CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Alexander 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=5831Sat, 27 Jun 2020 20:56:19 +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>UC BerkeleyTopological Quantum Field TheoryDavide 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=5824Fri, 19 Jun 2020 15:08:11 +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 TheoryAndré Henriques, 2020/09/25, 17h, Relative mapping class group representations via conformal nets
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5821
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5821Tue, 30 Jun 2020 13:04:44 +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 OxfordRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryNicolai 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, 25 Jun 2020 09:39:13 +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, BerkeleyRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryRobert Berman, 2020/09/15, 11h, An invitation to Kähler-Einstein metrics and random point processes
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5832
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5832Fri, 26 Jun 2020 18:49:22 +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 LisboaAlexis 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=5813Thu, 25 Jun 2020 09:38:15 +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 LilleRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryEzra Getzler, 2020/07/24, 17h, Gauge fixing in supersymmetric field theories with topological terms
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5807
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5807Thu, 25 Jun 2020 09:34:54 +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 UniversityRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryChristophe 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>Mon, 29 Jun 2020 11:25:27 +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=5818Thu, 25 Jun 2020 09:33:55 +0200Fri, 17 Jul 2020 18:00:00 +0200Fri, 17 Jul 2020 19:00:00 +0200Pedro Boavida de BritoInstituto Superior Técnico and CAMGSDRoom P3.10, Mathematics BuildingTopological 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, 25 Jun 2020 12:00:18 +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>Tue, 23 Jun 2020 18:49:02 +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, PragueLisbon 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>Tue, 23 Jun 2020 22:18:56 +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>Thu, 25 Jun 2020 09:32:43 +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, 30 Jun 2020 08:19:11 +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 SalernoLisbon 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>Sun, 28 Jun 2020 10:41:29 +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, Moduli spaces of differentials on curves
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>Wed, 01 Jul 2020 09:43:06 +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>Fri, 26 Jun 2020 07:56:50 +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>Thu, 25 Jun 2020 12:00:18 +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>Thu, 25 Jun 2020 11:59:16 +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>Thu, 25 Jun 2020 11:59:16 +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 TheoryJoe Huxford, 2020/05/20, 11h, Topological phases in $3+1D$: the Higher Lattice Gauge Theory Model and its excitations
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5759
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5759<p>Topological phases in $3+1D$ are less well understood than their lower dimensional counterparts. A useful approach to the study of such phases is to look at toy models that we can solve exactly. In this talk I will present new results for an existing model for certain topological phases in $3+1D$ (the model was first presented in [<a href="#bibHuxford1">1</a>]). This model is based on a generalisation of lattice gauge theory known as higher lattice gauge theory, which treats parallel transport of lines as well as points. I will first provide a brief introduction to higher lattice gauge theory and the Hamiltonian model constructed from it. Then we will look at the simple excitations (both point-like and loop-like) that are present in this model and how these excitations can be constructed explicitly using so-called ribbon and membrane operators. Some of the quasi-particles are confined and we discuss how this arises from a condensation-confinement transition. We will then look at the (loop-)braiding relations of the excitations and finish by examining the conserved topological charges realised by the Higher Lattice Gauge Theory Model.<br /><br /><a id="bibHuxford1" name="bibHuxford1">[1]</a> A Bullivant, M. Calcada et al., <em>Topological phases from higher gauge symmetry in 3+1D</em>, Phys. Rev. B 95, 155118 (2017).</p>Wed, 03 Jun 2020 09:48:44 +0200Wed, 20 May 2020 12:00:00 +0200Wed, 20 May 2020 13:00:00 +0200<a target='_content' href="https://www2.physics.ox.ac.uk/contacts/people/huxford">Joe Huxford</a>Oxford UniversityRoom P1, Mathematics BuildingQM<sup>3</sup> Quantum Matter meets MathsMichael Singer, 2020/05/19, 16h 30m, A construction of $D_k$ asymptotically locally flat gravitational instantons from Atiyah-Hitchin and Taub-NUT geometries
