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:20260422T225924Z UID:PhysiqueMathematique/1 DESCRIPTION:Title: Fused Hecke algebras and centralisers of tensor representatio ns of quantum sl(N)\nby Loïc Poulain d'Andecy (Laboratoire de Mathém atiques de Reims) as part of CRM-Séminaire Physique Mathématique\n\n\nAb stract\n(Joint work with Nicolas Crampé) The goal of the talk is to prese nt diagrammatic algebras and their deformations generalising the symmetric group and the Hecke algebra. We call these algebras\, respectively\, the algebra of fused permutations and the fused Hecke algebra. One motivatio n for considering these algebras is to write explicit Baxterisation formul as providing\, on an abstract/algebraic level\, solutions of the Yang-Baxt er equation. These formulas generalise the Baxterisation formula of the H ecke algebra related to the vector representation V of U_q(sl_N) (the spin 1/2 representation if N=2). The new Baxterisation formulas control the s olutions of YB equation on any symmetric power of the vector representatio n of U_q(sl_N) (the higher spin representations if N=2). Besides\, the me aning of these algebras in the context of the Schur-Weyl duality will be e xplained: they provide a description of the centralisers of tensor product s of symmetric powers of V. The representation theory of these new algebr as will be explained and\, from this\, the centralisers can be constructed as quotients\, both with a representation-theoretic and an algebraic/diag rammatic description. These results can be seen as analogues for higher s pins of a construction of the Temperley-Lieb algebras from the Hecke algeb ras.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik de Bie (Universiteit Gent) DTSTART:20200512T193000Z DTEND:20200512T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/2 DESCRIPTION:Title: The Dunkl intertwining operator\nby Hendrik de Bie (Unive rsiteit Gent) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstra ct\nThere are two crucial operators in the theory of Dunkl operators. The first is the Dunkl transform\, which generalizes the Fourier transform. Th e second is the intertwining operator\, which maps ordinary partial deriva tives to Dunkl operators. Although some abstract statements are known abou t the intertwining operator\, the explicit formula for classes of reflecti on groups is generally not known. In recent work Yuan Xu proposed a formul a in the case of dihedral groups and a restricted class of functions. We e xtend his formula to all functions and give a general strategy on how to o btain similar formulas for other reflections groups. This is based on join t work with Pan Lian\, available under arXiv:2002.09065.\n\nEn ligne/Web - Svp remplir ce formulaire/Please fill in this form: https://forms.gle/S1N cNQ8BxkzfAXcj9\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Maloney (McGill University) DTSTART:20200519T193000Z DTEND:20200519T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/3 DESCRIPTION:Title: Progress on Pure Gravity in Three Dimensions\nby Alex Mal oney (McGill University) as part of CRM-Séminaire Physique Mathématique\ n\n\nAbstract\nI will describe the challenges and progress in constructing a theory of "pure gravity" in three dimensions\, i.e. a theory which con tains only metric degrees of freedom and nothing else. Conformal bootstra p techniques provide strong constraints on the theory\, and indicate that the spectrum of the theory must contain new states in addition to graviton s and black holes. I will provide an interpretation for these new states .\n\nEn ligne/Web - Svp remplir ce formulaire/Please fill in this form: ht tps://forms.gle/S1NcNQ8BxkzfAXcj9\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexis Morin-Duchesne (Université Catholique de Louvain-la-Neuve) DTSTART:20200526T193000Z DTEND:20200526T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/4 DESCRIPTION:Title: Boundary emptiness formation probabilities in the six-vertex model at $\\Delta=- 1/2$\nby Alexis Morin-Duchesne (Université Cathol ique de Louvain-la-Neuve) as part of CRM-Séminaire Physique Mathématique \n\n\nAbstract\nThe connection between statistical mechanics and the combi natorics of alternating sign matrices is known since the work of Razumov a nd Stroganov on the spin-1/2 XXZ chain. One important example of this comb inatorial relation occurs in the study of the emptiness formation probabil ity $EFP_{N\,m}$. This observable is defined as the sum of the squares of the ground state components for the chain of length $N$\, restricted to co mponents where $m$ consecutive spins are aligned. At the combinatorial poi nt $\\Delta = - 1/2$\, it takes the form of a simple product of integers. This was proven in 2012 by L. Cantini\, who also found a combinatorial int erpretation for these probabilities in terms of plane partitions.