CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Yafet Sanchez Sanchez, 2019/09/18, 15h, 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>Tue, 30 Jul 2019 09:45:34 +0200Wed, 18 Sep 2019 16:00:00 +0200Wed, 18 Sep 2019 17:00:00 +0200Yafet Sanchez SanchezLeibniz University HannoverRoom P3.10, Mathematics BuildingMathematical RelativityRui 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 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 RelativityRenato 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 SystemsThomas 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 LisboaPietro Caputo, 2019/06/18, 13h 30m, The spectral gap of the interchange process: a review
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5128
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5128<p>Aldous’ spectral gap conjecture asserted that on any graph the random walk process and the interchange process have the same spectral gap. In this talk I will review the work in collaboration with T. M. Liggett and T. Richthammer from 2009, in which we proved the conjecture by means of a recursive strategy. The main idea, inspired by electric network reduction, was to reduce the problem to the proof of a new comparison inequality between certain weighted graphs, which we referred to as the <em>octopus inequality</em>. The proof of the latter inequality is based on suitable closed decompositions of the associated matrices indexed by permutations. I will first survey the problem, with background and consequences of the result, and then discuss the recursive approach based on network reduction together with some sketch of the proof. I will also present a more general, yet unproven conjecture.</p>Thu, 23 May 2019 15:29:36 +0200Tue, 18 Jun 2019 14:30:00 +0200Tue, 18 Jun 2019 15:30:00 +0200Pietro CaputoUniversità Roma TreRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsPietro Caputo, 2019/06/17, 13h 30m, Mixing time of the adjacent walk on the simplex
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5127
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5127<p>By viewing the $N$-simplex as the set of positions of $N-1$ ordered particles on the unit interval, the adjacent walk is the continuous time Markov chain obtained by updating independently at rate $1$ the position of each particle with a sample from the uniform distribution over the interval given by the two particles adjacent to it. We determine its spectral gap and mixing time and show that the total variation distance to the uniform distribution displays a cutoff phenomenon. The results are extended to a family of log-concave distributions obtained by replacing the uniform sampling by a symmetric Beta distribution. This is joint work with Cyril Labbe' and Hubert Lacoin.</p>Wed, 22 May 2019 11:26:42 +0200Mon, 17 Jun 2019 14:30:00 +0200Mon, 17 Jun 2019 15:30:00 +0200Pietro CaputoUniversità Roma TreRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsBrian Hall, 2019/06/05, 16h 30m, Eigenvalues of random matrices in the general linear group
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5124
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5124<p>I will begin by discussing the two standard prototype random matrix models, one for Hermitian matrices and one for general matrices. For large matrices, the eigenvalues follow the "semicircular law" in the first case and the "circular law" in the second case. Furthermore, there is a simple relationship between these two laws.</p><p>I will then discuss two "multiplicative" analogs of these models, in which the random matrices are chosen from the unitary group and the general linear group, respectively. In the unitary case, the limiting eigenvalue distribution was computed by Biane and exhibits an interesting phase transition when a certain scaling parameter equals 4. I will then describe recent results of mine with Driver and Kemp on the general linear case. The limiting distribution again undergoes a phase transition and turns out to have a remarkably simple structure. The talk will be self-contained with lots of pictures and possibly even a few jokes.</p>Sat, 18 May 2019 08:45:09 +0200Wed, 05 Jun 2019 17:30:00 +0200Wed, 05 Jun 2019 18:30:00 +0200<a target='_content' href="https://www3.nd.edu/~bhall/">Brian Hall</a>University of Notre DameRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryBrian Hall, 2019/06/04, 15h, Large-$N$ Segal-Bargmann transform with application to random matrices
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5123