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5761
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5761<p>Complete hyperKaehler 4-manifolds with cubic volume growth (and suitable decay of the curvature), also known as ALF gravitational instantons, are known to come in two families, according to the <em>fundamental group at infinity</em>. This group must be a finite subgroup of $SU(2)$ and the only possibilities compatible with cubic volume growth are the cyclic groups ($A_k$) and binary dihedral groups ($D_k$).</p><p>This talk will be about the construction of $D_k$ ALF gravitational instantons by a gluing construction in which the ingredients are the moduli space of centred charge-2 monopoles ($D_0$) and a particularly symmetric, but singular, $A_k$ ALF gravitational instanton. This construction was suggested in a paper of Sen (1997). It is also closely related to a construction due to Foscolo, in which hyperKaehler metrics are constructed on the $K3$ manifold that are “nearly” collapsed to a 3-dimensional space.</p><p>This is joint work with Bernd Schroers.</p>Mon, 15 Jun 2020 20:50:23 +0200Tue, 19 May 2020 17:30:00 +0200Tue, 19 May 2020 18:30:00 +0200<a target='_content' href="http://www.homepages.ucl.ac.uk/~ucahasi/">Michael Singer</a>University College LondonGeometria em LisboaBernold Fiedler, 2020/05/19, 16h, Sturm meanders: global attractors, Temperley-Lieb algebras, and black holes
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5769
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5769<p>Fusco and Rocha studied Neumann boundary value problems for scalar ODEs of second order via a shooting approach. They introduced the notion of what we now call Sturm permutations. These permutations relate, on the one hand, to a special class of meandering curves as introduced by Arnol’d in a singularity theory context. On the other hand, they became central in the study of global attractors of nonlinear parabolic partial differential equations of Sturm type.</p><p>We discuss relations of Sturm meanders with further areas: the multiplicative and trace structure in Temperley-Lieb algebras, discrete versions of Cartesian billiards, and the problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.</p><p>We report on joint work with Pablo Castañeda, Juliette Hell, Carlos Rocha, and Brian Smith. See also <a href="http://dynamics.mi.fu-berlin.de/">http://dynamics.mi.fu-berlin.de/</a></p><p>For further material we recommend the beautifully illustrated book “Meanders” by Anna Karnauhova, de Gruyter 2017.</p>Mon, 15 Jun 2020 09:50:34 +0200Tue, 19 May 2020 17:00:00 +0200Tue, 19 May 2020 18:00:00 +0200<a target='_content' href="http://dynamics.mi.fu-berlin.de/persons/fiedler.php">Bernold Fiedler</a>Institute of Mathematics, Freie Universität BerlinRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsShinji Hirano, 2020/05/18, 15h, Random Boundary Geometry and Gravity Dual of $T {\bar T}$ Deformation
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5789
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5789<p>We study the random geometry approach to the $T \bar T$ deformation of $2d$ conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the $T \bar T$ deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of $AdS_3$ spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant $T \bar T$ operator.</p>Mon, 18 May 2020 17:19:21 +0200Mon, 18 May 2020 16:00:00 +0200Mon, 18 May 2020 17:00:00 +0200Shinji HiranoUniversity of the WitwatersrandString TheoryBruno Amorim, 2020/05/13, 11h, Strain in two-dimensional materials
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5742
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5742<p>Graphene is the prototypical two-dimensional material. One of main features of two-dimensional materials is the ease with which their properties can be externally modified. Application of strain is one possible way. In this seminar we will review the geometrical description of strains in crystalline materials, with a focus on graphene. Using this method, we will study the form of the electron-lattice interaction. We will compare this model with the description of electrons in strained graphene in terms of a Dirac equation in curved space. An overview of anharmonic lattice effects in two-dimensional materials will also be made.</p>Wed, 03 Jun 2020 09:56:23 +0200Wed, 13 May 2020 12:00:00 +0200Wed, 13 May 2020 13:00:00 +0200<a target='_content' href="https://amorimbruno.weebly.com/">Bruno Amorim</a>Universidade do MinhoRoom P1, Mathematics BuildingQM<sup>3</sup> Quantum Matter meets MathsRui Loja Fernandes, 2020/05/12, 17h, Non-commutative integrable systems and their singularities
