BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Loïc Poulain d'Andecy (Laboratoire de Mathématiques de Reims) DTSTART:20200505T193000Z DTEND:20200505T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/1 DESCRIPTION:Title: Fused Hecke algebras and centralisers of tensor repres entations of quantum sl(N)\nby Loïc Poulain d'Andecy (Laboratoire de Mathématiques de Reims) as part of CRM-Séminaire Physique Mathématique\ n\n\nAbstract\n(Joint work with Nicolas Crampé) The goal of the talk is t o present diagrammatic algebras and their deformations generalising the sy mmetric group and the Hecke algebra. We call these algebras\, respectivel y\, the algebra of fused permutations and the fused Hecke algebra. One mo tivation for considering these algebras is to write explicit Baxterisation formulas providing\, on an abstract/algebraic level\, solutions of the Ya ng-Baxter equation. These formulas generalise the Baxterisation formula o f the Hecke algebra related to the vector representation V of U_q(sl_N) (t he spin 1/2 representation if N=2). The new Baxterisation formulas contro l the solutions of YB equation on any symmetric power of the vector repres entation of U_q(sl_N) (the higher spin representations if N=2). Besides\, the meaning of these algebras in the context of the Schur-Weyl duality wi ll be explained: they provide a description of the centralisers of tensor products of symmetric powers of V. The representation theory of these new algebras will be explained and\, from this\, the centralisers can be cons tructed as quotients\, both with a representation-theoretic and an algebra ic/diagrammatic description. These results can be seen as analogues for h igher spins of a construction of the Temperley-Lieb algebras from the Heck e algebras.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik de Bie (Universiteit Gent) DTSTART:20200512T193000Z DTEND:20200512T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/2 DESCRIPTION:Title: The Dunkl intertwining operator\nby Hendrik de Bie (Universiteit Gent) as part of CRM-Séminaire Physique Mathématique\n\n\ nAbstract\nThere are two crucial operators in the theory of Dunkl operator s. The first is the Dunkl transform\, which generalizes the Fourier transf orm. The second is the intertwining operator\, which maps ordinary partial derivatives to Dunkl operators. Although some abstract statements are kno wn about the intertwining operator\, the explicit formula for classes of r eflection groups is generally not known. In recent work Yuan Xu proposed a formula in the case of dihedral groups and a restricted class of function s. We extend his formula to all functions and give a general strategy on h ow to obtain similar formulas for other reflections groups. This is based on joint work with Pan Lian\, available under arXiv:2002.09065.\n\nEn lign e/Web - Svp remplir ce formulaire/Please fill in this form: https://forms. gle/S1NcNQ8BxkzfAXcj9\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Maloney (McGill University) DTSTART:20200519T193000Z DTEND:20200519T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/3 DESCRIPTION:Title: Progress on Pure Gravity in Three Dimensions\nby A lex Maloney (McGill University) as part of CRM-Séminaire Physique Mathém atique\n\n\nAbstract\nI will describe the challenges and progress in const ructing a theory of "pure gravity" in three dimensions\, i.e. a theory wh ich contains only metric degrees of freedom and nothing else. Conformal b ootstrap techniques provide strong constraints on the theory\, and indicat e that the spectrum of the theory must contain new states in addition to g ravitons and black holes. I will provide an interpretation for these new states.\n\nEn ligne/Web - Svp remplir ce formulaire/Please fill in this f orm: https://forms.gle/S1NcNQ8BxkzfAXcj9\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Morin-Duchesne (Université Catholique de Louvain-la-Neuve) DTSTART:20200526T193000Z DTEND:20200526T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/4 DESCRIPTION:Title: Boundary emptiness formation probabilities in the six- vertex model at $\\Delta=- 1/2$\nby Alexis Morin-Duchesne (Université Catholique de Louvain-la-Neuve) as part of CRM-Séminaire Physique Mathé matique\n\n\nAbstract\nThe connection between statistical mechanics and th e combinatorics of alternating sign matrices is known since the work of Ra zumov and Stroganov on the spin-1/2 XXZ chain. One important example of th is combinatorial relation occurs in the study of the emptiness formation p robability $EFP_{N\,m}$. This observable is defined as the sum of the squa res of the ground state components for the chain of length $N$\, restricte d to components where $m$ consecutive spins are aligned. At the combinator ial point $\\Delta = - 1/2$\, it takes the form of a simple product of int egers. This was proven in 2012 by L. Cantini\, who also found a combinator ial interpretation for these probabilities in terms of plane partitions.\n In joint work with C. Hagendorf and L. Cantini\, we define a new family of overlaps $C_{N\,m}$ for the spin-1/2 XXZ chain. It is equal to the linear sum of the groundstate components that have $m$ consecutive aligned spins . For reasons that will be discussed\, we refer to the ratio $C_{N\,m}/C_{ N\,0}$ as the {\\it boundary emptiness formation probability}. We compute $C_{N\,m}$ at the combinatorial point as a simple product of integers.\n\n En ligne/Web - Svp remplir ce formulaire/Please fill in this form: https:/ /forms.gle/S1NcNQ8BxkzfAXcj9\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Joris Van der Jeugt (Universiteit Gent) DTSTART:20200602T193000Z DTEND:20200602T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/5 DESCRIPTION:Title: Partition functions for paraboson and parafermion syst ems\nby Joris Van der Jeugt (Universiteit Gent) as part of CRM-Sémina ire Physique Mathématique\n\n\nAbstract\nParabosons and parafermions\, al gebraically characterized by triple relations rather than just (anti)-comm utation relations\, have been around for more than 60 years. Over the rec ent years\, new mathematical results have been obtained for their represen tations\, in particular character formulae. In the present talk\, we give a short review of the algebraic structures behind parabosons and paraferm ions\, and of their representations. We show how the new expressions for characters lead to proper forms of grand partition functions for systems o f parabosons and parafermions. These forms of the partition function allo w the computation of statistical and thermodynamic functions for such syst ems. We discuss some examples\, such as the average number of particles o n an orbital\, and the average number of particles in the system.\n\nEn li gne/Web - Svp remplir ce formulaire/Please fill in this form: https://form s.gle/S1NcNQ8BxkzfAXcj9\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Brandenberger (McGill University) DTSTART:20200609T193000Z DTEND:20200609T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/6 DESCRIPTION:Title: S-brane cosmology\nby Robert Brandenberger (McGill University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstrac t\nThe Hawking-Penrose singularity theorems are usually used to argue that there was a "Big Bang" singularity at the beginning of time. I will show that by adding an "S-brane"\, a distributional source\, to the matter act ion\, one can obtain a non-singular bouncing cosmology which obviates the need for a period of cosmological inflation.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Théo Pinet (Université de Montréal) DTSTART:20200616T193000Z DTEND:20200616T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/7 DESCRIPTION:Title: The structure of the representations of the affine Tem perley-Lieb algebras on the periodic XXZ chain\nby Théo Pinet (Univer sité de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\n Abstract\nThe affine Temperley-Lieb algebras aTLN(β) are a family of infi nite dimensional algebras generalizing the well-known Temperley-Lieb algeb ras TLN(β). They play\, for the periodic XXZ chain\, the role played by t he original Temperley-Lieb algebra for the open XXZ chain. Their represent ation theory is much richer than that of the original TL family and admits a lot of similiraties with the representation theory of the Virasoro alge bra Vir. In particular\, we will show in this talk that there exists aTLN( β)-modules (called critical) whose structure is akin that of the so-calle d Feigin-Fuchs Vir-modules. To do this\, we will highlight the link betwee n these critical modules and other canonical representations of aTLN(β) ( the standard modules) while building up on the well-known quantum Schur-We yl duality between TLN(β) and Uqsl2.\n\nL'exposé sera donné en françai s avec des diapositives en anglais - The talk be given in French with slid es written in English\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Chalifour (Université de Montréal) DTSTART:20200908T193000Z DTEND:20200908T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/8 DESCRIPTION:Title: General solution of the exceptional Hermite differenti al equation and its minimal surface representation\nby Vincent Chalifo ur (Université de Montréal) as part of CRM-Séminaire Physique Mathémat ique\n\n\nAbstract\nThe main aim of this presentation is the study of the general solution of the exceptional Hermite differential equation with fix ed partition and the construction of minimal surfaces associated with this solution. We derive a linear second-order ordinary differential equation associated with a specific family of exceptional polynomials of codimensio n two. We show that these polynomials can be expressed in terms of classic al Hermite polynomials. We find the general analytic solution of the excep tional Hermite differential equation which has no gap in its spectrum. We show that the spectrum is complemented by non-polynomial solutions. We pre sent an implementation of the obtained results for the surfaces expressed in terms of the general solution making use of the classical Enneper-Weier strass formula for the immersion in the Euclidean space $\\mathbb{E}^3$\, leading to minimal surfaces. Three-dimensional displays of these surfaces are presented.