CAMGSD Seminars
https://camgsd.tecnico.ulisboa.pt/seminarios
CAMGSD Seminar announcements60Simon Ross, 2020/03/02, 15h, KdV Charges in $2D$ CFT
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5662
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5662<p>Two-dimensional CFTs have an infinite set of commuting conserved charges, known as the quantum KdV charges, built out of the stress tensor. We compute the thermal correlation functions of the these KdV charges on a circle. We show that these correlation functions are given by quasi-modular differential operators acting on the torus partition function.</p>Sun, 24 Nov 2019 10:51:45 +0100Mon, 02 Mar 2020 16:00:00 +0100Mon, 02 Mar 2020 17:00:00 +0100Simon RossDurham UniversityRoom P3.10, Mathematics BuildingString TheoryMiguel Duarte, 2020/01/16, 14h 30m, Conformally flat slices of asymptotically flat spacetimes
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5663
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5663<p>For mathematical convenience initial data sets in numerical relativity are often taken to be conformally flat. Employing the dual-foliation formalism, we investigate the physical consequences of this assumption. Working within a large class of asymptotically flat spacetimes we show that the ADM linear momentum is governed by the leading Lorentz part of a boost even in the presence of supertranslation-like terms. Following up, we find that in spacetimes that are asymptotically flat, and admit spatial slices with vanishing linear momentum that are sufficiently close to conformal flatness, any boosted slice can not be conformally flat. Consequently there are no conformally flat boosted slices of the Schwarzschild spacetime. This confirms the previously anticipated explanation for the presence of junk-radiation in Brandt-Bruegmann puncture data.</p>Sat, 02 Nov 2019 16:12:04 +0100Thu, 16 Jan 2020 15:30:00 +0100Thu, 16 Jan 2020 16:30:00 +0100Miguel DuarteInstituto Superior TécnicoSeminar room (2.8.3), Physics BuildingMathematical RelativityDamião Júnio Araújo, 2020/01/08, 16h 30m, A two-phase free boundary problem ruled by the infinity laplacian
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=5688
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=5688<p>In this talk we discuss some regularity aspects for viscosity solutions of a non-variational two-phase free boundary problem ruled by the infinity Laplacian. Joint work with E. Teixeira (University of Central Florida - USA) and J. M. Urbano (Universidade de Coimbra - PT).</p>Tue, 03 Dec 2019 13:51:03 +0100Wed, 08 Jan 2020 17:30:00 +0100Wed, 08 Jan 2020 18:30:00 +0100Damião Júnio AraújoUniversidade Federal da ParaíbaRoom P3.10, Mathematics BuildingPartial Differential EquationsRita 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 RelativityRenato de Paula, 2019/12/17, 15h, From the porous medium model to the porous medium equation
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5683
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5683<p>The aim of this seminar is to present an overview of the porous medium model and its hydrodynamic equation, the porous medium equation. We will focus on exploring the main characteristics of this equation and how we can see it from the particle system's point of view.</p>Wed, 27 Nov 2019 17:28:03 +0100Tue, 17 Dec 2019 16:00:00 +0100Tue, 17 Dec 2019 17:00:00 +0100Renato de PaulaInstituto Superior TécnicoRoom P3.10, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsAndré Guerra, 2019/12/17, 14h, Compensated compactness and under constant rank constraints
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=5687
https://math.tecnico.ulisboa.pt/seminars/pde?action=show&id=5687<p>In this talk we will discuss the fundamental aspects of the theory of compensated compactness in the general A-free framework developed by Murat and Tartar, under the assumption that A has constant rank. We prove sharp weak continuity results for the compensated compactness quantities and we show that they are precisely the nonlinear quantities with Hardy space integrability, thus proposing an answer to a question raised by Coifman-Lions-Meyer-Semmes. This gives a link between compensated compactness and compensated regularity.</p>Wed, 27 Nov 2019 15:51:12 +0100Tue, 17 Dec 2019 15:00:00 +0100Tue, 17 Dec 2019 16:00:00 +0100André GuerraUniversity of OxfordRoom P3.10, Mathematics BuildingPartial Differential EquationsJoão Caetano, 2019/12/16, 15h, Integrability in and beyond AdS/CFT