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5771
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5771<p>The theory of singularities of non-commutative integrable systems (a.k.a isotropic fibrations), in contrast with the well-known theory for the commutative case (a.k.a. Lagrangian fibrations), is nonexistent. In this talk I will describe a few first steps toward such a theory.</p>Mon, 15 Jun 2020 20:51:37 +0200Tue, 12 May 2020 18:00:00 +0200Tue, 12 May 2020 19:00:00 +0200<a target='_content' href="https://faculty.math.illinois.edu/~ruiloja/">Rui Loja Fernandes</a>University of Illinois at Urbana-ChampaignGeometria em LisboaDiogo Oliveira e Silva, 2020/05/12, 16h 30m, Global maximizers for spherical restriction
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5753
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5753<p>We prove that constant functions are the unique real-valued maximizers for all $L^2-L^{2n}$ adjoint Fourier restriction inequalities on the unit sphere $\mathbb{S}^{d-1}\subset\mathbb{R}^d$, $d\in\{3,4,5,6,7\}$, where $n\geq 3$ is an integer. The proof uses tools from probability theory, Lie theory, functional analysis, and the theory of special functions. It also relies on general solutions of the underlying Euler-Lagrange equation being smooth, a fact of independent interest which we discuss. We further show that complex-valued maximizers coincide with nonnegative maximizers multiplied by the character $e^{i\xi\cdot\omega}$, for some $\xi$, thereby extending previous work of Christ & Shao (2012) to arbitrary dimensions $d\geq 2$ and general even exponents. This talk is based on results obtained with René Quilodrán.</p>Mon, 15 Jun 2020 09:51:39 +0200Tue, 12 May 2020 17:30:00 +0200Tue, 12 May 2020 18:30:00 +0200<a target='_content' href="http://web.mat.bham.ac.uk/~oliveird/">Diogo Oliveira e Silva</a>University of BirminghamRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsKevin Grosvenor, 2020/05/11, 15h, Information geometry in quantum field theory: lessons from simple examples
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5756
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5756<p>We study the Fisher metrics associated with a variety of simple systems and derive some general lessons that may have important implications for the application of information geometry in holography. Some sample systems of interest are the classical 2d Ising model and the corresponding 1d free fermion theory, the instantons in 3+1d massless phi-fourth theory, and coherent states of free bosons and fermions.</p>Sat, 02 May 2020 20:20:38 +0200Mon, 11 May 2020 16:00:00 +0200Mon, 11 May 2020 17:00:00 +0200Kevin GrosvenorUniversity of WuerzburgString TheoryAndrea de Luca, 2020/05/06, 11h, Generalized hydrodynamics with dephasing noise
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5740
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5740<p>I review recent advances in the development of generalized hydrodynamics, a flexible approach to the out-of-equilibrium dynamics of integrable quantum systems. I explain how this methodology has allowed exact calculations of transport in $1D$ system. Then, I consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we developed an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time- and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the non-linear Schrodinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures.</p>Mon, 15 Jun 2020 10:16:58 +0200Wed, 06 May 2020 12:00:00 +0200Wed, 06 May 2020 13:00:00 +0200<a target='_content' href="https://andreadeluca.online/">Andrea de Luca</a>University of Cergy-Pontoise, CNRSQM<sup>3</sup> Quantum Matter meets MathsAlexander Ritter, 2020/05/05, 17h, Invariance of symplectic cohomology under deformations
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5760
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5760<p>This is joint work with Gabriele Benedetti (Heidelberg).</p><p>I will describe how Floer cohomology changes as one deforms the symplectic form. I will then explain how these results are useful in applications in symplectic topology, e.g. finding generators for the Fukaya category of toric varieties or finding lower bounds on the number of magnetic geodesics.</p>Mon, 15 Jun 2020 20:52:21 +0200Tue, 05 May 2020 18:00:00 +0200Tue, 05 May 2020 19:00:00 +0200<a target='_content' href="https://www.maths.ox.ac.uk/people/alexander.ritter">Alexander Ritter</a>University of OxfordGeometria em LisboaFilippo Santambrogio, 2020/05/05, 16h, Optimal transport methods for the regularity of 2D functions of least gradient
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5752
