDanica Kosanović, 2020/05/29, 17h, Knot invariants from homotopy theory
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5765
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5765<p>The embedding calculus of Goodwillie and Weiss is a certain homotopy theoretic technique for studying spaces of embeddings. When applied to the space of knots this method gives a sequence of knot invariants which are conjectured to be universal Vassiliev invariants. This is remarkable since such invariants have been constructed only rationally so far and many questions about possible torsion remain open. In this talk I will present a geometric viewpoint on the embedding calculus, which enables explicit computations. In particular, we prove that these knot invariants are surjective maps, confirming a part of the universality conjecture, and we also confirm the full conjecture rationally, using some recent results in the field. Hence, these invariants are at least as good as configuration space integrals.</p>Fri, 05 Jun 2020 19:25:57 +0200Fri, 29 May 2020 18:00:00 +0200Fri, 29 May 2020 19:00:00 +0200<a target='_content' href="https://people.mpim-bonn.mpg.de/danica/">Danica Kosanović</a>Max-Planck Institut für MathematikTopological Quantum Field TheoryAchilleas Lazarides, 2020/05/27, 11h, Quantum order at infinite temperature, time crystals, and dissipation
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5735
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5735<p>Discrete time crystals is the name given to many-body systems displaying long-time dynamics that is sub-harmonic with respect to a driving frequency. While these were first discussed in closed quantum systems a few years ago, recent work (partly motivated by experiments) has focussed on including non-unitary effects such as due to an external environment ("dissipation").</p><p>In this talk I will begin by discussing general features of periodically-driven many-body systems, then concentrate on one of the unitary models for discrete time crystals. Time permitting, I will finally discuss a general framework for subharmonic oscillations stabilised by dissipative dynamics.</p>Wed, 03 Jun 2020 09:27:12 +0200Wed, 27 May 2020 12:00:00 +0200Wed, 27 May 2020 13:00:00 +0200<a target='_content' href="https://www.lboro.ac.uk/departments/maths/staff/academic/achilleas-lazarides/">Achilleas Lazarides</a>Loughborough UniversityQM<sup>3</sup> Quantum Matter meets MathsXavier Roulleau, 2020/05/26, 17h, On a special configuration of $12$ conics and a related $K3$ surface
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5782
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5782<p>A generalized Kummer surface $X$ obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a $9{\mathbf A}_{2}$-configuration of $(-2)$-curves (ie smooth rational curves). Such a configuration plays the role of the $16$ disjoint $(-2)$-curves for the usual Kummer surfaces.</p><p>In this talk we will explain how construct $9$ other such $9{\mathbf A}_{2}$-configurations on the generalized Kummer surface associated to the double cover of the plane branched over the sextic dual curve of a cubic curve.</p><p>The new $9{\mathbf A}_{2}$-configurations are obtained by taking the pullback of a certain configuration of $12$ conics which are in special position with respect to the branch curve, plus some singular quartic curves. We will then explain how construct some automorphisms of the K3 surface sending one configuration to another.</p><p>(Joint work with David Kohel and Alessandra Sarti).</p>Mon, 15 Jun 2020 20:41:19 +0200Tue, 26 May 2020 18:00:00 +0200Tue, 26 May 2020 19:00:00 +0200<a target='_content' href="http://www.i2m.univ-amu.fr/perso/xavier.roulleau/Site_Pro_English/Welcome.html">Xavier Roulleau</a>Université d’Aix-MarseilleGeometria em LisboaLuis Vega, 2020/05/26, 16h, The Vortex Filament Equation, the Talbot effect, and non-circular jets.
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5788
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5788<p>We will propose the vortex filament equation as a possible toy model for turbulence, in particular because of its striking similarity to the dynamics of non-circular jets. This similarity implies the existence of some type of Talbot effect due to the interaction of non-linear waves that propagate along the filament. Another consequence of this interaction is the existence of a new class of multi-fractal sets that can be seen as a generalization of the graph of Riemann’s non-differentiable function. Theoretical and numerical arguments about the transfer of energy will be also given. This a joint work with V. Banica and F. de la Hoz.</p>Fri, 29 May 2020 13:26:08 +0200Tue, 26 May 2020 17:00:00 +0200Tue, 26 May 2020 18:00:00 +0200<a target='_content' href="http://www.ehu.eus/luisvega/">Luis Vega</a>Basque Center for Applied MathematicsLisbon WADE — Webinar in Analysis and Differential EquationsMarcus Berg, 2020/05/25, 15h, Plane gravitational waves and Jacobi-Maass forms
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5779
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5779<p>I will first review the classical Kronecker 2<sup>nd</sup> limit formula, viewed as a relation between partition functions and Green’s functions in orbifolds of flat space (as discussed for example in <a href="https://arXiv.org/abs/1407.0027">arXiv:1407.0027</a>, appendix E). I will then discuss the generalization of this relation to orbifolds of the gravitational plane wave, a Penrose limit of AdS (dual of the BMN limit in gauge theory). This provides a natural one-parameter deformation of Kronecker-Eisenstein series, and more generally of Jacobi-Maass forms. This talk is based on <a href="https://arXiv.org/abs/1910.02745">arXiv:1910.02745</a>.</p>Tue, 02 Jun 2020 10:26:39 +0200Mon, 25 May 2020 16:00:00 +0200Mon, 25 May 2020 17:00:00 +0200Marcus BergKarlstad UniversityString TheorySergei Gukov, 2020/05/22, 17h, Hidden Algebraic Structures in Topology
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5768
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5768<p>Which 4-manifold invariants can detect the Gluck twist? And, which 3-manifold invariants can detect the difference between surgeries on mutant knots? What is the most powerful topological quantum field theory (TQFT)? Guided by questions like these, we will look for new invariants of 3-manifolds and smooth 4-manifolds. Traditionally, a construction of many such invariants and TQFTs involves a choice of certain algebraic structure, so that one can talk about "invariants for SU(2)" or a "TQFT defined by a given Frobenius algebra." Surprisingly, recent developments lead to an opposite phenomenon, where algebraic structures are labeled by 3-manifolds and 4-manifolds, so that one can speak of VOA-valued invariants of 4-manifolds or MTC-valued invariants of 3-manifolds. Explaining these intriguing connections between topology and algebra will be the main goal of this talk.</p>Tue, 16 Jun 2020 07:47:19 +0200Fri, 22 May 2020 18:00:00 +0200Fri, 22 May 2020 19:00:00 +0200<a target='_content' href="http://theory.caltech.edu/~gukov/">Sergei Gukov</a>California Institute of TechnologyTopological Quantum Field Theory