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Éric Dupuis (Université de Montréal) DTSTART:20200915T193000Z DTEND:20200915T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/9 DESCRIPTION:Title: Monopole operators in gauged Gross-Neveu models\nb y Éric Dupuis (Université de Montréal) as part of CRM-Séminaire Physiq ue Mathématique\n\n\nAbstract\nCompact quantum electrodynamics in 2+1 dim ensions with massless fermions (QED3) describes the quantum spin liquid ph ase in certain quantum magnets. This model includes monopoles whose proli feration may be prevented by the massless fermions. This screening effect is however lost if a fermion mass is generated\, which leads to confineme nt. Such confinement-deconfinement transitions are found in QED3-Gross-Ne veu (QED3-GN) models where the GN interaction induces the mass. Monopole operators are studied at the critical point of these theories. Using the state-operator correspondence\, we obtain the scaling dimension of monopol e operators at leading order in 1/N where 2N is the number of fermion flav ors. Two universality classes with distinct flavor symmetries are conside red. For a SU(2) x SU(N) symmetry\, a hierarchy is shown by constraining the magnetic spin of monopoles and comparing the scaling dimensions in the various spin sectors. The representation of monopoles reflects this hier archy and a degeneracy lifting relative to the QED3 case. For a SU(2N) sy mmetry\, the monopole scaling dimension is used to test a field theory dua lity.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Zelaya (Université de Montréal) DTSTART:20200922T193000Z DTEND:20200922T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/10 DESCRIPTION:Title: Fourth Painlevé and Ermakov equations: quantum invar iants and new exactly-solvable time-dependent Hamiltonians\nby Kevin Z elaya (Université de Montréal) as part of CRM-Séminaire Physique Mathé matique\n\n\nAbstract\nIn this talk\, we discuss a new realization of exac tly-solvable time-dependent Hamiltonians based on the solutions of the fou rth Painlevé and the Ermakov equations. The latter is achieved by introdu cing a shape-invariant condition between an unknown quantum invariant and a set of third-order intertwining operators with time-dependent coefficien ts. The new quantum invariant is constructed by adding a deformation term to the well-known parametric oscillator invariant. Such a deformation depe nds explicitly on time through the solutions of the Ermakov equation\, whi ch ensures the regularity of the new time-dependent potential of the Hamil tonian at each time. On the other hand\, with the aid of the proper repara metrization\, the fourth Painlevé equation appears\, the parameters of wh ich dictate the spectral behavior of the quantum invariant. In particular\ , the eigenfunctions of the third-order ladder operators lead to several s equences of solutions to the Schroedinger equation\, determined in terms o f the solutions of a Riccati equation\, Okamoto polynomials\, or nonlinear bound states of the derivative nonlinear Schroedinger equation. Remarkabl y\, it is noticed that the solutions in terms of the nonlinear bound state s lead to a quantum invariant with equidistant eigenvalues\, which contain s both an (N+1)-dimensional and an infinite sequence of eigenfunctions. Th e resulting family of time-dependent Hamiltonians is such that\, to the au thors' knowledge\, have been unnoticed in the literature of nonstationary systems.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Rayan (University of Saskatchevan) DTSTART:20200929T193000Z DTEND:20200929T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/11 DESCRIPTION:Title: The geometry and physics of Hitchin systems\nby S teven Rayan (University of Saskatchevan) as part of CRM-Séminaire Physiqu e Mathématique\n\n\nAbstract\nThe moduli space of stable Higgs bundles on a Riemann surface\, known as the Hitchin system\, arises as a space of ga uge-equivalent solutions to dimensionally-reduced self-dual Yang-Mills equ ations. This moduli space turns out to be the phase space for a non-trivi al completely integrable Hamiltonian system\, is a noncompact Calabi-Yau m anifold\, and has a mirror symmetry that is intertwined with Langlands dua lity. In this talk\, I will review a number of geometric features of the Hitchin system that have been discovered over the past 30 years. I will c onclude by speculating on connections between Higgs bundles and condensed- matter physics.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuela Girotti (Mila\, Université de Montréal) DTSTART:20201006T193000Z DTEND:20201006T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/12 DESCRIPTION:Title: Fredholm Determinant Solutions of the Painlevé II Hi erarchy and Gap Probabilities of Determinantal Point Processes\nby Man uela Girotti (Mila\, Université de Montréal) as part of CRM-Séminaire P hysique Mathématique\n\n\nAbstract\nWe study Fredholm determinants of a c lass of integral operators\, whose kernels can be expressed as double cont our integrals of a special type. Such Fredholm determinants appear in vari ous random matrix and statistical physics models. We show that the logarit hmic derivatives of the Fredholm determinants are directly related to solu tions of the Painlevé II hierarchy. This confirms and generalizes a recen t conjecture by Le Doussal\, Majumdar\, and Schehr (2018). In addition\, w e obtain asymptotics at infinity for the Painlevé transcendents and large gap asymptotics for the corresponding point processes. This is a joint wo rk with Mattia Cafasso (Univ. Angers) and Tom Claeys (UC Louvain).\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/12/ END:VEVENT BEGIN:VEVENT SUMMARY:John Harnad (Concordia University and Centre des recherches mathé matiques) DTSTART:20201013T193000Z DTEND:20201013T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/13 DESCRIPTION:Title: Fermionic approach to bilinear expansions of KP corre lators in terms of BKP correlators\nby John Harnad (Concordia Universi ty and Centre des recherches mathématiques) as part of CRM-Séminaire Phy sique Mathématique\n\n\nAbstract\nThis talk will present a synthesis and generalization of two results relating determinants and Pfaffians of minor s of a skew symmetric matrix\, with applications to solutions of the KP an d DKP integrable hierarchies. The first is an algebraic identity expressi ng the determinant of any minor of a skew matrix as a sum over products of Pfaffians of its principal minors\; the second an expression for Schur fu nctions as bilinear sums over Schur $Q$-functions. A general bilinear ide ntity\, of which these two results are special cases\, expresses determina ntal derivative correlators of $\\tau$-functions of the KP hierarchy as su ms over products of pairs of Pfaffian derivative correlators for the BKP $ \\tau$ function.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Escobar (Universidad Autonoma Metropolitana-Iztapalapa) DTSTART:20201117T203000Z DTEND:20201117T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/14 DESCRIPTION:Title: New infinite families of Nth-order superintegrable sy stems\nby Adrian Escobar (Universidad Autonoma Metropolitana-Iztapalap a) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nIn this talk\, a general description of quantum superintegrable systems in a two- dimensional Euclidean space is presented. We consider Hamiltonian systems allowing separation of variables in cartesian coordinates for which one po lynomial integral (symmetry) of second order in momentum variables and one more of Nth-order occur. The main properties of doubly exotic superintegr able potentials\, i.e. potentials $V(x\, y) = V_1(x) + V_2(y)$ where neith er $V_1(x)$ nor $V_2(y)$ satisfy any linear ordinary differential equation \, are discussed. In particular\, we present two new infinite families of $N$th order superintegrable systems with the property that $V_1(x)$ and $V _2(y)$ are given by the solution of a nonlinear ODE that passes the Painle v\\'e test. We conjecture that these potentials will always actually have the Painlev\\'e property. In the classical case the latter property disapp ears.