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5752<p>The least gradient problem (minimizing the BV norm with given boundary data), motivated by both image processing applications and connections with minimal surfaces, is known to be equivalent, in the plane, to the Beckmann minimal-flow problem (an alternative formulation of the $L^1$ Monge-Kantorovich optimal transport problem) with source and target measures located on the boundary of the domain. Hence, Sobolev regularity of functions of least gradient is equivalent in this setting to $L^p$ bounds on the solution of the Beckmann problem (i.e. on what is called the transport density) and can be attacked with techniques which are now standard in optimal transport. From the transport point of view, the novelty of the estimates that I will present, coming from a joint paper with S. Dweik, lies in the fact they are obtained for transport between measures which are concentrated on the boundary. From the BV point of view, a new result is the $W^{1,p}$ regularity of the least gradient function whenever the boundary datum is $W^{1,p}$ as a $1D$ function: moreover, the optimal transport framework is strong enough to deal with arbitrary strictly convex norms instead of the Euclidean one with almost no effort.</p>Mon, 15 Jun 2020 09:53:40 +0200Tue, 05 May 2020 17:00:00 +0200Tue, 05 May 2020 18:00:00 +0200<a target='_content' href="http://math.univ-lyon1.fr/~santambrogio/">Filippo Santambrogio</a>Université Claude Bernard - Lyon 1Room P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsEdward Hirst, 2020/05/04, 15h, Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5754
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5754<p>We apply machine-learning to the study of dessins d'enfants. Specifically, we investigate a class of dessins which reside at the intersection of the investigations of modular subgroups, Seiberg-Witten curves and extremal elliptic K3 surfaces. A deep feed-forward neural network with simple structure and standard activation functions without prior knowledge of the underlying mathematics is established and imposed onto the classification of extension degree over the rationals, known to be a difficult problem. The classifications exceeded 0.93 accuracy and around 0.9 confidence relatively quickly. The Seiberg-Witten curves for those with rational coefficients are also tabulated.</p>Wed, 15 Apr 2020 19:24:08 +0200Mon, 04 May 2020 16:00:00 +0200Mon, 04 May 2020 17:00:00 +0200Edward HirstUniversity of LondonString TheorySemyon Klevtsov, 2020/04/29, 11h, Laughlin states on Riemann surfaces
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5745
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5745<p>Laughlin state is an $N$-particle wave function, describing the fractional quantum Hall effect (FQHE). We define and construct Laughlin states on genus-$g$ Riemann surface, prove topological degeneracy and discuss adiabatic transport on the corresponding moduli spaces. Mathematically, the problems around Laughlin states involve subjects as asymptotics of Bergman kernels for higher powers of line bundle on a surface, large-$N$ asymptotics of Coulomb gas-type integrals, vector bundles on moduli spaces.</p>Mon, 15 Jun 2020 10:18:11 +0200Wed, 29 Apr 2020 12:00:00 +0200Wed, 29 Apr 2020 13:00:00 +0200<a target='_content' href="http://irma.math.unistra.fr/~klevtsov/">Semyon Klevtsov</a>IRMA, Université de StrasbourgQM<sup>3</sup> Quantum Matter meets MathsMichael Goldman, 2020/04/28, 16h, On an old conjecture of Almgren
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5748
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5748<p>In this talk I will give an overview on the few results available on the conjecture of Almgren regarding the convexity of drops subject to the action of an external potential. In particular I will present recent progress in this direction obtained with G. De Philippis on their connectedness. Together with an older result of McCann, this answers positively the conjecture in dimension two. The proof is inspired by the two-point function technique introduced by B. Andrews and is reminiscent of the doubling of variables trick in the context of viscosity solutions.</p>Mon, 15 Jun 2020 09:54:41 +0200Tue, 28 Apr 2020 17:00:00 +0200Tue, 28 Apr 2020 18:00:00 +0200<a target='_content' href="https://www.ljll.math.upmc.fr/~goldman/">Michael Goldman</a>Laboratoire Jacques-Louis Lions and Université Paris 7Room P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsJohn McKay, 2020/04/27, 15h, The Monster and its Moonshine Functions
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5739