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5123<p>I will describe the Segal-Bargmann transform for compact Liegroups, with emphasis on the case of the unitary group $U(N)$. In this case, the transform is a unitary map from the space of $L^2$ functions on $U(N)$ to the space of $L^2$ holomorphic functions on the "complexified" group $\operatorname{GL}(N;\mathbb{C})$. I will then discuss what happens in the limit as $N$ tends to infinity. Finally, I will describe an application to the eigenvalues of random matrices in $\operatorname{GL}(N;\mathbb{C})$. The talk will be self-contained and have lots of pictures.</p>Fri, 17 May 2019 11:27:49 +0200Tue, 04 Jun 2019 16:00:00 +0200Tue, 04 Jun 2019 17:00:00 +0200Brian HallUniversity of Notre DameRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsRichard Laugesen, 2019/06/03, 15h, Spectrum of the Robin Laplacian: recent results, and open problems
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5115
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5115<p>I will discuss two recent theorems and one recent conjecture about maximizing or minimizing the first three eigenvalues of the Robin Laplacian of a simply connected planar domain. Conformal mappings and winding numbers play a key role in the geometric constructions. In physical terms, these eigenvalues represent decay rates for heat flow assuming a “partially insulating” boundary.</p>Mon, 27 May 2019 08:42:49 +0200Mon, 03 Jun 2019 16:00:00 +0200Mon, 03 Jun 2019 17:00:00 +0200Richard LaugesenUniversity of Illinois at Urbana-ChampaignRoom P3.10, Mathematics BuildingGeometria em LisboaSimão Correia, 2019/05/30, 15h, Critical well-posedness for the modified Korteweg-de Vries equation and self-similar dynamics
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5126
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5126<p>We consider the modified Korteweg-de Vries equation over $\mathbb{R}$ $$ u_t + u_{xxx}=\pm(u^3)_x. $$ This equation arises, for example, in the theory of water waves and vortex filaments in fluid dynamics. A particular class of solutions to (mKdV) are those which do not change under scaling transformations, the so-called <em>self-similar</em> solutions. Self-similar solutions blow-up when $t\to 0$ and determine the asymptotic behaviour of the evolution problem at $t=+\infty$. The known local well-posedness results for the (mKdV) fail when one considers critical spaces, where the norm is scaling-invariant. This means that self-similar solutions lie outside of the scope of these results. Consequently, the dynamics of (mKdV) around self-similar solutions are currently unknown. In this talk, we will show existence and uniqueness of solutions to the (mKdV) lying on a critical space which includes both regular and self-similar solutions. Afterwards, we present several results regarding global existence, asymptotic behaviour at $t=+\infty$ and blow-up phenomena at $t=0$. This is joint work with Raphaël Côte and Luis Vega.</p>Thu, 23 May 2019 15:00:11 +0200Thu, 30 May 2019 16:00:00 +0200Thu, 30 May 2019 17:00:00 +0200Simão CorreiaFaculdade de Ciências, Universidade de LisboaRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsDiogo Arsénio, 2019/05/28, 15h, Recent progress on the mathematical theory of plasmas
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5125
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5125<p>The incompressible Navier–Stokes–Maxwell system is a classical model describing the evolution of a plasma (i.e. an electrically conducting fluid). Although small smooth solutions to this system (in the spirit of Fujita–Kato) are known to exist, the existence of large weak solutions (in the spirit of Leray) in the energy space remains unknown. This defect can be attributed to the difficulty of coupling the Navier–Stokes equations with a hyperbolic system. In this talk, we will describe recent results aiming at building solutions to Navier–Stokes–Maxwell systems in large functional spaces. In particular, we will show, for any initial data with finite energy, how a smallness condition on the electromagnetic field alone is sufficient to grant the existence of global solutions.</p>Tue, 21 May 2019 09:46:01 +0200Tue, 28 May 2019 16:00:00 +0200Tue, 28 May 2019 17:00:00 +0200Diogo ArsénioNew York University Abu DhabiRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsPhillipo Lappicy, 2019/05/22, 15h, Space of initial data for self-similar Schwarzschild solutions
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5069
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5069<p>The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic equation on the sphere with various singularities and nonlinearity being the prescribed scalar curvature of space. We focus on self-similar Schwarzschild solutions. Those describe, for example, the initial data for the interior of black holes. We construct the space of initial data for such solutions and show that the metric at the event horizon is constrained to the global attractors of such parabolic equations. Lastly, some properties of those attractors and its solutions are explored.</p>Mon, 06 May 2019 11:41:58 +0200Wed, 22 May 2019 16:00:00 +0200Wed, 22 May 2019 17:00:00 +0200Phillipo LappicyUniversidade de São PauloRoom P3.10, Mathematics BuildingMathematical RelativityCédric Bernardin, 2019/05/21, 15h, Microscopic models for multicomponents SPDE’s with a KPZ flavor