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Marquette (University of Queensland) DTSTART:20201103T203000Z DTEND:20201103T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/15 DESCRIPTION:Title: Embedding of Racah algebra and superintegrable system s\nby Ian Marquette (University of Queensland) as part of CRM-Séminai re Physique Mathématique\n\n\nAbstract\nThe rank-$1$ Racah algebra $R(3)$ plays a pivotal role in the theory of superintegrable systems. It appear s as the symmetry algebra of the $3$-parameter system on the $2$-sphere fr om which all second-order conformally flat superintegrable models in $2$D can be obtained by means of suitable limits and contractions. A higher ran k generalization of $R(3)$\, the so-called rank $n-2$ Racah algebra $R(n)$ \, has been considered recently and showed to be the symmetry algebra of t he general superintegrable model on the $(n-1)$-sphere. I will discuss how such an algebraic structure naturally arises as embedded inside a larger quadratic algebra characterizing $n$D superintegrable models with non-cent ral terms. This is shown both in classical and quantum mechanics through s uitable (symplectic or differential) realisations of the Racah and additio nal generators. I will also present an explicit construction of the comple te symmetry algebras for two families of $n$-dimensional maximally superin tegrable models\, the Smorodinsky-Winternitz system and the generalized Ke pler-Coulomb system. For both families\, the underlying symmetry algebras are higher-rank quadratic algebras containing the Racah algebra $R(n)$ as subalgebra. High-order algebraic relations among the generators of the fu ll quadratic algebras are also obtained both in the classical and quantum frameworks. However\, these approaches rely on explicit realizations as di fferential operators. I will also briefly discuss how an algebraic constru ction of the symmetry algebra of the generic superintegrable systems on th e 2-sphere can be generated from an underlying Lie algebra connected with intertwining operators.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Luc Vinet (Université de Montréal) DTSTART:20201110T203000Z DTEND:20201110T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/16 DESCRIPTION:Title: Sklyanin algebras\, Askey-Wilson polynomials and Heun operators\nby Luc Vinet (Université de Montréal) as part of CRM-Sé minaire Physique Mathématique\n\n\nAbstract\nI will discuss the connectio ns between Askey-Wilson polynomials\, Heun operators and degenerate Sklya nin algebras of dimensions three and four. The q-para Racah polynomials wi ll be seen to realize a basis for the finite dimensional representations o f the latter. The Heun-Askey-Wilson operator will also emerge in this cont ext.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Meng Cheng (Yale University) DTSTART:20210126T203000Z DTEND:20210126T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/17 DESCRIPTION:Title: Fractonic topological phases\nby Meng Cheng (Yale University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstrac t\nRecently a new type of gapped phases was discovered in (3+1) dimensions \, whose unusual properties appear to defy a conventional QFT description. Notably\, they support quasiparticles with reduced mobility\, sometimes c ompletely immobile\, and have an exponentially large number of locally ind istinguishable ground states on a three torus. In this talk I will review basic facts about fracton models\, and discuss recent progress in understa nding general structures of fractonic phases.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Marie Stephan (Université Lyon 1) DTSTART:20210202T203000Z DTEND:20210202T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/18 DESCRIPTION:Title: Fermionic limit shapes\nby Jean-Marie Stephan (Un iversité Lyon 1) as part of CRM-Séminaire Physique Mathématique\n\n\nAb stract\nI study a 1d translational invariant free fermions model in imagin ary time\, with nearest neighbor and next-nearest neighbor hopping terms\, for various types of boundary conditions. This type of model typically a rises when trying to solve 2d classical models such as dimer models\, or I sing models\, through the transfer matrix formalism. In the absence of th e next-nearest neighbor perturbation our fermion model is known to give ri se to phases separation and so-called arctic curves\, which have been stud ied extensively both in the physics and mathematical literature. The pert urbation considered here turns out to not be always positive\, that is\, t he corresponding statistical mechanical model does not always have positiv e Boltzmann weights. I discuss the conditions under which this is the cas e\, and what sense to make of it when not.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Jerzy Lewandowski (University of Warsaw) DTSTART:20210209T203000Z DTEND:20210209T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/19 DESCRIPTION:Title: Non-singular global Kerr-NUT-(A)dS spacetimes\nby Jerzy Lewandowski (University of Warsaw) as part of CRM-Séminaire Physiq ue Mathématique\n\n\nAbstract\nThe outstanding issue of a non-singular ex tension of the Kerr-NUT-(anti) de Sitter solutions to Einstein's equations is solved completely. The Misner's method of obtaining the extension for Taub-NUT spacetime is generalized in a non-singular manner. The Killing vectors that define non-singular spaces of non-null orbits are derived and applied. The global structure of spacetime is discussed. The non-singul ar conformal geometry of the infinities is derived. The Killing horizons are present.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/19/ END:VEVENT BEGIN:VEVENT SUMMARY:James Moran (Université de Montréal) DTSTART:20210309T203000Z DTEND:20210309T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/22 DESCRIPTION:Title: Non-linear ladder operators and coherent states for t he 2:1 oscillator\nby James Moran (Université de Montréal) as part o f CRM-Séminaire Physique Mathématique\n\n\nAbstract\nThe 2:1 two-dimensi onal anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators throu gh the use of non-commutative binomial theorems as well as solving recurre nce relations. The states generated are good candidates for the natural ge neralisation of the su(2) coherent states of the two-dimensional isotropic oscillator. The two-dimensional non-linear generalised ladder operators l ead to several chains of states which are connected in a non trivial way. The uncertainty relations of the defining chain of states are calculated a nd it is found that they admit a resolution of the identity and the spatia l distribution of the wavefunction produces Lissajous figures in correspon dence with the classical 2:1 oscillator.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Turbiner (UNAM\, Stony Brook University and CRM) DTSTART:20210223T203000Z DTEND:20210223T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/24 DESCRIPTION:Title: Anharmonic oscillator: a solution\nby Alexander T urbiner (UNAM\, Stony Brook University and CRM) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nAnharmonic oscillator (quantum pendu lum) is one of the oldest\, non-solvable exactly problems in quantum physi cs. For the one-dimensional quartic quantum anharmonic oscillator with $V (x)= x^2+g^2 x^4$ the Perturbation Theory (PT) in powers of $g^2$ (weak co upling regime) and the semiclassical expansion in powers of $\\hbar$ for e nergies coincide. It is due to the fact that the dynamics in $x$-space an d in $(gx)$-space corresponds to the same energy spectrum with effective c oupling constant $(\\hbar g^2)$. Two equations\, which govern the dynamic s in those two spaces\, the Riccati-Bloch (RB) and the Generalized Bloch ( GB) equations\, are derived. The PT in $g^2$ for the log of wave function leads to polynomial in $x$ coefficients for the RB equation and to the tr ue semiclassical expansion in powers of $\\hbar$ for the GB equation\, whi ch corresponds to a loop expansion for the density matrix in the path inte gral formalism. Matching these two expansions leads to a extremely compac t\, uniform approximation of the wavefunction in $x$-space with unpreceden ted accuracy $\\sim 10^{-6}$ locally and unprecedented accuracy $\\sim 10^ {-9}-10^{-10}$ in energy for any $g^2 \\geq 0$.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Knap (Technical University of Munich) DTSTART:20210216T203000Z DTEND:20210216T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/25 DESCRIPTION:Title: Hilbert Space Fragmentation\nby Michael Knap (Tec hnical University of Munich) as part of CRM-Séminaire Physique Mathémati que\n\n\nAbstract\nStrong interactions and frustration often lead to dynam ically constrained excitations of quantum matter. Examples include spin-ic e compounds whose spin moments are aligned to fulfill a local ice rule\, f rustrated quantum magnets with dimerized excitations\, and fracton phases with excitations that are only mobile in certain directions if at all. Her e\, we will discuss that the combination of charge and dipole conservation \, a characteristic of fractonic quantum matter\, leads to an extensive fr agmentation of the Hilbert space\, which in turn can lead to a breakdown o f thermalization. We characterize such a Hilbert space fragmentation by in troducing `statistically localized integrals of motion' (SLIOM)\, whose ei genvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense\, but appear localized to su b-extensive regions in space when their expectation value is taken in typi cal states with a finite density of particles. Furthermore\, we discuss th at there exist perturbations which destroy these integrals of motion in th e bulk of the system\, while keeping them on the boundary. This results in statistically localized strong zero modes\, leading to infinitely long-li ved edge magnetizations along with a thermalizing bulk\, constituting the first example of such strong edge modes in a non-integrable model. We also discuss that in a particular example\, these edge modes lead to the appea rance of topological string order in a certain subset of highly excited ei gen states. A variant of these models can be realized in Rydberg quantum s imulators.