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5661
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5661<p>In this talk, I am going to review some aspects of the current state of the art of Integrability in the AdS/CFT correspondence and beyond. I will first review a general nonperturbative approach to compute multipoint correlation functions of local operators in the $N=4$ SYM theory which allows us to explore the theory even beyond the planar level. In the second part, I will describe my recent work about exploring deformations of $N=4$ SYM by irrelevant operators, which revives an old attempt of generalizing the AdS/CFT correspondence. Here integrability seems to also play an important role and opens the door for its application for non-conformal field theories.</p>Sun, 17 Nov 2019 21:41:03 +0100Mon, 16 Dec 2019 16:00:00 +0100Mon, 16 Dec 2019 17:00:00 +0100João CaetanoSimons Center for Geometry and PhysicsRoom P3.10, Mathematics BuildingString TheoryAlan Coley, 2019/12/16, 10h 30m, Theoretical cosmology
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5694
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5694<p>This will be an informal talk on open problems in theoretical cosmology, suitable for a (relatively) general audience.</p>Tue, 10 Dec 2019 14:27:28 +0100Mon, 16 Dec 2019 11:30:00 +0100Mon, 16 Dec 2019 12:30:00 +0100Alan ColeyDalhousie UniversityRoom P3.10, Mathematics BuildingMathematical RelativityPaul Wedrich, 2019/12/11, 11h 30m, Invariants of $4$-manifolds from Khovanov-Rozansky link homology
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5692
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5692<p>Ribbon categories are $3$-dimensional algebraic structures that control quantum link polynomials and that give rise to $3$-manifold invariants known as skein modules. I will describe how to use Khovanov-Rozansky link homology, a categorification of the $\operatorname{\mathfrak{gl}}(N)$ quantum link polynomial, to obtain a $4$-dimensional algebraic structure that gives rise to vector space-valued invariants of smooth $4$-manifolds. The technical heart of this construction is the newly established functoriality of Khovanov-Rozansky homology in the $3$-sphere. Based on joint work with Scott Morrison and Kevin Walker <a href="https://arxiv.org/abs/1907.12194" rel="noreferrer noreferrer" target="_blank">https://arxiv.org/abs/1907.12194</a>.</p>Thu, 05 Dec 2019 09:26:46 +0100Wed, 11 Dec 2019 12:30:00 +0100Wed, 11 Dec 2019 13:30:00 +0100Paul WedrichMax Planck Institute and University of BonnRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryPaolo Benincasa, 2019/12/09, 15h, Understanding $\operatorname{AdS}_2$: From Calogero-like models and SLE to $4d$ 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>Extremal black holes show the presence of an $\operatorname{AdS}_2$ factor as an universal feature. This fact provides a strong motivation for getting a deeper understanding of $\operatorname{AdS}_2$ spacetimes. In this talk, I will argue how $\operatorname{AdS}_2$ systems have a natural description in terms of $1d$ Calogero-type models and, in turn to SLE curves, which describe the geodesic motion of particles in $\operatorname{AdS}_2$. This treatment allows to compute the dimension of the phase space of these geodesics, linking it to the leading Bekenstein-Hawking black hole entropy and the black hole degeneracy.</p>Tue, 03 Dec 2019 13:45:45 +0100Mon, 09 Dec 2019 16:00:00 +0100Mon, 09 Dec 2019 17:00:00 +0100Paolo BenincasaNiels Bohr InstituteRoom P3.10, Mathematics BuildingString TheoryErnesto Nungesser, 2019/12/06, 14h 30m, On the massless Einstein-Boltzmann system
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5665