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5122
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5122<p>The usual KPZ equation is the scaling limit of weakly asymmetric microscopic models with one conserved quantity. In this talk I will present some weakly asymmetric microscopic models with several conserved quantities for which it is possible to derive macroscopic SPDEs with a KPZ flavor.</p><p>Joint work with R. Ahmed, T. Funaki, P. Gonçalves, S. Sethuraman and M. Simon.</p>Tue, 21 May 2019 09:46:54 +0200Tue, 21 May 2019 16:00:00 +0200Tue, 21 May 2019 17:00:00 +0200Cédric BernardinUniversity of Nice Sophia-AntipolisRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsVishnu Jejjala, 2019/05/20, 15h, Experiments with Machine Learning in Geometry & Physics
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=4978
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=4978<p>Identifying patterns in data enables us to formulate questions that can lead to exact results. Since many of the patterns are subtle, machine learning has emerged as a useful tool in discovering these relationships. We show that topological features of Calabi–Yau geometries are machine learnable. We indicate the broad applicability of our methods to existing large data sets by finding relations between knot invariants, in particular, the hyperbolic volume of the knot complement and the Jones polynomial.</p>Mon, 29 Apr 2019 15:04:44 +0200Mon, 20 May 2019 16:00:00 +0200Mon, 20 May 2019 17:00:00 +0200Vishnu JejjalaUniversity of the WitwatersrandRoom P3.10, Mathematics BuildingString TheoryCarlos Herdeiro, 2019/05/15, 15h 30m, Light ring stability in ultra-compact objects
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=4972
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=4972<p>We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e., they have a light ring) must have at least two light rings, and one of them is stable. It has been argued that stable light rings generally lead to nonlinear spacetime instabilities. Our result implies that smooth, physically and dynamically reasonable ultracompact objects are not viable as observational alternatives to black holes whenever these instabilities occur on astrophysically short time scales. The proof of the theorem has two parts: (i) We show that light rings always come in pairs, one being a saddle point and the other a local extremum of an effective potential. This result follows from a topological argument based on the Brouwer degree of a continuous map, with no assumptions on the spacetime dynamics, and hence it is applicable to any metric gravity theory where photons follow null geodesics. (ii) Assuming Einstein's equations, we show that the extremum is a local minimum of the potential (i.e., a stable light ring) if the energy-momentum tensor satisfies the null energy condition.</p>Wed, 24 Apr 2019 08:15:43 +0200Wed, 15 May 2019 16:30:00 +0200Wed, 15 May 2019 17:30:00 +0200Carlos HerdeiroInstituto Superior TécnicoRoom P4.35, Mathematics BuildingMathematical RelativityConrado Costa, 2019/05/14, 15h, Random walks in cooling random environments: stable and unstable behaviors under regular diverging cooling maps
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=4996
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=4996<p>Random Walks in Cooling Random Environments (RWCRE), a model introduced by L. Avena, F. den Hollander, is a dynamic version of Random Walk in Random Environment (RWRE) in which the environment is fully resampled along a sequence of deterministic times, called refreshing times. In this talk I will consider effects of the ressampling map on the fluctuations associated with the annealed law and the Large Deviation principle under the quenched measure. I conclude clarifying the paradox of different fluctuations and identical LDP for RWCRE and RWRE. This is a joint work with L. Avena, Y. Chino, and F. den Hollander.</p>Tue, 09 Apr 2019 09:08:56 +0200Tue, 14 May 2019 16:00:00 +0200Tue, 14 May 2019 17:00:00 +0200Conrado CostaLeiden UniversityRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsMark Lawson, 2019/05/09, 11h, Non-commutative Boolean algebras
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5000
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5000<p>In this talk, I shall explain how the classical theory of Stone duality may be generalized to a non-commutative setting. This theory has connections with étale groupoids, quantales, groups and inverse semigroups.</p><p>Some of the work was joint with Alina Vdovina. I shall assume no prior exposure to this theory.</p>Mon, 06 May 2019 13:02:18 +0200Thu, 09 May 2019 12:00:00 +0200Thu, 09 May 2019 13:00:00 +0200<a target='_content' href="http://www.macs.hw.ac.uk/~markl/">Mark Lawson</a>Heriot-Watt UniversityRoom P3.10, Mathematics BuildingAlgebraIsabelle Charton, 2019/05/09, 11h, Hamiltonian $S^1$-spaces with large equivariant pseudo-index.