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Johan van de Leur (Utrecht University) DTSTART:20210316T193000Z DTEND:20210316T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/26 DESCRIPTION:Title: Polynomial solutions of KP and Gelfand-Dickey hierarc hies\nby Prof. Johan van de Leur (Utrecht University) as part of CRM-S éminaire Physique Mathématique\n\n\nAbstract\nIt is a wellknown result o f M. Sato that all Schur functions are solutions of the KP hierarchy and that a general solution can be expressed  as a possibly infinite linear c ombination of these Schur functions. However\, not all linear combination s are solutions of this KP hierarchy. In this talk I will address the top ic of polynomial solutions of various hierarchies. In particular\, I will give a simple formula that describes all polynomial solutions for both th e KP and Gelfand-Dickey hierarchies.  This is based on joint work with Vi ctor Kac.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Del Monte (CRM) DTSTART:20210323T193000Z DTEND:20210323T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/27 DESCRIPTION:Title: Isomonodromic tau functions on Riemann Surfaces throu gh free fermions and four-dimensional QFTs\nby Fabrizio Del Monte (CRM ) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nUsing ar guments from two-dimensional Conformal Field Theory\, Gamayun Iorgov and L isovyy provided in 2012 an explicit expression for the tau function of the sixth\nPainlevé equation as a Fourier transform of Virasoro conformal bl ocks of a free fermion CFT\, which has an explicit combinatorial (converge nt) expansion as the so-called\ndual partition function of a corresponding four-dimensional supersymmetric Quantum Field Theory. This "Kiev formula" has been later generalized to more general isomonodromic problems on the sphere\, with both regular and irregular punctures\, and the combinatorial expansion has been shown to arise from the minor expansion of an associat ed Fredholm determinant\, in terms of which the tau function can be formul ated.\n\nIn this talk I will show how the above picture can be generalized to the case of Riemann Surfaces with nonzero genus and marked points\, wh ere new features arise due to the nontriviality of the moduli space of fla t connections. I will consider in detail the example of the punctured toru s\, for which I will show that the tau function can be written as a free f ermion conformal block from two-dimensional CFT\, and as a Fredholm determ inant of Cauchy operators\, whose minor expansion reproduces the conformal block itself.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Bertola (Concordia University) DTSTART:20210330T193000Z DTEND:20210330T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/28 DESCRIPTION:Title: Padé approximants on Riemann surfaces and KP tau fun ctions\nby Marco Bertola (Concordia University) as part of CRM-Sémina ire Physique Mathématique\n\n\nAbstract\nThe talk has two relatively dist inct but connected goals\; the first is to define the notion of Padé appr oximation of Weyl-Stieltjes transforms on an arbitrary compact Riemann sur face of higher genus. The data consists of a contour in the Riemann surfa ce and a measure on it\, together with the additional datum of a local coo rdinate near a point and a divisor of degree g. The denominators of the r esulting Padé–like approximation also satisfy an orthogonality relation and are sections of appropriate line bundles. A Riemann–Hilbert proble m for a square matrix of rank two is shown to characterize these orthogona l sections\, in a similar fashion to the ordinary orthogonal polynomial ca se.   \n\nThe second part extends this idea to explore its connection to integrable systems. The same data can be used to define a pairing betwee n two sequences of line bundles. The locus in the deformation space where the pairing becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kado mtsev–Petviashvili hierarchy with respect to either deformation paramete rs\, and a certain modification of the 2–Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is related to the Krichever construction of algebro–geometric solutions. \n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Natasha Rozhkovskaya (Kansas State University) DTSTART:20210406T193000Z DTEND:20210406T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/29 DESCRIPTION:Title: Polynomial tau-functions of the KP and BKP bilinear identities\nby Natasha Rozhkovskaya (Kansas State University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nThe KP hierarchy o f evolution equations of soliton type was introduced by M.Sato. The idea s were further developed by the members of Kyoto school and other researc hers\,  discovering many new examples of soliton type hierarchies and st udying their  solutions  by  the methods of mathematical physics\, alg ebraic geometry and representation theory. In particular\,  tau functions of bilinear identities that correspond to these hierarchies  provide  f amilies  of  solutions of the original evolution equations.   In this t alk we will compare    constructions of   polynomial tau-function of th e  KP and the BKP bilinear identities  based on representation theory me thods.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Mickael Nahon (Université Savoie Mont Blanc (1/3)) DTSTART:20210321T150000Z DTEND:20210321T170000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/30 DESCRIPTION:Title: Degenerate free discontinuity problems and quantitati ve spectral inequalities\nby Mickael Nahon (Université Savoie Mont Bl anc (1/3)) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\ nWe study a semilinear eigenvalue problem involving the Laplace operator w ith Robin boundary conditions among sets of fixed measure in R n. In part icular\, consider a solid D with a constant volumetric heat source and a t hin layer of insulator on its surface\, and let T(D) be the mean temperatu re of D at equilibrium. We will present a proof of T(D) ≤ T(D∗ ) − C.d(D\, D∗ ) 2 \, where d is the L 1 distance between sets up to transla tion and D∗ is the ball with same measure as D. This will be obtained t hrough a shape optimisation problem involving both free discontinuity and free boundary phenomena.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Hanna Kim (University of Illinois (2/3)) DTSTART:20210321T150000Z DTEND:20210321T170000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/31 DESCRIPTION:Title: Maximization of the second Laplacian eigenvalue on th e sphere\nby Hanna Kim (University of Illinois (2/3)) as part of CRM-S éminaire Physique Mathématique\n\n\nAbstract\nThe second nonzero eigenva lue of the Laplacian on S m becomes maximal as the surface degenerates to two disjoint spheres\, by a result of Nadirashvili for which Petrides late r gave another proof. This talk builds on recent developments on the hype rbolic center of mass to simplify the proof\, yielding also the analogous result in higher dimensions.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Perez-Ayala (University of Notre Dame (3/3)) DTSTART:20210321T150000Z DTEND:20210321T170000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/32 DESCRIPTION:Title: Extremal Eigenvalues of the Conformal Laplacian\n by Samuel Perez-Ayala (University of Notre Dame (3/3)) as part of CRM-Sém inaire Physique Mathématique\n\n\nAbstract\nI will report on joint work w ith Mathew J. Gursky in which we consider the problem of extremizing eige nvalues of the conformal laplacian in fixed conformal classes. I will exp lain the connection of these extremal metrics to constant curvature metric s (Yamabe metrics)\, to the existence of harmonic maps into spheres\, and to nodal solutions of a Yamabe type equation (first noticed by Ammann-Humb ert).\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Garneau-Desroches (Université de Montréal) DTSTART:20210413T193000Z DTEND:20210413T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/33 DESCRIPTION:Title: Ladder operators and coherent states for rational ext ensions of the Rosen-Morse system\nby Simon Garneau-Desroches (Univers ité de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nA bstract\nThe quantum (hyperbolic) Rosen-Morse system is known for a long t ime to be exactly solvable from its shape invariance property in supersymm etric quantum mechanics (SUSY QM). Nevertheless\, the construction of ladd er operators for this system has appeared to be more complex than it is fo r other one-dimensional shape invariant systems. Recently\, an analogy wit h classical mechanics has led to the realization of the Rosen-Morse ladder operators (Delisle-Doray & Hussin\, 2020). I will present a simplified co nstruction of these ladder operators from operators involved in the system ’s shape invariant supersymmetric transformation. From this new construc tion are obtained ladder operators for rational extensions of the Rosen-Mo rse system. Coherent states for such rational extensions are constructed. I will discuss their properties with respect to those of the coherent stat es of the (non-extended) Rosen-Morse system.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Buckingham (University of Cincinnati) DTSTART:20210420T193000Z DTEND:20210420T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/34 DESCRIPTION:Title: Nonintersecting Brownian bridges on the unit circle w ith drift and generalized Hastings-McLeod functions.\nby Robert Buckin gham (University of Cincinnati) as part of CRM-Séminaire Physique Mathém atique\n\n\nAbstract\nNonintersecting Brownian bridges on the unit circle form a determinantalstochastic process exhibiting random matrix statistics for large numbers ofwalkers. We investigate the effect of adding a drift term to walkers on the circle conditioned to start and end at the same pos ition.  