\nIn join t work with C. Hagendorf and L. Cantini\, we define a new family of overla ps $C_{N\,m}$ 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 r easons 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\nEn lign e/Web - Svp remplir ce formulaire/Please fill in this form: https://forms. gle/S1NcNQ8BxkzfAXcj9\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Joris Van der Jeugt (Universiteit Gent) DTSTART:20200602T193000Z DTEND:20200602T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/5 DESCRIPTION:Title: Partition functions for paraboson and parafermion systems \nby Joris Van der Jeugt (Universiteit Gent) as part of CRM-Séminaire Phy sique Mathématique\n\n\nAbstract\nParabosons and parafermions\, algebraic ally characterized by triple relations rather than just (anti)-commutation relations\, have been around for more than 60 years. Over the recent yea rs\, new mathematical results have been obtained for their representations \, in particular character formulae. In the present talk\, we give a shor t review of the algebraic structures behind parabosons and parafermions\, and of their representations. We show how the new expressions for charact ers lead to proper forms of grand partition functions for systems of parab osons and parafermions. These forms of the partition function allow the c omputation of statistical and thermodynamic functions for such systems. W e discuss some examples\, such as the average number of particles on an or bital\, and the average number of particles in the system.\n\nEn ligne/Web - Svp remplir ce formulaire/Please fill in this form: https://forms.gle/S 1NcNQ8BxkzfAXcj9\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Brandenberger (McGill University) DTSTART:20200609T193000Z DTEND:20200609T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/6 DESCRIPTION:Title: S-brane cosmology\nby Robert Brandenberger (McGill Univer sity) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\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 b y adding an "S-brane"\, a distributional source\, to the matter action\, o ne can obtain a non-singular bouncing cosmology which obviates the need fo r a period of cosmological inflation.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Théo Pinet (Université de Montréal) DTSTART:20200616T193000Z DTEND:20200616T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/7 DESCRIPTION:Title: The structure of the representations of the affine Temperley- Lieb algebras on the periodic XXZ chain\nby Théo Pinet (Université d e Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstrac t\nThe affine Temperley-Lieb algebras aTLN(β) are a family of infinite di mensional algebras generalizing the well-known Temperley-Lieb algebras TLN (β). They play\, for the periodic XXZ chain\, the role played by the orig inal Temperley-Lieb algebra for the open XXZ chain. Their representation t heory is much richer than that of the original TL family and admits a lot of similiraties with the representation theory of the Virasoro algebra Vir . In particular\, we will show in this talk that there exists aTLN(β)-mod ules (called critical) whose structure is akin that of the so-called Feigi n-Fuchs Vir-modules. To do this\, we will highlight the link between these critical modules and other canonical representations of aTLN(β) (the sta ndard modules) while building up on the well-known quantum Schur-Weyl dual ity between TLN(β) and Uqsl2.\n\nL'exposé sera donné en français avec des diapositives en anglais - The talk be given in French with slides writ ten in English\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Chalifour (Université de Montréal) DTSTART:20200908T193000Z DTEND:20200908T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/8 DESCRIPTION:Title: General solution of the exceptional Hermite differential equa tion and its minimal surface representation\nby Vincent Chalifour (Uni versité de Montréal) as part of CRM-Séminaire Physique Mathématique\n\ n\nAbstract\nThe main aim of this presentation is the study of the general solution of the exceptional Hermite differential equation with fixed part ition and the construction of minimal surfaces associated with this soluti on. We derive a linear second-order ordinary differential equation associa ted with a specific family of exceptional polynomials of codimension two. We show that these polynomials can be expressed in terms of classical Herm ite polynomials. We find the general analytic solution of the exceptional Hermite differential equation which has no gap in its spectrum. We show th at the spectrum is complemented by non-polynomial solutions. We present an implementation of the obtained results for the surfaces expressed in term s of the general solution making use of the classical Enneper-Weierstrass formula for the immersion in the Euclidean space $\\mathbb{E}^3$\, leading to minimal surfaces. Three-dimensional displays of these surfaces are pre sented.