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5109
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5109<p>Let \((M,\omega)\) be a compact symplectic manifold of dimension \(2n\) endowed with a Hamiltonian circle action with only isolated fixed points. Whenever \(M\) admits a toric \(1\)-skeleton \(\mathcal{S}\), which is a special collection of embedded \(2\)-spheres in \(M\), we define the notion of equivariant pseudo-index of \(\mathcal{S}\): this is the minimum of the evaluation of the first Chern class \(c_1\) on the spheres of \(\mathcal{S}\).</p><p>In this talk we will discuss upper bounds for the equivariant pseudo-index. In particular, when the even Betti numbers of \(M\) are unimodal, we prove that it is at most \(n+1\) . Moreover, when it is exactly \(n+1\), \(M\) must be homotopically equivalent to \(\mathbb{C}P^n\).</p>Fri, 03 May 2019 14:10:13 +0200Thu, 09 May 2019 12:00:00 +0200Thu, 09 May 2019 13:00:00 +0200Isabelle ChartonUniversity of CologneRoom P4.35, Mathematics BuildingGeometria em LisboaFederico Cantero, 2019/05/07, 12h, Higher Steenrod squares for Khovanov homology
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5099
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5099<p>We describe stable cup-$i$ products on the cochain complex with $\mathbb{F}_2$ coefficients of any augmented semi-simplicial object in the Burnside category. An example of such an object is the Khovanov functor of Lawson, Lipshitz and Sarkar. Thus we obtain explicit formulas for cohomology operations on the Khovanov homology of any link.</p>Fri, 26 Apr 2019 20:29:18 +0200Tue, 07 May 2019 13:00:00 +0200Tue, 07 May 2019 14:00:00 +0200Federico CanteroUniversity of Barcelona, SpainRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryNils Carqueville, 2019/05/07, 10h, TQFTS, Orbifolds and Topological Quantum Computation
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5003
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5003<p>I will review basic notions and results in topological quantum field theory and discuss its orbifolds, with the aim to apply them in the context of topological quantum computation.</p>Thu, 02 May 2019 08:26:25 +0200Tue, 07 May 2019 11:00:00 +0200Tue, 07 May 2019 12:00:00 +0200Nils CarquevilleUniversity of ViennaRoom P5.18, Mathematics BuildingString TheoryCeyda Simsek, 2019/05/06, 15h, Spacetime geometry of non-relativistic string theory
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=4994
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=4994<p>Non-relativistic string theory is described by a sigma model that maps a two dimensional string worldsheet to a non-relativistic spacetime geometry. We discuss recent developments in understanding the spacetime geometry of non-relativistic string theory trying to provide several new insights. We show that the non-relativistic string action admits a surprisingly large number of symmetries. We introduce a non-relativistic limit to obtain the non-relativistic string action which also provides us the non-relativistic T-duality transformation rules and spacetime equations of motion.</p>Thu, 02 May 2019 08:23:50 +0200Mon, 06 May 2019 16:00:00 +0200Mon, 06 May 2019 17:00:00 +0200Ceyda SimsekUniversity of GroningenRoom P3.10, Mathematics BuildingString TheoryJoão Fontinha, 2019/04/24, 14h 30m, A primer on the Section Conjecture — a bridge between arithmetic and homotopy
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5051
https://math.tecnico.ulisboa.pt/seminars/algebra?action=show&id=5051<p>In 1983, Grothendieck wrote a letter to Faltings in which he formulated a conjecture for hyperbolic curves over fields which are finitely generated over the rationals. Remaining open to date, it carries the study of rational points on an algebraic variety to the realm of profinite groups. Assuming only a working knowledge of basic Algebraic Geometry, we formulate and motivate the Section Conjecture and outline some modern attempts to tackle it.</p>Thu, 04 Apr 2019 07:54:10 +0200Wed, 24 Apr 2019 15:30:00 +0200Wed, 24 Apr 2019 16:30:00 +0200João FontinhaETH ZurichRoom P4.35, Mathematics BuildingAlgebra