We use Riemann-Hilbert analysis of a family of discrete orthogona l polynomials with a complex weight to compute the asymptotic distribution of total winding numbers in the scaling regime in which the expected tota l winding is finite.\nFurthermore\, we show that an appropriate double sca ling of the drift and return time leads to a generalization of the tacnode process expressed in terms of generalized Hastings-McLeod functions.  We further investigate the large-degree asymptotic behavior of the generaliz ed Hastings-McLeod functions\, which have arisen in a variety of integrabl e probability contexts.\nThis is joint work with Karl Liechty (DePaul Univ ersity) and Kurt Schmidt (University of Cincinnati).\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Shai Chester (Weizmann Institute for Science) DTSTART:20210427T193000Z DTEND:20210427T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/35 DESCRIPTION:Title: Monopole operators in Quantum Electrodynamics\nby Shai Chester (Weizmann Institute for Science) as part of CRM-Séminaire P hysique Mathématique\n\n\nAbstract\nQuantum electrodynamics in 2+1 dimens ions with N flavors of matter is at the forefront of theoretical physics\, as it describes new exotic phases of matter that are currently being inve stigated experimentally\, and also is at the center of a recently proposed "web of dualities" between 3d quantum field theories that challenges our very notion of QFT. The key players in both of these applications are mono pole operators\, which unlike most local operators cannot be described usi ng fields from the Lagrangian. I will discuss recent results on the repres entation theory of monopole operators\, and how their scaling dimensions c an be computed perturbatively using the large N or 4-epsilon expansions\, and non-perturbatively using lattice simulations or the conformal bootstra p.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Mattia Cafasso (Université d'Angers) DTSTART:20210504T193000Z DTEND:20210504T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/36 DESCRIPTION:Title: Tau functions as Widom constants\nby Mattia Cafas so (Université d'Angers) as part of CRM-Séminaire Physique Mathématique \n\n\nAbstract\nWidom constants originally appeared in the study of the as ymptotics of block Toeplitz determinants\, and have been used to generaliz e the strong Szegő theorem to the case of block matrices. During my talk I will explain how one can identify tau functions with Widom constants\, both in the isomonodromic and isospectral setting\, and why this identific ation is interesting\, both from a theoretical point of view and in applic ations. \nThe results I will speak about have been obtained in collaborat ion with Chaozhong Wu\, Di Yang\, Ann Du Crest\, Oleg Lisovyy and Pavlo Ga vrylenko.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Korotkin (Concordia University) DTSTART:20210511T193000Z DTEND:20210511T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/37 DESCRIPTION:Title: Generating function of monodromy symplectomorphism\, isomonodromic tau-function and its WKB expansion\nby Dmitry Korotkin ( Concordia University) as part of CRM-Séminaire Physique Mathématique\n\n \nAbstract\nWe discuss three closely related problems. First\, we conside r the SL(n) character variety of the Riemann surface of genus g with n pun ctures and show how to invert the Goldman Poisson structure on its symplec tic leaf in terms of Fock-Goncharov coordinates.  A version of this resul t for the extended character variety proposed by L.Jeffrey in 1994 is pres ented.    \n\nSecond\, we apply this formalism to study the generating f unction of the monodromy symplectomorphism for the Fuchsian system on the Riemann sphere. In our framework the symplectic potential on the (extend ed) character variety is expressed via Fock-Goncharov coordinates. This g enerating function can be naturally identified with the Jimbo-Miwa tau-fun ction\, which allows to fix the dependence of the tau-function on monodrom y data. As a by-product we obtain a new hamiltonian formulation of Schles inger system which involves quadratic Poisson brackets with dynamical r-m atrix.   \n\nThird\, we study the WKB expansion of the generating functi on\; these calculations are based on WKB expansion of Fock-Goncharov coord inates in terms of certain Abelian integrals\, known as Voros symbols.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Tamara Grava (Scuola Internazionale Superiore di Studi Avanzati) DTSTART:20210518T193000Z DTEND:20210518T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/38 DESCRIPTION:Title: Correlation functions for unitary invariant ensembles and Hurwitz numbers\nby Tamara Grava (Scuola Internazionale Superiore di Studi Avanzati) as part of CRM-Séminaire Physique Mathématique\n\n\n Abstract\nWe  provide effective formulae for generating functions of mult ipoint correlators  for unitary invariants ensembles.As an application we show that  the multipoint correlators  of  the Laguerre and the Jacobi ensembles are obtained in terms of Hahn polynomials and  Wilson polynomi als generalising earlier formula for one-point correlators. Finally we pr ovide an enumerative interpretation of the topological expansion of these multipoint correlators. \nThis is a joint work with M. Gisonni and G. R uzza.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Semeon Artamonov (Berkeley) DTSTART:20210525T193000Z DTEND:20210525T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/39 DESCRIPTION:by Semeon Artamonov (Berkeley) as part of CRM-Séminaire Physi que Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Claeys (UC Louvain) DTSTART:20210601T193000Z DTEND:20210601T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/40 DESCRIPTION:Title: Airy kernel determinants\, the KdV equation\, and con ditional point processes\nby Tom Claeys (UC Louvain) as part of CRM-S éminaire Physique Mathématique\n\n\nAbstract\nA family of unbounded solu tions to the Korteweg-de Vries equation arose recently in the context of t he Kardar-Parisi-Zhang equation. These solutions can be constructed as lo g-derivatives of deformed Airy kernel Fredholm determinants\, and are also related to an integro-differential Painlevé II equation. In my talk\, I will will give an overview of these developments\, and I will discuss in more detail the initial data of this family of solutions and the connectio n with conditional Airy point processes.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Bothner (University of Bristol) DTSTART:20210608T193000Z DTEND:20210608T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/41 DESCRIPTION:Title: Momenta spacing distributions in anharmonic oscillato rs\nby Thomas Bothner (University of Bristol) as part of CRM-Séminair e Physique Mathématique\n\n\nAbstract\nThis talk will highlight new resul ts for the edge momentum distribution function of a noninteracting fermion ic quantum many-body system when confined to an anharmonic trap at finite temperature. Based on arXiv:2101.03557\, joint with M. Cafasso and S. T arricone.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Rufus Boyack (Université de Montréal) DTSTART:20210914T193000Z DTEND:20210914T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/42 DESCRIPTION:Title: Critical properties of quantum spin liquid phase tran sitions described by gauged Gross-Neveu quantum field theories\nby Ruf us Boyack (Université de Montréal) as part of CRM-Séminaire Physique Ma thématique\n\n\nAbstract\nAn important class of quantum phase transitions (QPTs) from an underlying Dirac spin liquid to either a magnetically-orde red phase or a topological spin liquid can be described by gauged Gross Ne veu (GN) quantum field theories. In particular\, recent sign-problem-free quantum Monte Carlo simulations of lattice quantum electrodynamics (QED) with N flavours of fermions on the square lattice have found evidence of c ontinuous QPTs between a critical deconfined phase at small gauge coupling and confined antiferromagnetic or valence-bond-solid phases at large gaug e coupling. Here I outline the explicit QED-GN models for these transition s and present results for their critical exponents using epsilon and large -N expansions at the stable critical points. Another important aspect of lattice QED is the presence of monopole operators. I will present results for minimal-charge monopole scaling dimensions to sub-leading order in 1/N for transitions from a DSL to two different topological spin liquids. The se results agree with operators predicted to be equal due to a conjectured duality between three-dimensional QED-GN and the CP1 model.