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5665<p>There are several recent important results concerning the massless Einstein-Vlasov system such as the stability of Minkowski space or the stability of De Sitter spacetime. In this talk I will present some recent progress on the massless Einstein-Boltzmann system in both directions, initial singularity and long time behaviour:</p><ul><li>The massless Einstein-Boltzmann system with a conformal-gauge singularity in an FLRW background: <a data-saferedirecturl="https://www.google.com/url?q=https://arxiv.org/abs/1903.06067&source=gmail&ust=1574179545208000&usg=AFQjCNFrxBn451vUdW_gS4Uvb0AWEN6UYg" href="https://arxiv.org/abs/1903.06067" target="_blank">https://arxiv.org/abs/1903.<wbr />06067</a></li><li>On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology: <a data-saferedirecturl="https://www.google.com/url?q=https://arxiv.org/abs/1911.04937&source=gmail&ust=1574179545208000&usg=AFQjCNErCThD2ERGzTmag3mrPSWuYtVaBg" href="https://arxiv.org/abs/1911.04937" target="_blank">https://arxiv.org/abs/1911.<wbr />04937</a></li></ul><p>This is joint work with Ho Lee and Paul Tod.</p>Fri, 06 Dec 2019 13:03:14 +0100Fri, 06 Dec 2019 15:30:00 +0100Fri, 06 Dec 2019 16:30:00 +0100Ernesto NungesserUniversidad Politécnica de MadridRoom P3.10, Mathematics BuildingMathematical RelativityAnna Siffert, 2019/12/03, 17h, Construction of harmonic mappings
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5686
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5686<p>Geometric variational problems frequently lead to analytically extremely hard, non-linear partial differential equations, where the standard methods fail. Thus finding non-trivial solutions is challenging. The idea is to study solutions with a certain minimum level of symmetry (i.e. group actions with low cohomogeneity), and use the symmetry to reduce the original problem to systems of non-linear ordinary differential equations, typically with singular boundary values. In my talk I explain how to construct harmonic mappings between manifolds with a lot of symmetry (i.e. cohomogeneity one manifolds). If time permits, I will discuss applications of the developed methods.</p>Thu, 28 Nov 2019 14:43:45 +0100Tue, 03 Dec 2019 18:00:00 +0100Tue, 03 Dec 2019 19:00:00 +0100Anna SiffertMax-Planck-Institut, BonnRoom P3.10, Mathematics BuildingGeometria em LisboaAlex Bullivant, 2019/11/29, 11h 30m, Topological Quantum Computing with loops
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5655
https://math.tecnico.ulisboa.pt/seminars/QM3?action=show&id=5655<p>Non-abelian statistics of anyons in two dimensions have attracted considerable interest in the past 20 years, in part due to the potential for realising fault-tolerant quantum computation. In comparison, in three dimensions there exists a no-go theorem for point particles realising non-abelian statistics. However, three-dimensional condensed matter systems naturally support spatially extended excitations, such as loops, which can admit non-abelian statistics.<br /><br />In this talk I will give a brief overview of topological quantum computing with anyons, utilising the connections between the mathematics of topological quantum field theories and Hamiltonian models of topological phases of matter. Building on this connection I will then discuss the ongoing work of describing non-abelian exchange statistics of loop excitations in three dimensions and the potential applications to quantum computation.</p>Tue, 19 Nov 2019 23:30:51 +0100Fri, 29 Nov 2019 12:30:00 +0100Fri, 29 Nov 2019 13:30:00 +0100<a target='_content' href="https://eps.leeds.ac.uk/maths/staff/5710/alex-bullivant">Alex Bullivant</a>University of LeedsRoom P3.10, Mathematics Building$QM^3$ Quantum Matter meets MathsAlex Bullivant, 2019/11/27, 15h, $3+1D$ Dijkgraaf-Witten theory and the Categorified Quantum Double
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5685
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5685<p>The quantum double is a quasi-triangular Hopf algebra whose category of representations can be interpreted physically as describing the processes of fusion and braiding of anyons in the $2+1D$ Dijkgraaf-Witten TQFT. Motivated by the possibilities of topological quantum computing in $3+1D$, in this talk I will give an informal overview of my ongoing research towards understanding the categorified quantum double and its bicategory of $2$-representations. In particular, I will focus on the relation between such constructions and the Hamiltonian formulation of $3+1D$ Dijkgraaf-Witten TQFT in order to describe the braiding and fusion of extended excitations such as loops. <span> </span></p>Sat, 23 Nov 2019 12:36:03 +0100Wed, 27 Nov 2019 16:00:00 +0100Wed, 27 Nov 2019 17:00:00 +0100<a target='_content' href="https://eps.leeds.ac.uk/maths/staff/5710/alex-bullivant">Alex Bullivant</a>University of LeedsRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryÁngel González-Prieto, 2019/11/27, 11h 15m, Topological recursion in the motivic theory of character varieties
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5684
