CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Rita Teixeira da Costa, 2020/01/03, 14h, Mode stability for the Teukolsky equation on extremal Kerr black hole spacetimes
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5651
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5651<p>We prove that there are no exponentially growing modes nor modes on the real axis for the Teukolsky equation on extremal Kerr black hole spacetimes. While the result was previously known for subextremal spacetimes, we show that the proof for the latter cannot be extended to the extremal case as the nature of the event horizon changes radically in the extremal limit.</p><p>Finally, we explain how mode stability could serve as a preliminary step towards understanding boundedness, scattering and decay properties of general solutions to the Teukolsky equation on extremal Kerr black holes.<br /> </p>Wed, 09 Oct 2019 15:17:10 +0200Fri, 03 Jan 2020 15:00:00 +0100Fri, 03 Jan 2020 16:00:00 +0100Rita Teixeira da CostaUniversity of CambridgeRoom P3.10, Mathematics BuildingMathematical RelativityPaolo Benincasa, 2019/12/09, 15h, An SLE approach to four dimensional black hole microstate entropy
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5656
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5656<p>We model the Bekenstein-Hawking entropy of a four dimensional extremal black hole in terms of classifying particles moving in its near horizon $AdS_2$ geometry. We use the framework of SLE curves in $AdS_2$ to classify these particle trajectories in terms of their boundary conditions.</p>Tue, 15 Oct 2019 15:10:31 +0200Mon, 09 Dec 2019 16:00:00 +0100Mon, 09 Dec 2019 17:00:00 +0100Paolo BenincasaNiels Bohr InstituteRoom P3.10, Mathematics BuildingString TheoryFrancesca Ferrari, 2019/11/18, 15h, $3d$ Modularity
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5628
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5628<p>We find and propose an explanation for a large variety of modularity-related symmetries in problems of $3$-manifold topology and physics of $3d$ $N=2$ theories, where such structures a priori are not manifest.</p>Thu, 03 Oct 2019 09:21:33 +0200Mon, 18 Nov 2019 16:00:00 +0100Mon, 18 Nov 2019 17:00:00 +0100Francesca FerrariSISSA TriesteRoom P3.10, Mathematics BuildingString TheoryAngelo Carollo, 2019/11/15, 11h 30m, Continuous-Time Crystals in Open Quantum Systems
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5654
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5654<p>I will briefly review the idea, proposed by F. Wilczek, of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. Recently, it has been demonstrated that the possibility of time crystals at equilibrium, i.e. in the canonical ensemble of "not-too-long-range" Hamiltonians, is ruled out. The search for time crystals in non-equilibrium systems remains still open. I will show that in the general context of a stable state of a "not-too-long-range" Markovian open dynamics, spontaneous break of continuous time symmetry is also forbidden.</p>Sun, 20 Oct 2019 10:07:51 +0200Fri, 15 Nov 2019 12:30:00 +0100Fri, 15 Nov 2019 13:30:00 +0100<a target='_content' href="https://pure.unipa.it/en/persons/angelo-carollo-4">Angelo Carollo</a>University of PalermoRoom P3.10, Mathematics Building$QM^3$ Quantum Matter meets MathsEmilio Franco, 2019/11/06, 15h, Introduction to Mirror Symmetry on the Hitchin System
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5659
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5659<p>This will be an introductory talk for the <a href="https://www.math.tecnico.ulisboa.pt/~efranco/EFranco_web/seminars/mirror_symmetry_hitchin_system.html">Working Seminar on Mirror Symmetry on the Hitchin System</a>. During this minicourse, organized by T. Sutherland and myself, we aim to understand Mirror Symmetry on Higgs moduli spaces as a classical limit of the Geometric Langlands program. In this talk I will briefly describe the geometrical objects involved in this program and provide a motivation for it coming from mathematical physics. The structure of the working seminar will also be discussed.</p>Sat, 19 Oct 2019 09:45:52 +0200Wed, 06 Nov 2019 16:00:00 +0100Wed, 06 Nov 2019 17:00:00 +0100Emilio FrancoCAMGSD, Instituto Superior TécnicoRoom P4.35, Mathematics BuildingGeometria em LisboaAlessandra Occelli, 2019/11/05, 15h, KPZ universality for last passage percolation models.