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5739<p>This group of astronomical order is slowly yielding its secrets. It is the symmetry group of a rational conformal field theory. In this introductory talk, I will discuss the functions that constitute monstrous moonshine and explain the importance of the monster group and its connections with better established parts of mathematics.</p>Sun, 05 Apr 2020 18:12:24 +0200Mon, 27 Apr 2020 16:00:00 +0200Mon, 27 Apr 2020 17:00:00 +0200John McKayConcordia UniversityString TheoryTomaž Prosen, 2020/04/22, 11h, The Rule 54: Completely Solvable Statistical Mechanics Model of Deterministic Interacting Dynamics
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5736
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5736<p>Derivation of macroscopic statistical laws, such as Fourier's, Ohm's or Fick's laws, from reversible microscopic equations of motion is one of the central fundamental problems of statistical physics. In recent years we have witnessed a remarkable progress in understanding the dynamics and nonequilibrium statistical physics of integrable systems. This encourages us to attempt to understand the aforementioned connection at least in specific classes of nontrivial integrable systems with strong interactions. In my talk I will introduce a family of reversible cellular automata, which model systems of interacting particles, and for which we can prove the existence of diffusion and exactly solve several interesting paradigms of statistical physics, e.g.: nonequilibrium steady states of the system between two stochastic reservoirs, the problem of relaxation to the nonequilibrium steady state, or even the problem of explicit time evolution of macroscopic states, for instance, the solution of inhomogeneous quench problems and the calculation of dynamical structure factor in highly entropic equilibrium states.</p>Mon, 15 Jun 2020 10:19:05 +0200Wed, 22 Apr 2020 12:00:00 +0200Wed, 22 Apr 2020 13:00:00 +0200<a target='_content' href="https://chaos.fmf.uni-lj.si/?page_id=7">Tomaž Prosen</a>University of LjubljanaQM<sup>3</sup> Quantum Matter meets MathsMatthias Röger, 2020/04/21, 16h, An obstacle type problem as a limit of a model for cell polarization
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5744
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5744<p>We consider the polarization of a cell in response to an outer signal. The mathematical model consists of a diffusion equation in the inner volume coupled to a reaction diffusion system on the cell membrane. In a certain asymptotic limit we rigorously prove the convergence towards a generalized obstacle problem. In term of this limit system we derive conditions for the onset of polarization. The results will be mainly presented for the stationary case, we will briefly discuss some extensions to the time-dependent case.</p><p>(This is joint work with Barbara Niethammer, Juan Velazquez, and Anna Logioti)</p>Mon, 15 Jun 2020 09:55:32 +0200Tue, 21 Apr 2020 17:00:00 +0200Tue, 21 Apr 2020 18:00:00 +0200<a target='_content' href="http://www.mathematik.tu-dortmund.de/lsxi/roeger/">Matthias Röger</a>Technische Universität DortmundRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsGábor Sárosi, 2020/04/20, 15h, Holographic Probes of Inner Horizons
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5725
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5725<p>In the context of the AdS/CFT correspondence, charged and rotating thermal ensembles are dual to black holes with inner Cauchy horizons. We argue that an uneventful inner horizon requires certain analytic properties of correlation functions in the dual boundary ensemble which are not consistent with causality and unitarity for charged black holes and rotating black holes in $D>3$. However, they are satisfied for correlators of a holographic $2d$ CFT in a rotating thermal ensemble. This suggests that strong cosmic censorship is enforced in gravity theories with a CFT dual, with the possible exception of the rotating BTZ black hole. </p>Fri, 17 Apr 2020 19:16:01 +0200Mon, 20 Apr 2020 16:00:00 +0200Mon, 20 Apr 2020 17:00:00 +0200Gábor SárosiTheory Division CERNString TheoryEva-Maria Graefe, 2020/04/15, 11h, Evolution of Gaussian wave packets generated by a non-Hermitian Hamiltonian in the semiclassical limit
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5747
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5747<p>In recent years there has been growing interest in open quantum systems described by non-Hermitian Hamiltonians in various fields. In this talk I present results on the quantum evolution of Gaussian wave packets generated by a non-Hermitian Hamiltonian in the semiclassical limit of small $\hbar$. This yields a generalisation of the Ehrenfest theorem for the dynamics of observable expectation values. The resulting equations of motion for dynamical variables are coupled to an equation of motion for the phase-space metric — a phenomenon having no analogue in Hermitian theories. The insight that can be gained by this classical description will be demonstrated for a number of example systems.</p>Mon, 15 Jun 2020 10:20:23 +0200Wed, 15 Apr 2020 12:00:00 +0200Wed, 15 Apr 2020 13:00:00 +0200<a target='_content' href="https://www.imperial.ac.uk/people/e.graefe">Eva-Maria Graefe</a>Imperial College LondonQM<sup>3</sup> Quantum Matter meets MathsDorin Bucur, 2020/04/14, 16h, Boundary behaviour of Robin problems and isoperimetric spectral inequalities