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Doyon (King’s College London) DTSTART:20210921T193000Z DTEND:20210921T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/43 DESCRIPTION:Title: The hydrodynamics of many-body integrable systems \nby Benjamin Doyon (King’s College London) as part of CRM-Séminaire Ph ysique Mathématique\n\n\nAbstract\nHydrodynamics is a powerful theory for the emergent behaviours at large scales of space-time in many-body system s. The theory says that only few degrees of freedom are sufficient in orde r to describe what is observed at such scales\, and it provides equations for the dynamics of these degrees of freedom. Think of the simple water wa ves emerging from the motion and interaction of a myriad of water molecule s. It is strongly based on the presence of microscopic conservation laws i n the many-body model\, such as conservation of energy\, momentum and mass . But the standard equations of hydrodynamics fail to describe one-dimensi onal integrable systems\, including the ultracold atomic gases observed in experiments. Integrable systems admit an extensive number of conservation laws\, which must be taken into account in the emergent hydrodynamic theo ry. Recently this theory\, dubbed ``generalised hydrodynamics”\, has bee n developed. In this talk\, I will review fundamental aspects of hydrodyna mics and the main idea and equations of generalised hydrodynamics. I will discuss recent cold-atom experiments that confirm the theory\, some of the exact results that can be obtained with this formalism such as nonequilib rium steady states and asymptotic of correlation functions\, and if time p ermit some mathematically rigorous results in these directions.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Maloney (McGill University) DTSTART:20210928T193000Z DTEND:20210928T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/44 DESCRIPTION:Title: The Siegel-Weil Formula and Quantum Gravity as an Ave rage\nby Alex Maloney (McGill University) as part of CRM-Séminaire Ph ysique Mathématique\n\n\nAbstract\nI will explore the idea that certain t heories of gravity are not traditional quantum theories\, but are instead  averages over ensembles of quantum theories.  Remarkably\, this idea c an be explored quantitatively using ideas from number theory.  I will co nsider the average over free boson conformal field theories in two dimen sions\, and compute the genus g partition function using the Siegel-Weil formula.  The result is a real analytic Eisenstein series which can be interpreted as the sum over geometries in a certain exotic - but in a se nse exactly solvable - theory of quantum gravity.  The techniques used a re similar to those used to study high dimensional sphere packing by  averaging over spaces of lattices\, suggesting an analogy between semi-cla ssical gravity and a theory of random lattices (or sphere packings) in h igh dimensions.  This talk is a review of work done in collaboration with E. Witten\, and is intended to be accessible to mathematicians without a specialized physics background.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Costello (Perimeter Institute) DTSTART:20211005T193000Z DTEND:20211005T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/45 DESCRIPTION:Title: Celestial holography and twistors\nby Kevin Coste llo (Perimeter Institute) as part of CRM-Séminaire Physique Mathématique \n\n\nAbstract\nThe celestial holography program aims to describe scatteri ng amplitudes of gauge theory and gravity in terms of a conformal field th eory living on the celestial sphere. I will explain an approach to celest ial holography based on twistors\, which recasts it in a formulation much closer to ordinary holography. I will also discuss the role of gauge anom alies on twistor space\, and a Green-Schwarz mechanism\, in celestial holo graphy at loop-level. This is joint with Natalie Paquette.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sung-Sik Lee (McMaster University\, Perimeter Institute) DTSTART:20211012T193000Z DTEND:20211012T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/46 DESCRIPTION:Title: Quantum Renormalization Group\nby Sung-Sik Lee (M cMaster University\, Perimeter Institute) as part of CRM-Séminaire Physiq ue Mathématique\n\n\nAbstract\nThe renormalization group (RG) flow descri bes the change of effective theories as the momentum cutoff is lowered. H owever\, it is often hard to compute the exact effective action because op erators composed of arbitrary numbers of fields and space derivatives are generated under the exact RG flow. This difficulty is alleviated in quant um RG\, which is an exact reformulation of the Wilsonian RG. It significa ntly reduces the number of operators that need to be included as the full RG flow is projected onto a measure zero subspace of couplings while the c ouplings in the subspace are promoted to dynamical variables. In this tal k\, we review the basic idea of quantum RG and present the exact effective action of the large-N Wilson-Fisher fixed point obtained from quantum RG. Below four dimensions\, the exact effective action is a transcendental f unction of two leading scaling operators with infinitely many derivatives. \n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Koroteev (Berkeley) DTSTART:20211026T193000Z DTEND:20211026T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/47 DESCRIPTION:Title: q-Opers\, QQ-systems and Bethe Ansatz\nby Peter K oroteev (Berkeley) as part of CRM-Séminaire Physique Mathématique\n\n\nA bstract\nWe introduce the notions of (G\,q)-opers and establish a one-to-o ne correspondence between them and the set of nondegenerate solutions of a system of Bethe Ansatz equations (which are in turn dual to the so-called QQ-system). Additionally we associate to a (G\,q)-oper a class of meromor phic sections of a G-bundle\, satisfying certain difference equations\, wh ich we refer to as generalized q-Wronskians. We show that the QQ-systems a nd their extensions emerge as the relations between generalized minors\, t hereby putting the Bethe Ansatz equations in the framework of cluster muta tions known in the theory of double Bruhat cells.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Vinet\; Gabriel Longpré (University of Waterloo\; Unive rsité de Montréal) DTSTART:20211102T193000Z DTEND:20211102T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/48 DESCRIPTION:Title: Excitations and ergodicity of critical quantum spin c hains from non-equilibrium classical dynamics\nby Stéphane Vinet\; Ga briel Longpré (University of Waterloo\; Université de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nWe study a quantu m spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. T he Hamiltonian is obtained for the general disordered case with non-unifor m Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoq uastic\, and depends on the Ising couplings normalized by the bath's tempe rature. We give its exact ground states. Proceeding with uniform couplin gs\, we study the one- and two-magnon excitations. Solutions for the latt er are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime \, the two-magnon branch states show intricate behavior\, especially regar ding their hybridization with the continuum. We find that that the gaples s chain hosts multiple dynamics at low energy as seen through the presence of multiple dynamical critical exponents. Finally\, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclude that the system is non-integrable for generic parameters\, or eq uivalently\, that the corresponding non-equilibrium classical dynamics are ergodic.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg Lisovyy (Université de Tours) DTSTART:20211130T203000Z DTEND:20211130T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/49 DESCRIPTION:Title: Accessory parameters in Heun equations and classical conformal blocks\nby Oleg Lisovyy (Université de Tours) as part of CR M-Séminaire Physique Mathématique\n\n\nAbstract\nWe will discuss accesso ry parameters of Floquet type in the Heun equation and some of its conflue nt versions. A conjecture by Zamolodchikov relates them to quasiclassica l limit of conformal blocks of the Virasoro algebra. I will explain an ex tension of this conjectural relation to another class of accessory parame ter functions that are defined by inverting all-order Bohr-Sommerfeld peri ods for the confluent and biconfluent Heun equation.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Frédéric Dupont-Dupuis (Université de Montréal) DTSTART:20220111T203000Z DTEND:20220111T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/50 DESCRIPTION:by Frédéric Dupont-Dupuis (Université de Montréal) as part of CRM-Séminaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Its (Indiana University–Purdue University Indianapolis (IUPUI)) DTSTART:20211116T203000Z DTEND:20211116T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/51 DESCRIPTION:Title: Isomonodrtomy aspects of the tt* equations of cecotti and vafa. Iwasawa factorization and asymptotics\nby Alexander Its (In diana University–Purdue University Indianapolis (IUPUI)) as part of CRM- Séminaire Physique Mathématique\n\n\nAbstract\nThe talk is concerned wit h the global asymptotic analysis of the tt* - Toda equation\, 2(wi)tt = 􀀀e2(wi+1􀀀wi) + e2(wi􀀀wi+1)\; where\, for all i\, wi = wi+n+1 (per iodicity)\,wi = wi(jtj) (radial condi- tion)\, and wi + w􀀀i􀀀1 = 0 (\ \anti-symmetry"). The problem has been intensively studied since the earl y 90s work of Cecotti and Vafa. In these work a prominent role of the tt* - equations in the classi\ncation of su- persymmetric \neld theories had b een revealed and a series of important conjectures about their solutions h as been formulated. Assuming n = 3 (the \nrst case beyond the known Painl eve III situa- tion)\, we study the question using a combination of metho ds from p.d.e.