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5643
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5643<p>In this seminar we consider last passage percolation on $\mathbb{Z}^2$, a model in the Kardar–Parisi–Zhang (KPZ) universality class. We will investigate the universality of the limit distributions of the last passage time for different settings. In the first part we analyze the correlations of two last passage times for different ending points in a neighbourhood of the characteristic. For a general class of random initial conditions, we prove the universality of the first order correction when the two observation times are close. In the second part we consider a model of last passage percolation in half-space and we obtain the distribution of the last passage time for the stationary initial condition.</p>Tue, 15 Oct 2019 09:57:20 +0200Tue, 05 Nov 2019 16:00:00 +0100Tue, 05 Nov 2019 17:00:00 +0100Alessandra OccelliInstituto Superior TécnicoRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsBruno Mera, 2019/10/31, 15h, The geometry and topology of free fermions
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5653
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5653<p>In this talk, rather than presenting new results, I will discuss relatively recent results in condensed matter which bring geometry and topology to the realm of quantum matter. In particular, I will focus on systems of free fermions. The ground state of a gapped translation invariant charge conserving free fermion Hamiltonian on a $d-$dimensional lattice can be described by a smooth map from a $d-$dimensional torus of quasi-momenta to a Grassmannian manifold. This map gives rise to a vector bundle over the torus whose isomorphism class determines the topological phase of the system. In particular, in $d = 2$, the Chern class can be naturally associated with the transverse Hall conductivity of the system. By considering families of systems of free fermions one can see phase transitions associated to the gap closing points in momentum space. The change in topology can be understood in terms of a transversal crossing of the image of the Hamiltonian in the space of Hermitian matrices with the subvariety formed by those matrices having multiple eigenvalues. Further geometric aspects will be discussed if time permits to do so.</p>Fri, 18 Oct 2019 17:31:33 +0200Thu, 31 Oct 2019 16:00:00 +0100Thu, 31 Oct 2019 17:00:00 +0100<a target='_content' href="https://www.it.pt/Members/Index/5851">Bruno Mera</a>Security and Quantum Information Group of Instituto de TelecomunicaçõesAdvanced studies room (2.8.11), Physics Building$QM^3$ Quantum Matter meets MathsAlessandra Occelli, 2019/10/29, 15h, A short KPZ story
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5642
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5642<p>The aim of this talk is to present a few models in the Kardar–Parisi–Zhang (KPZ) universality class, a class of stochastic growth models that have been widely studied in the last 30 years. We will focus in particular on last passage percolation (LPP) models. They provide a <em>physical</em> description of combinatorial problems, such as Ulam's problem, in terms of zero temperature directed polymers; but also a geometric interpretation of an interacting particle system, the totally asymmetric simple exclusion process (TASEP); and of a system of queues and servers. Moreover, in the large time limit, they share statistical features with certain ensembles of random matrices.</p>Tue, 15 Oct 2019 09:57:40 +0200Tue, 29 Oct 2019 16:00:00 +0100Tue, 29 Oct 2019 17:00:00 +0100Alessandra OccelliInstituto Superior TécnicoRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsTertuliano Franco, 2019/10/25, 16h, A Mini-course in large deviations
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5648
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5648<p>Large deviations have importance and applications in different areas, as Probability, Statistics, Dynamical Systems, and Statistical Mechanics. In plain words, large deviations correspond to finding and proving the (exponentially small) probability of observing events not expected by the law of large numbers. In this mini-course we introduce the topic including a discussion on the general statement of large deviations and the some of the usual challenges when facing the upper/lower bound large deviations.</p>Sat, 19 Oct 2019 09:33:25 +0200Fri, 25 Oct 2019 17:00:00 +0200Fri, 25 Oct 2019 18:00:00 +0200Tertuliano FrancoUniversidade Federal da BahiaRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsAntónio Girão, 2019/10/24, 14h, Dirac's theorem for random regular graphs
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5631