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5743
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5743<p>Consider the Poisson equation with Robin boundary conditions in a (nonsmooth) domain with a bounded, nonnegative right hand side. Given a point on the boundary, the question is whether the solution has a strictly positive lower limit at this point. If the domain is smooth the answer is positive as a consequence of the Hopf maximum principle. If the domain is not smooth, the answer may be positive or negative, depending on the geometry of the domain around the point. This question was raised in a probabilistic context by Bass, Burdzy and Chen in 2008, when they obtained results for Lipschitz sets and cuspidal domains.</p><p>Our motivation is related to the fact that positive answers to the question above, together with a control of the infimum of the boundary values, lead to sharp quantitative forms of isoperimetric inequalities of spectral type for the Robin Laplacian.</p><p>In this talk, I will make the point on recent advances on isoperimetric inequalities involving the Robin Laplacian and I will show how the boundary behaviour pops up in the quantitative form of the inequalities. If times remains, I will present a variational approach to deal with the boundary behaviour for general elliptic operators and various geometric contexts.</p><p>The results were obtained together with A. Giacomini and M. Nahon.</p>Mon, 15 Jun 2020 09:56:15 +0200Tue, 14 Apr 2020 17:00:00 +0200Tue, 14 Apr 2020 18:00:00 +0200<a target='_content' href="http://www.lama.univ-savoie.fr/pagesmembres/bucur/">Dorin Bucur</a>Université de SavoieRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsAlejandra Castro, 2020/04/13, 15h, The Holographic Landscape of Symmetric Product Orbifolds
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5746
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5746<p>I will discuss the application of Siegel paramodular forms to constructing new examples of holography. These forms are relevant to investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. The main finding is that the landscape of symmetric product theories decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which indicates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on $AdS_3$. I will provide a simple diagnostic which places any symmetric product orbifold in either region. The examples I will present open a path to novel realizations of $AdS_3/CFT_2$.</p>Sun, 05 Apr 2020 17:54:44 +0200Mon, 13 Apr 2020 16:00:00 +0200Mon, 13 Apr 2020 17:00:00 +0200Alejandra CastroUniversity of AmsterdamString TheoryBruno Mera, 2020/04/08, 11h, Localization anisotropy and complex geometry in two-dimensional insulators
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5734
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5734<p>The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic limit, it defines a flat Riemannian metric over the twist-angle space, topologically a torus, which endows this space with a complex structure, described by a complex parameter τ . It is shown that the latter is a physical observable related to the anisotropy of the system. The quantity τ and the Riemannian volume of the twist-angle space provide an invariant way to parametrize the flat quantum metric obtained in the thermodynamic limit. Moreover, if by changing the couplings of the theory, the system undergoes quantum phase transitions in which the gap closes, the complex structure τ is still well defined, although the metric diverges (metallic state), and it is fixed by the form of the Hamiltonian near the gap closing points. The Riemannian volume is responsible for the divergence of the metric at the phase transition.</p><p>[1] Bruno Mera. Localization anisotropy and complex geometry in two-dimensional insulators. Phys. Rev. B, 101:115128, Mar 2020.</p>Mon, 15 Jun 2020 10:23:49 +0200Wed, 08 Apr 2020 12:00:00 +0200Wed, 08 Apr 2020 13:00:00 +0200<a target='_content' href="https://sites.google.com/view/bmera/home">Bruno Mera</a>Security and Quantum Information Group of Instituto de TelecomunicaçõesQM<sup>3</sup> Quantum Matter meets MathsSusanna Terracini, 2020/04/07, 16h, Pattern Formation Through Spatial Segregation
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5741