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5684<p>The algebraic structure of the moduli spaces of representations of surface groups (aka character varieties) has been widely studied due to their tight relation with moduli spaces of Higgs bundles. In particular, Hodge-type invariants, like the so-called E-polynomial, has been objective of intense research over the past decades. However, subtler algebraic invariants as their motivic classes in the Grothendieck ring of algebraic varieties remain unknown in the general case.</p><p>In this talk, we will construct a Topological Quantum Field Theory that computes the motivic classes of representation varieties. This tool gives rise to an effective computational method based on topological recursion on the genus of the surface. As application, we will use it to compute the motivic classes of parabolic $\operatorname{SL}(2,\mathbb{C})$-character varieties over any compact orientable surface.</p>Sat, 23 Nov 2019 11:30:32 +0100Wed, 27 Nov 2019 12:15:00 +0100Wed, 27 Nov 2019 13:15:00 +0100<a target='_content' href="http://www.mat.ucm.es/~joseag12/">Ángel González-Prieto</a>ICMAT (Madrid)Room P3.10, Mathematics BuildingTopological Quantum Field TheoryEmilio Franco, 2019/11/20, 15h, The derived category of coherent sheaves II
https://math.tecnico.ulisboa.pt/seminars/hitchin?action=show&id=5681
https://math.tecnico.ulisboa.pt/seminars/hitchin?action=show&id=5681<p>In our journey towards homological mirror symmetry, we will resume our study of the derived category of coherent sheaves focusing on the functors involved in the definition of Fourier-Mukai transforms: push-forward, pull-back and tensor product. We will describe the associated derived functors and some relations among them, namely the projection formula and base change theorems.</p>Thu, 14 Nov 2019 15:54:43 +0100Wed, 20 Nov 2019 16:00:00 +0100Wed, 20 Nov 2019 17:00:00 +0100<a target='_content' href="https://www.math.tecnico.ulisboa.pt/~efranco/">Emilio Franco</a>CAMGSD (IST, U. Lisboa)Room P3.31, Mathematics BuildingWorking Seminar on mirror symmetry on the Hitchin systemBruno Colbois, 2019/11/19, 16h 30m, On the shape of a Riemannian manifold with large first nonzero eigenvalue for the Laplacian and the Dirichlet-to-Neumann operator
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5615
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5615<p>Classically, there is a strong relationship between the shape of a Riemannian manifold and the spectrum of its Laplace-operator, and, more generally, with the spectrum of Laplace type operators. In particular, for the spectrum of the Laplacian, the presence of a large first nonzero eigenvalue is related to some concentration phenomena. In the first part of the talk, I will recall these classical relations. In the second part of the talk, I will introduce the Dirichlet-to-Neumann operator on a manifold with boundary. I will survey the same types of questions in this context (existence of large first nonzero eigenvalue, concentration phenomena) without going into the technical details. This second part corresponds to work in progress with Alexandre Girouard.</p>Sat, 09 Nov 2019 16:39:36 +0100Tue, 19 Nov 2019 17:30:00 +0100Tue, 19 Nov 2019 18:30:00 +0100Bruno ColboisUniversité de NeuchâtelRoom P3.10, Mathematics BuildingGeometria em LisboaFrancesca Ferrari, 2019/11/18, 15h, A look into $3d$ modularity
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5628
https://math.tecnico.ulisboa.pt/seminars/strings?action=show&id=5628<p>Since the 1980s, the study of invariants of 3-dimensional manifolds has benefited from the connections between topology, physics and number theory. Motivated by the recent discovery of a new homological invariant (corresponding to the half-index of certain $3d$ $N=2$ theories), in this talk I describe the role of quantum modular forms, mock and false theta functions in the study of $3$-manifold invariants. The talk is based on <a href="https://arxiv.org/abs/1809.10148">1809.10148</a> and work in progress with Cheng, Chun, Feigin, Gukov, and Harrison.</p>Sun, 17 Nov 2019 10:50:32 +0100Mon, 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, On quantumness in multi-parameter quantum critical metrology