\, isomonodromic deformations (Riemann-Hilbert method)\, and loop groups (Iwasawa factorization). We place these global solutions int o the broader context of solutions which are smooth near 0. For such solu tions\, we compute explicitly the Stokes data and connection matrix of the as- sociated meromorphic system\, in the resonant cases as well as in the non-resonant case. This allows us to give a complete picture of the mono dromy data\, holomorphic data\, and asymptotic data of the global solution s and prove some of Cecotti-Vafa conjectures. In the talk\, the above men tioned results will be presented in detail with an outline of the key step s in their derivation. Also\, the relation to 1998 work of Tracy and Wido m on the tt*-Toda equation will be discussed. This is a joint work with M artin Guest and Chang-Shou Lin\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Ken McLaughlin (Colorado State University) DTSTART:20211109T203000Z DTEND:20211109T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/52 DESCRIPTION:Title: Some intuition and some asymptotic analysis: from tw o solitons to a continuum limit of solitons\nby Ken McLaughlin (Colora do State University) as part of CRM-Séminaire Physique Mathématique\n\n\ nAbstract\nWe will work our way from 2-solitons interactions through to a gas of solitons\, and conclude with the description of a single soliton in teracting with this soliton gas. Intuition will be developed in the compl etely tractable examples of a single soliton\, and a pair of solitons lock ed in a mild battle before turning to dense limits.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Conte (ENS Paris-Saclay\, The university of Hong Kong) DTSTART:20211123T203000Z DTEND:20211123T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/53 DESCRIPTION:Title: Réductions d'une équation de sine-Gordon en 2+1 dim ensions\nby Robert Conte (ENS Paris-Saclay\, The university of Hong Ko ng) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\n(Joint work with Michel Grundland). \n\nWe establish all the reductions of the system of two coupled 2+1-dimensional sine-Gordon equations introduced by Konopelchenko and Rogers to ordinary di erential equations (ODE). There i s only one such reduction\, to an ODE of Chazy\, algebraic transform of th e sixth Painlevé equation. Various degeneracies also lead to the fiffth\ , third and second Painlevé equations and to elliptic functions.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Bertrand Eynard (Institut de Physique Théorique\, CEA (Commissari at à l'Energie Atomique et aux Energies Alternative)) DTSTART:20211207T203000Z DTEND:20211207T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/54 DESCRIPTION:Title: Integrable systems from a Newton polygon\nby Bert rand Eynard (Institut de Physique Théorique\, CEA (Commissariat à l'Ener gie Atomique et aux Energies Alternative)) as part of CRM-Séminaire Physi que Mathématique\n\n\nAbstract\nLet $P(x\,y)\\in \\mathbb C[x\,y]$ a biva riate polynomial\, written $P(x\,y)=\\sum_{(i\,j)\\in N}P_{i\,j} x^i y^j$. The polytope $N\\subset \\mathbb Z\\times \\mathbb Z$ is called the Newt on's polytope and its convex envelope is the Newton's polygon. The locus of solutions $P(x\,y)=0$ in $\\mathbb C\\times \\mathbb C$ is a plane curv e (an immersed Riemann surface). Its geometry can be produced from the co mbinatorics of the Newton's polygon. This allows to construct a Baker-Akh iezer function and a Lax pair associated to $P(x\,y)$\, in other words an integrable system. In fact there are several integrable systems that can be associated to P. The easiest is the isospectral system\, following the Krichever's reconstruction method\, and the others can be seen as "quantu m" deformations. In particular we can get an isomonodromic system and oth er deformations. We shall illustrate on the elliptic curve $P(x\,y)=y^2-x ^3+g_2 x+x_3$.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Parez (Université de Montréal) DTSTART:20220118T203000Z DTEND:20220118T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/55 DESCRIPTION:by Gilles Parez (Université de Montréal) as part of CRM-Sém inaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuan Miao (University of Amsterdam) DTSTART:20220125T203000Z DTEND:20220125T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/56 DESCRIPTION:by Yuan Miao (University of Amsterdam) as part of CRM-Séminai re Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Clément Berthière (Université de Montréal) DTSTART:20220201T203000Z DTEND:20220201T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/57 DESCRIPTION:Title: Entanglement of skeletal regions\nby Clément Ber thière (Université de Montréal) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nThe entanglement entropy encodes key properties o f quantum many-body systems. It is usually calculated for a subregion of finite volume (or area in 2d). In this talk\, I will discuss entanglement properties of subsystems possessing no volume\, dubbed « skeletal » ( e.g. a line in 2d/3d). I will show that skeletal entanglement displays n ew behavior compared to its bulk counterpart\, and leads to distinct unive rsal quantities. We discovered signatures including skeletal topological entanglement entropy\, novel bulk and boundary cusp terms\, and strict are a-law scaling for metals. I will focus on quantum systems with emergent L orentz and scale invariance\, with an incursion into non-relativistic Lifs hitz field theories.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Delacretaz (University of Chicago) DTSTART:20220215T203000Z DTEND:20220215T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/58 DESCRIPTION:Title: Nonlinear bosonization of Fermi liquids\nby Luca Delacretaz (University of Chicago) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nLandau's theory of Fermi liquids is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid t heory as an effective field theory of bosonic degrees of freedom\, using t he mathematical formalism of coadjoint orbits. While at the linear level\ , this theory reduces to multidimensional bosonization\, it necessarily fe atures nonlinear corrections that are fixed by the geometry of the Fermi s urface. These are crucial to reproduce nonlinear response and certain oth er aspects of Fermi liquid theory phenomenology that are not captured by c urrent bosonization approaches. The effective field theory framework furt hermore systematically parametrizes corrections to Fermi liquid behavior\, and provides a new angle to approach non-Fermi liquids. (Based on upcomi ng work with: Yi-Hsien Du\, Umang Mehta\, and Dam Thanh Son).\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Cenke Xu (University of California\, Santa Barbara) DTSTART:20220308T203000Z DTEND:20220308T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/59 DESCRIPTION:Title: Phases and Phase Transitions with Fractal Symmetries: Models and Experimental Platform\nby Cenke Xu (University of Californ ia\, Santa Barbara) as part of CRM-Séminaire Physique Mathématique\n\n\n Abstract\nIn recent years\, generalizations of the notion of symmetry have significantly broadened our view on states of matter. We will discuss som e recent progress of understanding and realizing the "fractal symmetry"\, where the symmetric charge i.e. the generator of the symmetry is defined o n a fractal subset of the system with a noninteger or more generally irrat ional Hausdorff dimension. We will introduce a series of models with exoti c fractal symmetries\, which can in general be deduced from a "Pascal Tria ngle" (also called Yang Hui Triangle in ancient China) symmetry. We will d iscuss their various features including quantum phase transitions. We will also discuss the potential realization of these phases and phase transiti ons in experimental systems\, such as the highly tunable platform of Rydbe rg atoms.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael Nepomechie (University of Miami) DTSTART:20220322T193000Z DTEND:20220322T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/60 DESCRIPTION:Title: Bethe ansatz and quantum computing\nby Rafael Nep omechie (University of Miami) as part of CRM-Séminaire Physique Mathémat ique\n\n\nAbstract\nWe begin with a brief review of the Heisenberg quantum spin chain and its remarkable solution found by Bethe. We then review a p robabilistic algorithm for preparing exact eigenstates of this model on a quantum computer. An exact formula for the success probability is presente d\, and the computation of correlation functions is discussed. A generaliz ation of the algorithm to open chains with boundaries is also noted.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Terwilliger (University of Wisconsin-Madison) DTSTART:20220208T203000Z DTEND:20220208T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/61 DESCRIPTION:Title: The alternating central extension of the $q$-Onsager algebra\nby Paul Terwilliger (University of Wisconsin-Madison) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nThe $q$-Onsager a lgebra $O_q$ is a quantized enveloping algebra for the Onsager Lie algebra $O$. Recently Baseilhac\, Koizumi\, and Shigechi introduced an algebra $ \\mathcal O_q$ called the alternating central extension of $O_q$. In this talk\, our goal is to describe how $O_q$ is related to $\\mathcal O_q$. To motivate this description\, we first consider a toy model\, involving t he positive part $U^+_q$ of $U_q(\\widehat{\\mathfrak{sl}}_2)$ and its alt ernating central extension $\\mathcal U^+_q$. We will see that $O_q$ is r elated to $\\mathcal O_q$ in essentially the same way as $U^+_q$ is relate d to $\\mathcal U^+_q$. We finish with an open problem.