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Éric Dupuis (Université de Montréal) DTSTART:20200915T193000Z DTEND:20200915T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/9 DESCRIPTION:Title: Monopole operators in gauged Gross-Neveu models\nby Éric Dupuis (Université de Montréal) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nCompact quantum electrodynamics in 2+1 dimensions with massless fermions (QED3) describes the quantum spin liquid phase in certain quantum magnets. This model includes monopoles whose proliferatio n may be prevented by the massless fermions. This screening effect is how ever lost if a fermion mass is generated\, which leads to confinement. Su ch confinement-deconfinement transitions are found in QED3-Gross-Neveu (QE D3-GN) models where the GN interaction induces the mass. Monopole operato rs are studied at the critical point of these theories. Using the state-o perator correspondence\, we obtain the scaling dimension of monopole opera tors at leading order in 1/N where 2N is the number of fermion flavors. T wo universality classes with distinct flavor symmetries are considered. F or a SU(2) x SU(N) symmetry\, a hierarchy is shown by constraining the mag netic spin of monopoles and comparing the scaling dimensions in the variou s spin sectors. The representation of monopoles reflects this hierarchy a nd a degeneracy lifting relative to the QED3 case. For a SU(2N) symmetry\ , the monopole scaling dimension is used to test a field theory duality.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Zelaya (Université de Montréal) DTSTART:20200922T193000Z DTEND:20200922T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/10 DESCRIPTION:Title: Fourth Painlevé and Ermakov equations: quantum invariants a nd new exactly-solvable time-dependent Hamiltonians\nby Kevin Zelaya ( Université de Montréal) as part of CRM-Séminaire Physique Mathématique \n\n\nAbstract\nIn this talk\, we discuss a new realization of exactly-sol vable time-dependent Hamiltonians based on the solutions of the fourth Pai nlevé and the Ermakov equations. The latter is achieved by introducing a shape-invariant condition between an unknown quantum invariant and a set o f third-order intertwining operators with time-dependent coefficients. The new quantum invariant is constructed by adding a deformation term to the well-known parametric oscillator invariant. Such a deformation depends exp licitly on time through the solutions of the Ermakov equation\, which ensu res the regularity of the new time-dependent potential of the Hamiltonian at each time. On the other hand\, with the aid of the proper reparametriza tion\, the fourth Painlevé equation appears\, the parameters of which dic tate the spectral behavior of the quantum invariant. In particular\, the e igenfunctions of the third-order ladder operators lead to several sequence s of solutions to the Schroedinger equation\, determined in terms of the s olutions of a Riccati equation\, Okamoto polynomials\, or nonlinear bound states of the derivative nonlinear Schroedinger equation. Remarkably\, it is noticed that the solutions in terms of the nonlinear bound states lead to a quantum invariant with equidistant eigenvalues\, which contains both an (N+1)-dimensional and an infinite sequence of eigenfunctions. The resul ting family of time-dependent Hamiltonians is such that\, to the authors' knowledge\, have been unnoticed in the literature of nonstationary systems .\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Rayan (University of Saskatchevan) DTSTART:20200929T193000Z DTEND:20200929T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/11 DESCRIPTION:Title: The geometry and physics of Hitchin systems\nby Steven R ayan (University of Saskatchevan) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nThe moduli space of stable Higgs bundles on a Rie mann surface\, known as the Hitchin system\, arises as a space of gauge-eq uivalent solutions to dimensionally-reduced self-dual Yang-Mills equations . This moduli space turns out to be the phase space for a non-trivial com pletely integrable Hamiltonian system\, is a noncompact Calabi-Yau manifol d\, and has a mirror symmetry that is intertwined with Langlands duality. In this talk\, I will review a number of geometric features of the Hitchi n system that have been discovered over the past 30 years. I will conclud e by speculating on connections between Higgs bundles and condensed-matter physics.