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 introduce a measure of quantum-ness in quantum multi-parameter estimation problems. One can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér-Rao bound. We apply this measure to quantitatively assess the quantum character of phase transition phenomena in peculiar quantum critical models. We consider a paradigmatic class of lattice fermion systems, which shows equilibrium quantum phase transition and dissipative non-equilibrium steady-state phase transitions.</p>Tue, 19 Nov 2019 10:55:49 +0100Fri, 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 MathsStefano Scotta, 2019/11/14, 16h, Equilibrium fluctuations for symmetric exclusion with long jumps and infinitely extended reservoirs
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5677
https://math.tecnico.ulisboa.pt/seminars/cam/?action=show&id=5677<p>The aim of this work is the analysis of fluctuations around equilibrium for a diffusive and symmetric exclusion process with long jumps and infinitely extended reservoirs (introduced in [<a href="https://arxiv.org/abs/1702.07216">BGJO</a>]). In particular we study how the parameters characterizing the model change the behavior of the stochastic fluctuations of the macroscopic density of particles around the equilibrium. We will see how the SPDE involved will pass from the one which solution is a generalized Ornstein-Uhlenbeck process when the reservoirs are <em>weak</em>, to an SPDE without diffusive term when the reservoirs are so <em>strong</em> that the fluctuations are only caused by their action.</p><p>Joint work with C. Bernardin, P. Gonçalves and M. Jara.</p><h3>Reference</h3><p>[BGJO] Bernardin, C., Gonçalves, P. and Oviedo Jimenez, B. <em>Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps</em>.</p>Wed, 13 Nov 2019 13:32:44 +0100Thu, 14 Nov 2019 17:00:00 +0100Thu, 14 Nov 2019 18:00:00 +0100Stefano ScottaInstituto Superior TécnicoRoom P4.35, Mathematics BuildingAnalysis, Geometry, and Dynamical SystemsTom Sutherland, 2019/11/13, 15h, The derived category of coherent sheaves
https://math.tecnico.ulisboa.pt/seminars/hitchin?action=show&id=5679
https://math.tecnico.ulisboa.pt/seminars/hitchin?action=show&id=5679<p>Motivated by its role in homological mirror symmetry, this talk will introduce the derived category of coherent sheaves on a smooth projective variety. We will see that many of the typical operations on coherent sheaves can be lifted to derived functors, respecting the triangulated structure of the derived category. This paves the way for the systematic study of these functors as Fourier-Mukai transforms.</p>Sat, 09 Nov 2019 08:37:50 +0100Wed, 13 Nov 2019 16:00:00 +0100Wed, 13 Nov 2019 17:00:00 +0100<a target='_content' href="https://webpages.ciencias.ulisboa.pt/~tasutherland/index.html">Tom Sutherland</a>Faculdade de Ciências, Universidade de LisboaRoom P3.31, Mathematics BuildingWorking Seminar on mirror symmetry on the Hitchin systemMichela Zedda, 2019/11/12, 16h 30m, Projectively induced Ricci-flat Kaehler metrics
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5645
https://math.tecnico.ulisboa.pt/seminars/geolis?action=show&id=5645<p>The aim of this talk is to discuss the problem of classifying Kaehler-Einstein manifolds which admit an isometric and holomorphic immersion into the complex projective space. We start giving an overview of the problem focusing in particular on the Ricci-flat case. Ricci-flat non-flat Kaehler manifolds are conjectured to be not projectively induced. Next, we give evidence to this conjecture for Calabi’s Ricci-flat metrics on holomorphic line bundles over compact Kaehler-Einstein manifolds.</p>Sun, 10 Nov 2019 08:16:47 +0100Tue, 12 Nov 2019 17:30:00 +0100Tue, 12 Nov 2019 18:30:00 +0100Michela ZeddaUniversità di ParmaRoom P3.10, Mathematics BuildingGeometria em LisboaGabriel Lopes Cardoso, 2019/11/08, 16h, Weyl metrics and Wiener-Hopf factorization
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5664