https://math.tecnico.ulisboa.pthttps://wade.ulisboa.pt?action=show&id=5741<p>Reaction-diffusion systems with strong interaction terms appear in many multi-species physical problems as well as in population dynamics. The qualitative properties of the solutions and their limiting profiles in different regimes have been at the center of the community's attention in recent years. A prototypical example is the system of equations \[\left\{\begin{array}{l}<br />-\Delta u+a_1u = b_1|u|^{p+q-2}u+cp|u|^{p-2}|v|^qu,\\<br />-\Delta v+a_2v = b_2|v|^{p+q-2}v+cq|u|^{p}|v|^{q-2}v<br />\end{array}<br />\right.<br />\] in a domain $\Omega\subset \mathbb{R}^N$ which appears, for example, when looking for solitary wave solutions for Bose-Einstein condensates of two different hyperfine states which overlap in space. The sign of $b_i$ reflects the interaction of the particles within each single state. If $b_i$ is positive, the self interaction is attractive (focusing problems). The sign of $c$, on the other hand, reflects the interaction of particles in different states. This interaction is attractive if $c>0$ and repulsive if $c<0$. If the condensates repel, they eventually separate spatially giving rise to a free boundary. Similar phenomena occurs for many species systems. As a model problem, we consider the system of stationary equations: \[<br />\begin{cases}<br />-\Delta u_i=f_i(u_i)-\beta u_i\sum_{j\neq i}g_{ij}(u_j)\;\\<br />u_i>0\;.<br />\end{cases}<br />\] The cases $g_{ij}(s)=\beta_{ij}s$ (Lotka-Volterra competitive interactions) and $g_{ij}(s)=\beta_{ij}s^2$ (gradient system for Gross-Pitaevskii energies) are of particular interest in the applications to population dynamics and theoretical physics respectively.</p><p>Phase separation and has been described in the recent literature, both physical and mathematical. Relevant connections have been established with optimal partition problems involving spectral functionals. The classification of entire solutions and the geometric aspects of phase separation are of fundamental importance as well. We intend to focus on the most recent developments of the theory in connection with the emergence of spiralling and other special type of solutions.</p>Mon, 15 Jun 2020 09:56:54 +0200Tue, 07 Apr 2020 17:00:00 +0200Tue, 07 Apr 2020 18:00:00 +0200<a target='_content' href="https://sites.google.com/site/susannaterracini/">Susanna Terracini</a>Università di TorinoRoom P1, Mathematics BuildingLisbon WADE — Webinar in Analysis and Differential EquationsPaul A. McClarty, 2020/04/01, 11h, Topological Magnons
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5733
https://math.tecnico.ulisboa.pthttps://qm3.tecnico.ulisboa.pt?action=show&id=5733<p>I give an overview of the insights we and other people have had into the band structure of magnons and discuss in some detail three main topics from our work: (i) the robustness of topological edge states in the presence of magnon interactions (ii) visualization of spin-momentum locking in magnon systems (iii) the non-Hermitian topology of spontaneous magnon decay.</p><p> </p>Sun, 21 Jun 2020 11:41:16 +0200Wed, 01 Apr 2020 12:00:00 +0200Wed, 01 Apr 2020 13:00:00 +0200Paul A. McClartyMax Planck Institute for the Physics of Complex SystemsQM<sup>3</sup> Quantum Matter meets MathsGábor Sárosi, 2020/03/23, 15h, Holographic Probes of Inner Horizons
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5728
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5728<p>We study the inner horizons of rotating and charged black holes in anti-de Sitter space. These black holes have a classical analytic extension through the inner horizon to additional asymptotic regions. If this extension survives in the quantum theory, it requires particular analytic properties in a dual CFT, which give a prescription for calculating correlation functions for operators placed on any asymptotic boundary of the maximally extended spacetime. We show that for charged black holes in three or greater dimensions, and rotating black holes in four or greater dimensions, these analytic properties are inconsistent in the dual CFT, implying the absence of an analytic extension for quantum fields past the inner horizon. Thus, we find that strong cosmic censorship holds for all AdS black holes except rotating BTZ.</p>Sun, 22 Mar 2020 12:24:34 +0100Mon, 23 Mar 2020 16:00:00 +0100Mon, 23 Mar 2020 17:00:00 +0100Gábor SárosiTheory Division CERNRoom P3.10, Mathematics BuildingString TheorySimon Ross, 2020/03/02, 15h, Generalized Gibbs Ensemble and KdV charges in 2d CFTs
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5662
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5662<p>2d CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges. There is a generalised Gibbs ensemble for these theories where we turn on chemical potentials for these charges. I will describe some partial results on calculating this partition function, both in the limit of large charges and perturbatively in the chemical potentials.</p>Sun, 22 Mar 2020 12:24:34 +0100Mon, 02 Mar 2020 16:00:00 +0100Mon, 02 Mar 2020 17:00:00 +0100Simon RossDurham UniversityRoom P3.10, Mathematics BuildingString Theory