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5631<p>In 1952, Dirac proved that any graph on $n$ vertices with minimum degree $n/2$ contains a Hamiltonian cycle, i.e. a cycle which passes through every vertex of the graph exactly once. We prove a resilience version of Dirac’s Theorem in the setting of random regular graphs. More precisely, we show that, whenever $d$ is sufficiently large compared to $\epsilon \gt 0$, a.a.s. the following holds: let $G_0$ be any subgraph of the random $n$-vertex $d$-regular graph $G_{n,d}$ with minimum degree at least $(1/2 + \epsilon)d$. Then, $G_0$ is Hamiltonian. This proves a conjecture of Ben-Shimon, Krivelevich and Sudakov. Our result is best possible: firstly, the condition that $d$ is large cannot be omitted, and secondly, the minimum degree bound cannot be improved. This is joint work with Padraig Condon, Alberto Espuny Díaz, Daniela Kuhn and Deryk Osthus.</p>Wed, 16 Oct 2019 11:47:49 +0200Thu, 24 Oct 2019 15:00:00 +0200Thu, 24 Oct 2019 16:00:00 +0200<a target='_content' href="https://sites.google.com/view/antonio-girao/home">António Girão</a>University of BirminghamRoom P4.35, Mathematics BuildingAlgebraTertuliano Franco, 2019/10/23, 16h, A Mini-course in large deviations
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5647
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5647<p>Large deviations have importance and applications in different areas, as Probability, Statistics, Dynamical Systems, and Statistical Mechanics. In plain words, large deviations correspond to finding and proving the (exponentially small) probability of observing events not expected by the law of large numbers. In this mini-course we introduce the topic including a discussion on the general statement of large deviations and the some of the usual challenges when facing the upper/lower bound large deviations.</p>Sat, 19 Oct 2019 09:33:51 +0200Wed, 23 Oct 2019 17:00:00 +0200Wed, 23 Oct 2019 18:00:00 +0200Tertuliano FrancoUniversidade Federal da BahiaRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsJorge António, 2019/10/23, 14h, Derived Geometry and its applications
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5657
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5657<p>In this talk, we are going to present a user-friendly approach to derived geometry. One of our goals is to convince the audience that the notions of derived manifold / scheme / space / stack are just as natural as their classical counterparts. After having introduced the basic techniques, we will apply them to study certain moduli spaces of geometrical origin. Derived geometry also has recently found applications in arithmetics, which we will try to explain in the last part of the talk.</p>Sat, 19 Oct 2019 09:40:19 +0200Wed, 23 Oct 2019 15:00:00 +0200Wed, 23 Oct 2019 16:00:00 +0200Jorge AntónioUniversité Paul Sabatier (Toulouse III)Room P3.10, Mathematics BuildingAlgebraManuel Araújo, 2019/10/23, 11h 30m, Topological Field Theory in dimension $3$
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5658
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5658<p>I will give an overview of some aspects of $3d$ TFT, from the Turaev-Viro and Reshetikin-Turaev invariants of oriented $3$-manifolds, to the more recent classifications of fully extended theories in terms of fusion categories and once extended theories in terms of Modular Tensor Categories.</p>Sat, 19 Oct 2019 09:35:40 +0200Wed, 23 Oct 2019 12:30:00 +0200Wed, 23 Oct 2019 13:30:00 +0200Manuel AraújoInstituto Superior TécnicoRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryMichele Cirafici, 2019/10/22, 16h, Supersymmetric line operators and their spectral problem
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5618
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5618<p>I will discuss BPS invariants associated with quantum line operators in certain supersymmetric quantum field theories. Such operators can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR they are described by representation theory data. I will discuss the associated BPS spectral problem and the relevant indices.</p>Tue, 08 Oct 2019 19:48:19 +0200Tue, 22 Oct 2019 17:00:00 +0200Tue, 22 Oct 2019 18:00:00 +0200Michele CiraficiUniversity of TriesteRoom P3.10, Mathematics BuildingString TheoryTertuliano Franco, 2019/10/21, 16h, A Mini-course in large deviations
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5646