https://math.tecnico.ulisboa.pt/seminars/mr?action=show&id=5664<p>We consider the Riemann-Hilbert factorization approach to the construction of Weyl metrics in four space-time dimensions. We present, for the first time, a rigorous proof of the remarkable fact that the canonical Wiener-Hopf factorization of a matrix obtained from a general (possibly unbounded) monodromy matrix, with respect to an appropriately chosen contour, yields a solution to the non-linear gravitational field equations. This holds regardless of whether the dimensionally reduced metric in two dimensions has Minkowski or Euclidean signature. We show moreover that, by taking advantage of a certain degree of freedom in the choice of the contour, the same monodromy matrix generally yields various distinct solutions to the field equations. Our proof, which fills various gaps in the existing literature, is based on the solution of a second Riemann-Hilbert problem and highlights the deep role of the spectral curve, the normalization condition in the factorization and the choice of the contour. This approach allows for the explicit construction of solutions, including new ones, to the non-linear gravitational field equations, using simple complex analytic results. As an illustration, we show that by factorizing a simple rational diagonal matrix, we explicitly obtain a class of Weyl metrics which includes, in particular, the solution describing the interior region of the Schwarzschild black hole, a cosmological Kasner solution and the Rindler metric.</p>Mon, 28 Oct 2019 14:58:41 +0100Fri, 08 Nov 2019 17:00:00 +0100Fri, 08 Nov 2019 18:00:00 +0100Gabriel Lopes CardosoInstituto Superior TécnicoRoom P3.10, Mathematics BuildingMathematical RelativityPedro Brito, 2019/11/06, 16h 30m, Galois symmetries in geometry
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5674
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5674<p>I’ll say a few words about some homotopical (“higher”) methods to study knot spaces and diffeomorphism groups. A fascinating appearance, and one of my current obsessions, is made by the absolute Galois group of the rationals.</p>Sun, 03 Nov 2019 11:12:34 +0100Wed, 06 Nov 2019 17:30:00 +0100Wed, 06 Nov 2019 18:00:00 +0100Pedro BritoInstituto Superior TécnicoRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryAleksandar Mikovic, 2019/11/06, 16h, Categorification of LQG spin-network basis
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5673
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5673<p>We describe an approach of how to find a $2$-group generalization of the spin-network basis from Loop Quantum Gravity. This gives a basis of spin-foam functions which are generalizations of the Wilson surface holonomy invariant for the $3$-dimensional Euclidean $2$-group.</p><p> </p>Sun, 03 Nov 2019 11:23:27 +0100Wed, 06 Nov 2019 17:00:00 +0100Wed, 06 Nov 2019 17:30:00 +0100Aleksandar MikovicUniversidade LusófonaRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryEmilio Franco, 2019/11/06, 15h, Introduction to Mirror Symmetry on the Hitchin System
https://math.tecnico.ulisboa.pt/seminars/hitchin?action=show&id=5660
https://math.tecnico.ulisboa.pt/seminars/hitchin?action=show&id=5660<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>Tue, 22 Oct 2019 15:49:45 +0200Wed, 06 Nov 2019 16:00:00 +0100Wed, 06 Nov 2019 17:00:00 +0100Emilio FrancoCAMGSD, Instituto Superior TécnicoRoom P4.35, Mathematics BuildingWorking Seminar on mirror symmetry on the Hitchin systemEmilio 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 LisboaManuel Araújo, 2019/11/06, 14h 30m, Coherence for $3$-dualizable objects
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5672
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5672<p>I will explain the notion of coherence for duals and adjoints in higher categories. I will discuss a strategy for using knowledge of coherence data and the cobordism hypothesis to give presentations of fully extended bordism categories and mention some progress in dimension $3$.</p>Mon, 04 Nov 2019 14:06:47 +0100Wed, 06 Nov 2019 15:30:00 +0100Wed, 06 Nov 2019 16:00:00 +0100Manuel AraújoInstituto Superior TécnicoRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryJohn Huerta, 2019/11/06, 14h, Higher structures on supermanifolds
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5671
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5671<p>My recent work has concerned two projects, both concerned with higher structures on supermanifolds. I will probably focus on my work extending the classification theorems for gerbes to supermanifolds, with an eye to examples on super Lie groups. My other project, that I will probably not discuss, concerns applying cyclic cohomology to super-Yang-Mills theory in the so-called superspace formalism (i.e., formulated as a theory on a supermanifold).<br /> </p>Sun, 03 Nov 2019 11:13:40 +0100Wed, 06 Nov 2019 15:00:00 +0100Wed, 06 Nov 2019 15:30:00 +0100John HuertaInstituto Superior TécnicoRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryMarco Mackaay, 2019/11/06, 11h 30m, $2$-Representation theory