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Crampe (Université de Tours) DTSTART:20220222T203000Z DTEND:20220222T213000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/62 DESCRIPTION:Title: Absorption or emission of solitons\nby Nicolas Cr ampe (Université de Tours) as part of CRM-Séminaire Physique Mathématiq ue\n\n\nAbstract\nI will present how to obtain integrable differential equ ations with particular boundary conditions which admit solutions where the soliton can be absorbed or emitted by the boundary. After an introductio n to classical integrable systems with boundary conditions and solitonic s olutions\, I will explain how an algebraic question lead to consider time- dependent boundary conditions. In this case\, special solutions have been computed where the number of solitons is not preserved.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Bouchard (University of Alberta) DTSTART:20220315T193000Z DTEND:20220315T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/63 DESCRIPTION:Title: Transalgebraic Spectral Curves\, Quantum Curves\, an d Atlantes Hurwitz Numbers\nby Vincent Bouchard (University of Alberta ) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nPhysics is a great source of ideas for pure mathematics. The topological recursion of Chekhov-Eynard-Orantin (CEO) is an example of this approach: it was or iginally developed to solve matrix models in physics\, but was then abstra cted away from its physics origins. The result is a mathematical formalism that has found numerous applications in various areas of mathematics\, pa rticularly in enumerative geometry. \n\nThe Topological Recursion/Quantum Curve (TR/QC) correspondence\, which also originated in the context of mat rix models\, states that the CEO topological recursion (and its higher ana log)\, which associates a sequence of differentials to a spectral curve\, can be used to reconstruct the WKB asymptotic solution of a differential e quation that is a quantization of the spectral curve (known as a "quantum curve"). In this work we prove the TR/QC correspondence for a class of tra nsalgebraic spectral curves\; those are curves with exponential singularit ies\, which can be obtained as limits of sequences of algebraic spectral c urves. To this end\, we construct a generalization of topological recursio n that is consistent with limits of sequences of algebraic curves\; it inc ludes contributions from the exponential singularities. The prototypical e xample is the spectral curve which is known to give rise to r-spin Hurwitz numbers via the usual topological recursion\; we show that\, for the same spectral curve\, our natural generalization of the topological recursion instead computes atlantes Hurwitz numbers\, and reconstructs the WKB solut ion of the appropriate quantum curve. This is particularly interesting giv en that atlantes Hurwitz numbers had so far evaded topological recursion m ethods.\n\nThis is joint work with Reinier Kramer and Quinten Weller.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Semeon Artamonov (Université de Montréal) DTSTART:20220329T193000Z DTEND:20220329T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/64 DESCRIPTION:by Semeon Artamonov (Université de Montréal) as part of CRM- Séminaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Galina Filipuk (University of Warsaw) DTSTART:20220419T193000Z DTEND:20220419T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/66 DESCRIPTION:by Galina Filipuk (University of Warsaw) as part of CRM-Sémin aire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Loic Poulain D'Andecy (Université de Reims) DTSTART:20220426T193000Z DTEND:20220426T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/67 DESCRIPTION:by Loic Poulain D'Andecy (Université de Reims) as part of CRM -Séminaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Cliff (Université de Sherbrooke) DTSTART:20220412T193000Z DTEND:20220412T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/68 DESCRIPTION:Title: Moduli spaces of principal 2-group bundles and a cate gorification of the Freed-Quinn line bundle\nby Emily Cliff (Universit é de Sherbrooke) as part of CRM-Séminaire Physique Mathématique\n\n\nAb stract\nA 2-group is a higher categorical analogue of a group\, while a sm ooth 2-group is a higher categorical analogue of a Lie group. An importan t example is the string 2-group in the sense of Schommer-Pries. We study the notion of principal bundles for smooth 2-groups\, and investigate the moduli "space" of such objects. In particular in the case of flat princip al bundles for a finite 2-group over a Riemann surface\, we prove that the moduli space gives a categorification of the Freed--Quinn line bundle. T his line bundle has as its global sections the state space of Chern--Simon s theory for the underlying finite group. We can also use our results to better understand the notion of geometric string structures (as previously studied by Waldorf and Stolz--Teichner). This is based on joint work wit h Dan Berwick-Evans\, Laura Murray\, Apurva Nakade\, and Emma Phillips.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Del Monte (Université de Montréal) DTSTART:20220503T193000Z DTEND:20220503T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/69 DESCRIPTION:Title: Supersymmetric partition functions and isomonodromic tau functions\nby Fabrizio Del Monte (Université de Montréal) as par t of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nClass S theories are four-dimensional N=2 QFTs that are obtained by wrapping M5-branes on Riemann surfaces with singular points. In recent years a correspondence be tween class S theories and isomonodromic deformations equations (whose sim plest examples are the six Painlevé equations) is emerging\, where the so -called isomonodromic tau function is identified with the dual partition f unction of the QFT. The tau functions can be tipycally written as Fredholm determinants or Pfaffians\, providing a fully nonperturbative approach to study partition functions of class S theories\, relying only on the geome tric data entering in the string theory construction\, and not on a classi cal action.\n\nAfter reviewing the Fredholm determinant formulation of tau functions for spheres with regular singularities\, corresponding to linea r quiver gauge theories\, I will show how the description can be extended to tau functions with orthogonal gauge groups\, that are written as Fredho lm Pfaffians\, and to tau functions for tori with regular singularities\, corresponding to circular quiver gauge theories. I will conclude by showin g how the tau function description allows to study the S-duality transform ation of the resulting gauge theory dual partition function.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/69/ END:VEVENT BEGIN:VEVENT SUMMARY:David Aasen (Microsoft Station Q and KITP) DTSTART:20220510T193000Z DTEND:20220510T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/70 DESCRIPTION:by David Aasen (Microsoft Station Q and KITP) as part of CRM-S éminaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrzej Pokraka (McGill University) DTSTART:20220405T193000Z DTEND:20220405T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/71 DESCRIPTION:Title: The duals of Feynman integrals\nby Andrzej Pokrak a (McGill University) as part of CRM-Séminaire Physique Mathématique\n\n \nAbstract\nWe elucidate the vector space (twisted relative cohomology) th at is Poincaré dual to the vector space of Feynman integrals (twisted coh omology) in general spacetime dimension. The pairing between these spaces — an algebraic invariant called the intersection number — extracts int egral coefficients for a minimal basis\, bypassing the generation of integ ration-by-parts identities. Dual forms turn out to be much simpler than th eir Feynman counterparts: they are supported on maximal cuts of various su b-topologies (boundaries). Thus\, they provide a systematic approach to ge neralized unitarity\, the reconstruction of amplitudes from on-shell data. As an application of our formalism\, we derive compact differential equat ions satisfied by arbitrary one-loop integrals in non-integer spacetime di mension and show how to use the intersection number to express a scatterin g amplitude in terms of a minimal basis of integrals. We also examine the 4-dimensional limit of our formalism and provide prescriptions for extract ing rational terms.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Dimitra Karabali (Lehman College CUNY) DTSTART:20220517T193000Z DTEND:20220517T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/72 DESCRIPTION:by Dimitra Karabali (Lehman College CUNY) as part of CRM-Sémi naire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliàn Barragan Amado (Université de Sherbrooke) DTSTART:20220913T193000Z DTEND:20220913T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/73 DESCRIPTION:Title: Quasinormal modes via isomonodromy\nby Juliàn Ba rragan Amado (Université de Sherbrooke) as part of CRM-Séminaire Physiqu e Mathématique\n\n\nAbstract\nIn this talk\, I will introduce the method of isomonodromic deformations to study the quasinormal modes (QNMs) of a c harged scalar field on a Reissner-Nordström anti-de Sitter (RN-AdS5) blac k hole. Namely\, we need to recast the boundary value problem of the radi al second-order ordinary differential equation in terms of an initial valu e problem of an isomonodromic tau function. Then we can obtain asymptotic expansions for the fundamental QNMs in the small radius and the near extr emal black hole limit.\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Marquette (University of Queensland) DTSTART:20221004T193000Z DTEND:20221004T203000Z DTSTAMP:20260404T095717Z UID:PhysiqueMathematique/74 DESCRIPTION:by Ian Marquette (University of Queensland) as part of CRM-Sé minaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PhysiqueMathematique/74/ END:VEVENT END:VCALENDAR