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5646<p>Large deviations have importance and applications in different areas, as Probability, Statistics, Dynamical Systems, and Statistical Mechanics. In plain words, large deviations correspond to finding and proving the (exponentially small) probability of observing events not expected by the law of large numbers. In this mini-course we introduce the topic including a discussion on the general statement of large deviations and the some of the usual challenges when facing the upper/lowerbound large deviations.</p>Sat, 19 Oct 2019 09:34:19 +0200Mon, 21 Oct 2019 17:00:00 +0200Mon, 21 Oct 2019 18:00:00 +0200Tertuliano FrancoUniversidade Federal da BahiaRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsAmol Sasane, 2019/10/21, 11h, Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5621
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5621<p>The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in flat Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.</p>Mon, 23 Sep 2019 16:23:33 +0200Mon, 21 Oct 2019 12:00:00 +0200Mon, 21 Oct 2019 13:00:00 +0200Amol SasaneLondon School of EconomicsRoom P3.10, Mathematics BuildingMathematical RelativityTomás Reis, 2019/10/18, 11h 30m, Resurgence, Superconductors and Renormalons
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5652
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5652<p>In this talk I will cover the recent work of M. Mariño and I (<a href="https://arxiv.org/abs/1905.09569" rel="noreferrer" target="_blank">https://arxiv.org/abs/1905.09569</a>, <a href="https://arxiv.org/abs/1905.09575" rel="noreferrer" target="_blank">https://arxiv.org/abs/1905.09575</a>) about an application of resurgence to superconductive quantum many-body systems. I will start by introducing the core idea of resurgence. Then, I will overview how to use the TBA to find the perturbative series of the ground-state of the Gaudin-Yang model (and other integrable models) to all orders. Finally, I will show how a resurgence analysis of such series connects to superconductivity and renormalon effects, leading to a concrete conjecture linking the Borel-summability of the perturbative series to the superconductor energy gap.</p>Sat, 12 Oct 2019 11:07:43 +0200Fri, 18 Oct 2019 12:30:00 +0200Fri, 18 Oct 2019 13:30:00 +0200Tomás ReisUniversity of GenevaRoom P3.10, Mathematics Building$QM^3$ Quantum Matter meets MathsRoger Picken, 2019/10/09, 11h 30m, Quantum theory via (higher) groupoids and quantum measures
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5640
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5640<p>The idea of this informal seminar is to present, in cherry-picking fashion, some fascinating work by Ciaglia, Ibort and Marmo, who formulate the Schwinger approach to quantum theory using the contemporary language of groupoids and $2$-groupoids. By bringing in the notion of quantum measures, due to Sorkin, they achieve an elegant description of examples like the qubit or the two-slit experiment.</p><p>The aim is for the seminar to be comprehensible also to students with some awareness of quantum theory, and hopefully will be followed up by future seminars around quantum maths topics such as topological quantum computation and entanglement.</p><h3>Main references</h3><p>Ciaglia, Ibort, Marmo: <a href="https://arxiv.org/abs/1905.12274">https://arxiv.org/abs/1905.12274</a>, <a href="https://arxiv.org/abs/1907.03883">https://arxiv.org/abs/1907.03883</a>, <a href="https://arxiv.org/abs/1909.07265">https://arxiv.org/abs/1909.07265</a></p>Wed, 09 Oct 2019 07:41:30 +0200Wed, 09 Oct 2019 12:30:00 +0200Wed, 09 Oct 2019 13:15:00 +0200Roger PickenDepartamento de Matemática, Instituto Superior TécnicoRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryUgo Bruzzo, 2019/10/01, 16h, On a conjecture about curve semistable Higgs bundles
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5614
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5614<p>We say that a Higgs bundle $E$ over a projective variety $X$ is curve semistable if for every morphism $f : C \to X$, where $C$ is a smooth irreducible projective curve, the pullback $f^\ast E$ is semistable. We study this class of Higgs bundles, reviewing the status of a conjecture about their Chern classes.</p>Tue, 17 Sep 2019 08:33:58 +0200Tue, 01 Oct 2019 17:00:00 +0200Tue, 01 Oct 2019 18:00:00 +0200Ugo BruzzoSISSA, Itália & Universidade Federal da Paraíba, Brazil.Room P3.10, Mathematics BuildingGeometria em LisboaGunter Schutz, 2019/10/01, 15h, The Fibonacci family of dynamical universality classes
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5629