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5670
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5670<p>The $2$-representation theory of $2$-categories is a categorical analogue of the representation theory of algebras. In my talk, I will recall its origins, its purposes, its basic features and explain some important examples. This talk is based on joint work with Mazorchuk, Miemietz, Tubbenhauer and Zhang.</p>Wed, 13 Nov 2019 19:22:16 +0100Wed, 06 Nov 2019 12:30:00 +0100Wed, 06 Nov 2019 13:30:00 +0100Marco MackaayUniversidade do AlgarveRoom P3.10, Mathematics BuildingTopological Quantum Field TheoryMarko Stosic, 2019/11/05, 17h 30m, On Colored HOMFLY homology
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5669
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5669<p>I’ll try to give a brief description of the categorification of colored HOMFLY polynomial for knots, and discuss various open problems related with these invariants, including their definition, properties, relationship with string theory, as well as surprising combinatorial identities and properties of these invariants in special cases of torus knots and rational knots.</p>Sun, 03 Nov 2019 11:14:28 +0100Tue, 05 Nov 2019 18:30:00 +0100Tue, 05 Nov 2019 19:00:00 +0100Marko StosicInstituto Superior TécnicoRoom P3.31, Mathematics BuildingTopological Quantum Field TheoryPedro Lopes, 2019/11/05, 17h, Research topics in persistent tangles and hyperfinite knots
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5668
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5668<p>We look into persistent tangles i.e., tangles such that its presence in a diagram implies that diagram is knotted and remark their prevalence. We also look into hyperfinite knots i.e., limits of sequences of classes of knots and relate them to wild knots.</p>Sun, 03 Nov 2019 11:15:06 +0100Tue, 05 Nov 2019 18:00:00 +0100Tue, 05 Nov 2019 18:30:00 +0100Pedro LopesInstituto Superior TécnicoRoom P3.31, Mathematics BuildingTopological Quantum Field TheoryJoão Esteves, 2019/11/05, 16h, A quantization of the Loday-Ronco Hopf algebra
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5667
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5667<p>In previous works we considered a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco and showed that extending this Hopf Algebra by identifying pairs of nearest neighbour leaves and thus producing graphs with loops we obtain the full recursion formula of Eynard and Orantin. We also discussed the algebraic structure of the spaces of correlation functions in $g=0$ and in $g\gt 0$. By taking a classical and a quantum product respectively we endowed both spaces with a ring structure. Here we will show that the extended algebra of graphs is in fact a Hopf algebra and can be seen as a sort of quantization of the Loday-Ronco Hopf algebra. This is work in progress.</p>Sun, 03 Nov 2019 11:15:27 +0100Tue, 05 Nov 2019 17:00:00 +0100Tue, 05 Nov 2019 17:30:00 +0100João EstevesInstituto Superior TécnicoRoom P3.31, Mathematics BuildingTopological Quantum Field TheoryRoger Picken, 2019/11/05, 15h 30m, Research topics in higher gauge theory, knot theory, and anyons
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5666
https://math.tecnico.ulisboa.pt/seminars/tqft?action=show&id=5666<p>Under the heading higher gauge theory I will briefy discuss:</p><ul><li>gerbes on supergroups (to be described by John Huerta in his talk).</li><li>the relation between 2-group (discretized) connections and transports (with Jeff Morton).</li><li>surface transport in 3D quantum gravity (with Jeanette Nelson).</li></ul><p>I will then focus on two projects:</p><ul><li>development of the Eisermann invariant of knots (based on previous work with João Faria Martins).</li><li>(higher) gauge theoretical models for anyons in topological quantum computation.</li></ul>Sun, 03 Nov 2019 11:15:48 +0100Tue, 05 Nov 2019 16:30:00 +0100Tue, 05 Nov 2019 17:00:00 +0100Roger PickenInstituto Superior TécnicoRoom P3.31, Mathematics BuildingTopological Quantum Field TheoryAlessandra 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>Tue, 19 Nov 2019 22:39:28 +0100Thu, 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>Tue, 22 Oct 2019 09:36:21 +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>Wed, 20 Nov 2019 11:14:05 +0100Fri, 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 BuildingAlgebra