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5629<p>We use the theory of nonlinear fluctuating hydrodynamics to study stochastic transport far from thermal equilibrium in terms of the dynamical structure function which is universal at low frequencies and for large times and which encodes whether transport is diffusive or anomalous. For generic one-dimensional systems we predict that transport of mass, energy and other locally conserved quantities is governed by mode-dependent dynamical universality classes with dynamical exponents $z$ which are Kepler ratios of neighboring Fibonacci numbers, starting with $z = 2$ (corresponding to a diffusive mode) or $z = 3/2$ (Kardar-Parisi-Zhang (KPZ) mode). If neither a diffusive nor a KPZ mode are present, all modes have as dynamical exponent the golden mean $z=(1+\sqrt 5)/2$. The universal scaling functions of the higher Fibonacci modes are Lévy distributions. The theoretical predictions are confirmed by Monte-Carlo simulations of a three-lane asymmetric simple exclusion process.</p>Thu, 26 Sep 2019 21:45:07 +0200Tue, 01 Oct 2019 16:00:00 +0200Tue, 01 Oct 2019 17:00:00 +0200Gunter SchutzJüelich UniversityRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsDebashis Ghoshal, 2019/09/27, 16h, Designing matrix models for zeta functions
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5617
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5617<p>The apparently random pattern of the non-trivial zeroes of the Riemann zeta function (all on the critical line, according to the Riemann hypothesis) has led to the suggestion that they may be related to the spectrum of an operator. It has also been known for some time that the statistical properties of the eigenvalue distribution of an ensemble of random matrices resemble those of the zeroes of the zeta function. With the objective to identify a suitable operator, we start by assuming the Riemann hypothesis and construct a unitary matrix model (UMM) for the zeta function. Our approach, however, could be termed <em>piecemeal</em>, in the sense that, we consider each factor (in the Euler product representation) of the zeta function to get a UMM for each prime, and then assemble these to get a matrix model for the full zeta function. This way we can write the partition function as a trace of an operator. Similar construction works for a family of related zeta functions.</p>Sat, 07 Sep 2019 11:48:15 +0200Fri, 27 Sep 2019 17:00:00 +0200Fri, 27 Sep 2019 18:00:00 +0200Debashis GhoshalJawaharlal Nehru UniversityRoom P3.10, Mathematics BuildingString TheoryYafet Sanchez Sanchez, 2019/09/20, 14h, Quantum Observables in low regularity spacetimes
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=4989
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=4989<p>In this talk I will describe how to construct the algebra of observables of a quantized scalar field when the spacetime metric is not smooth. I will show the main difference with the smooth case, the technical difficulties that arise and how we addressed them.</p><p>This is joint work with G. Hörmann, C. Spreitzer and J. Vickers.</p>Mon, 16 Sep 2019 19:55:34 +0200Fri, 20 Sep 2019 15:00:00 +0200Fri, 20 Sep 2019 16:00:00 +0200Yafet Sanchez SanchezLeibniz University HannoverRoom P4.35, Mathematics BuildingMathematical RelativityMarcel de Jeu, 2019/09/13, 11h, Positive representations of algebras of continuous functions
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5616
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5616<p>It is well known from linear algebra that a family of mutually commuting normal operators on a finite dimensional complex inner product space can be simultaneously diagonalised. Strongly related to this is the fact that a representation of a commutative C*-algebra on a Hilbert space is generated by a so-called spectral measure, taking its values in the orthogonal projections. A result by Ruoff and the lecturer asserts that a similar phenomenon occurs for positive representations of algebras of continuous functions on a substantial class of Banach lattices.</p><p>Recently, it has become clear that these two facts for Hilbert spaces and Banach lattices can be understood from one underlying general theorem for positive homomorphisms of algebras of continuous functions into partially ordered algebras. This result can be proved by purely order-theoretic methods.</p><p>In this lecture, we shall explain this theorem and how it relates to the two special cases mentioned above. We shall also sketch the theory of measure and integration in partially ordered vector spaces that is necessary to formulate and establish it.</p><p>This is joint work with Xingni Jiang.</p>Wed, 04 Sep 2019 15:37:12 +0200Fri, 13 Sep 2019 12:00:00 +0200Fri, 13 Sep 2019 13:00:00 +0200Marcel de JeuLeiden University and University of PretoriaRoom P3.10, Mathematics BuildingAlgebraRui Loja Fernandes, 2019/07/19, 15h, Stability of symplectic leaves
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5609
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5609<p>In this talk I will give a gentle introduction to Poisson manifolds, which can be thought of as (singular) symplectic foliations. As an illustration of the kind of problems one deals in Poisson geometry, I will discuss and give some results on stability of symplectic leaves.</p>Tue, 16 Jul 2019 11:02:40 +0200Fri, 19 Jul 2019 16:00:00 +0200Fri, 19 Jul 2019 17:00:00 +0200Rui Loja FernandesUniversity of Illinois at Urbana-ChampaignRoom P3.10, Mathematics BuildingGeometria em LisboaHansjörg Geiges, 2019/07/17, 14h, Constructions of contact manifolds with controlled Reeb dynamics
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5113
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5113<p>The Reeb flow of a contact form is a generalisation of Hamiltonian flows on energy hypersurfaces in classical mechanics. In this talk I shall address the question of how "complicated" such flows can be. Among other things, I plan to discuss a construction of Reeb flows with a global surface of section on which the Poincaré return map is a pseudorotation. This is joint work with Peter Albers and Kai Zehmisch</p>Thu, 11 Jul 2019 08:54:55 +0200Wed, 17 Jul 2019 15:00:00 +0200Wed, 17 Jul 2019 16:00:00 +0200Hansjörg GeigesUniversität zu KölnRoom P3.10, Mathematics BuildingGeometria em LisboaFrédéric Bourgeois, 2019/07/17, 10h 30m, Geography of (bi)linearized Legendrian contact homology
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5114
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5114<p>The study of Legendrian submanifolds in contact geometry presents some similarities with knot theory. In particular, invariants are needed to distinguish Legendrian isotopy classes. Linearized Legendrian contact homology is one of these, and is based on the count of holomorphic curves. It is obtained after linearizing a differential graded algebra using an augmentation. A bilinearized version using two augmentations was introduced with Chantraine.</p><p>After a self-contained introduction to this context, the geography of these invariants will be described. In the linearized case, it was obtained with Sabloff and Traynor. The bilinearized case turned out to be far more general and was studied with Galant.</p>Mon, 15 Jul 2019 10:05:16 +0200Wed, 17 Jul 2019 11:30:00 +0200Wed, 17 Jul 2019 12:30:00 +0200Frédéric BourgeoisUniversité Paris SudRoom P3.10, Mathematics BuildingGeometria em LisboaMartin Evans, 2019/07/05, 15h, Generalisations to Multispecies
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5139
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5139<p>Second class particle; multispecies exclusion process; hierarchical matrix solution and proof; queueing interpretation.</p>Sun, 02 Jun 2019 15:15:16 +0200Fri, 05 Jul 2019 16:00:00 +0200Fri, 05 Jul 2019 17:30:00 +0200Martin EvansEdinburgh UniversityRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsMartin Evans, 2019/07/04, 15h, Generalisations to Multispecies
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5138
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5138<p>Second class particle; multispecies exclusion process; hierarchical matrix solution and proof; queueing interpretation.</p>Sun, 02 Jun 2019 15:15:34 +0200Thu, 04 Jul 2019 16:00:00 +0200Thu, 04 Jul 2019 17:30:00 +0200Martin EvansEdinburgh UniversityRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsMartin Evans, 2019/07/03, 15h, Phase Diagram
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5137
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5137<p>Complex zeros of nonequilibrium partition function; open ASEP phase transitions; continuous and discontinuous transitions; coexistence line.</p>Sun, 02 Jun 2019 15:16:10 +0200Wed, 03 Jul 2019 16:00:00 +0200Wed, 03 Jul 2019 17:30:00 +0200Martin EvansEdinburgh UniversityRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsMartin Evans, 2019/07/02, 15h, Matrix Product Solution
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5136
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5136<p>Matrix product ansatz; proof of stationarity; computation of partition function $Z_L$; large $L$ asymptotics of $Z_L$; current and density profile; combinatorial approaches.</p>Sun, 02 Jun 2019 15:16:30 +0200Tue, 02 Jul 2019 16:00:00 +0200Tue, 02 Jul 2019 17:30:00 +0200Martin EvansEdinburgh UniversityRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsMartin Evans, 2019/07/01, 15h, Open Boundary ASEP
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5135
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5135<p>The asymmetric simple exclusion process (ASEP) has been studied in probability theory since Spitzer in 1970. Remarkably a version with open boundaries had already been introduced as a model for RNA translation in 1968. This “open ASEP” has since the 1990’s been widely studied in the theoretical physics community as a model of a nonequilibrium system, which sustains a stationary current. In these lectures I will introduce and motivate the model then present a construction — the matrix product ansatz — which yields the exact stationary state for all system sizes. I will derive the phase diagram and analyse the nonequilibrium phase transitions. Finally I will discuss how the approach generalises to multispecies systems.</p><p>In this first lecture I will introduce the motivations; correlation functions; mean-field theory and hydrodynamic limit; dynamical mean-field theory; domain wall theory.</p>Sun, 02 Jun 2019 15:19:48 +0200Mon, 01 Jul 2019 16:00:00 +0200Mon, 01 Jul 2019 17:30:00 +0200Martin EvansEdinburgh UniversityRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsJoe Chen, 2019/06/28, 15h, Random walks, electric networks, moving particle lemma, and hydrodynamic limits
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5153
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5153<p>While the title of my talk is a riff on the famous monograph <em>Random walks and electric networks</em> by Doyle and Snell, the contents of my talk are very much inspired by the book. I'll discuss how the concept of electrical resistance can be applied to the analysis of interacting particle systems on a weighted graph. I will start by summarizing the results of Caputo-Liggett-Richthammer, myself, and Hermon-Salez connecting the many-particle stochastic process to the one-particle random walk process on the level of Dirichlet forms. Then I will explain how to use this type of energy inequality to bound the cost of transporting particles by the effective resistance, and to perform coarse-graining on a class of state spaces which are bounded in the resistance metric. This new method plays a crucial role in the proofs of scaling limits of boundary-driven exclusion processes on the Sierpinski gasket.</p>Mon, 17 Jun 2019 17:13:58 +0200Fri, 28 Jun 2019 16:00:00 +0200Fri, 28 Jun 2019 17:00:00 +0200Joe ChenColgate UniversityRoom P3.31, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsGabriel Nahum, 2019/06/28, 14h, On the algebraic solvability of the MPA approach to the Multispecies SSEP
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5551
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5551On this mini-course we will learn how to extend the MPA formulation to the multispecies case with the very simple SSEP dynamics. Due to the jump symmetries of each particle in the bulk, this formulation allows us to compute any phisical quantity without resorting to the matrices representation. Nevertheless, their existence is still a necessary condition for the formulation to work. We will give an example of such matrices and focus on the exploitation of the induced algebra.Sun, 23 Jun 2019 11:36:39 +0200Fri, 28 Jun 2019 15:00:00 +0200Fri, 28 Jun 2019 16:00:00 +0200Gabriel NahumInstituto Superior TécnicoRoom P3.31, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsHugo Tavares, 2019/06/27, 15h, Least energy solutions of Hamiltonian elliptic systems with Neumann boundary conditions
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5146
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5146<p>In this talk, we will discuss existence, regularity, and qualitative properties of solutions to the Hamiltonian elliptic system $$ -\Delta u = |v|^{q-1} v\ \ \ \text{in} \ \Omega,\quad -\Delta v = |u|^{p-1} u\ \ \ \text{in} \ \Omega,\quad \partial_\nu u=\partial_\nu v=0\ \ \ \text{on} \ \partial\Omega,$$with $\Omega\subset \mathbb R^N$ bounded, both in the sublinear $pq< 1$ and superlinear $pq>1$ problems, in the subcritical regime. In balls and annuli, we show that least energy solutions are <em>not</em> radial functions, but only partially symmetric (namely foliated Schwarz symmetric). A key element in the proof is a new $L^t$-norm-preserving transformation, which combines a suitable flipping with a decreasing rearrangement. This combination allows us to treat annular domains, sign-changing functions, and Neumann problems, which are nonstandard settings to use rearrangements and symmetrizations. Our theorems also apply to the scalar associated model, where our approach provides new results as well as alternative proofs of known facts.</p>Wed, 12 Jun 2019 23:27:33 +0200Thu, 27 Jun 2019 16:00:00 +0200Thu, 27 Jun 2019 17:00:00 +0200Hugo TavaresFaculdade de Ciências, Universidade de LisboaRoom P3.31, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsRenato De Paula, 2019/06/27, 14h, Matrix product ansatz for the totally asymmetric exclusion process
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5454
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5454<p>Generally, it is very difficult to compute nonequilibrium stationary states of a particle system. It turns out that, in some cases, you can find a solution with a quite interesting structure. The goal of this first part of the seminar is to present the structure of this solution — known as matrix product solution (or matrix product ansatz) — using the totally asymmetric exclusion process (TASEP) as a toy model.</p>Mon, 24 Jun 2019 10:02:09 +0200Thu, 27 Jun 2019 15:00:00 +0200Thu, 27 Jun 2019 16:00:00 +0200Renato De PaulaInstituto Superior TécnicoRoom P3.31, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsRodrigo Fontana, 2019/06/27, 14h, Quasinormal modes of black holes: field propagation and stability
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5461
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5461<p>The propagation of probe fields around black hole geometries is an interesting tool for the investigation of two important aspects: the stability of these geometry and the quasinormal modes spectra. In general, for simple enough metrics (e. g. spherically symmetric), the field equation reduces to a wave-like form with a specific potential. This turns the problem of integration into a wave scattering problem with a potential barrier similar to that of a Schrödinger equation in quantum mechanics. With the proper boundary conditions the spectrum is that of damped waves, the quasinormal modes. These represents the characteristic response of black holes in general to linear perturbations and give information about the stability of the geometry. In this talk I will refer some examples of quasinormal modes and destabilization of geometries in black holes in which a non-minimally coupled scalar field act, in the context of Horndeski theory. By using the same tools of field propagation, I still present some of our previous results in relation to the violation of strong cosmic censorship in charged geometries.</p>Mon, 24 Jun 2019 15:22:50 +0200Thu, 27 Jun 2019 15:00:00 +0200Thu, 27 Jun 2019 16:00:00 +0200Rodrigo FontanaUniversidade Federal da Fronteira do Sul - UFFS ChapecóSeminar room (2.8.3), Physics BuildingMathematical RelativityThomas Fuehrer, 2019/06/26, 14h 30m, Introduction to the DPG method: Abstract framework and applications
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=5428
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=5428<p>In this talk I will present the basic ideas of the D(iscontinuous)-P(etrov)-G(<wbr />alerkin) method with optimal test functions which was introduced by Demkowicz and Gopalakrishnan in 2009. We will have a look at the abstract theory and in particular at the concept of optimal test functions. Then, I will define an ultraweak formulation of Poisson's equation and explain how to apply the abstract ideas of DPG methods to this particular case. Finally, I will discuss several problems where the DPG method has been used successfully. These applications range from singular perturbation problems to plate bending problems.</p>Thu, 20 Jun 2019 16:21:33 +0200Wed, 26 Jun 2019 15:30:00 +0200Wed, 26 Jun 2019 16:30:00 +0200<a target='_content' href="http://www.mat.uc.cl/~tofuhrer/">Thomas Fuehrer</a>Pontificia Universidad Católica de ChileRoom P3.10, Mathematics BuildingPartial Differential EquationsStefano Andriolo, 2019/06/24, 15h, The Weak Gravity Conjecture
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5112
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5112<p>We discuss various versions of the weak gravity conjecture.</p>Wed, 08 May 2019 14:18:48 +0200Mon, 24 Jun 2019 16:00:00 +0200Mon, 24 Jun 2019 17:00:00 +0200Stefano AndrioloHong Kong University of Science and TechnologyRoom P3.10, Mathematics BuildingString TheoryJo Nelson, 2019/06/21, 11h, Equivariant and nonequivariant contact homology
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5116
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5116<p>I will explain how to make use of geometric methods to obtain three related flavors of contact homology, a Floer theoretic contact invariant. In particular, I will discuss joint work with Hutchings which constructs nonequivariant and a family floer equivariant version of contact homology. Both theories are generated by two copies of each Reeb orbit over $\mathbb{Z}$ and capture interesting torsion information. I will then explain how one can recover the original cylindrical theory proposed by Eliashberg-Givental-Hofer via our constructions.</p>Sat, 08 Jun 2019 09:07:44 +0200Fri, 21 Jun 2019 12:00:00 +0200Fri, 21 Jun 2019 13:00:00 +0200Jo NelsonRice UniversityRoom P3.10, Mathematics BuildingGeometria em Lisboa