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuela Girotti (Mila\, Université de Montréal) DTSTART:20201006T193000Z DTEND:20201006T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/12 DESCRIPTION:Title: Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes\nby Manuela Gi rotti (Mila\, Université de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nWe study Fredholm determinants of a class of integral operators\, whose kernels can be expressed as double contour int egrals of a special type. Such Fredholm determinants appear in various ran dom matrix and statistical physics models. We show that the logarithmic de rivatives of the Fredholm determinants are directly related to solutions o f the Painlevé II hierarchy. This confirms and generalizes a recent conje cture by Le Doussal\, Majumdar\, and Schehr (2018). In addition\, we obtai n asymptotics at infinity for the Painlevé transcendents and large gap as ymptotics for the corresponding point processes. This is a joint work with Mattia Cafasso (Univ. Angers) and Tom Claeys (UC Louvain).\n LOCATION:https://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:20260422T225924Z UID:PhysiqueMathematique/13 DESCRIPTION:Title: Fermionic approach to bilinear expansions of KP correlators in terms of BKP correlators\nby John Harnad (Concordia University and Centre des recherches mathématiques) as part of CRM-Séminaire Physique M athématique\n\n\nAbstract\nThis talk will present a synthesis and general ization of two results relating determinants and Pfaffians of minors of a skew symmetric matrix\, with applications to solutions of the KP and DKP i ntegrable hierarchies. The first is an algebraic identity expressing the determinant of any minor of a skew matrix as a sum over products of Pfaffi ans of its principal minors\; the second an expression for Schur functions as bilinear sums over Schur $Q$-functions. A general bilinear identity\, of which these two results are special cases\, expresses determinantal de rivative correlators of $\\tau$-functions of the KP hierarchy as sums over products of pairs of Pfaffian derivative correlators for the BKP $\\tau$ function.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Escobar (Universidad Autonoma Metropolitana-Iztapalapa) DTSTART:20201117T203000Z DTEND:20201117T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/14 DESCRIPTION:Title: New infinite families of Nth-order superintegrable systems\nby Adrian Escobar (Universidad Autonoma Metropolitana-Iztapalapa) as p art of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nIn this talk\, a general description of quantum superintegrable systems in a two-dimensi onal Euclidean space is presented. We consider Hamiltonian systems allowin g separation of variables in cartesian coordinates for which one polynomia l integral (symmetry) of second order in momentum variables and one more o f Nth-order occur. The main properties of doubly exotic superintegrable po tentials\, i.e. potentials $V(x\, y) = V_1(x) + V_2(y)$ where neither $V_1 (x)$ nor $V_2(y)$ satisfy any linear ordinary differential equation\, are discussed. In particular\, we present two new infinite families of $N$th o rder 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 Painlev\\'e t est. We conjecture that these potentials will always actually have the Pai nlev\\'e property. In the classical case the latter property disappears.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Marquette (University of Queensland) DTSTART:20201103T203000Z DTEND:20201103T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/15 DESCRIPTION:Title: Embedding of Racah algebra and superintegrable systems\n by Ian Marquette (University of Queensland) as part of CRM-Séminaire Phys ique Mathématique\n\n\nAbstract\nThe rank-$1$ Racah algebra $R(3)$ plays a pivotal role in the theory of superintegrable systems. It appears as th e symmetry algebra of the $3$-parameter system on the $2$-sphere from whic h all second-order conformally flat superintegrable models in $2$D can be obtained by means of suitable limits and contractions. A higher rank gener alization 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 the gene ral superintegrable model on the $(n-1)$-sphere. I will discuss how such a n algebraic structure naturally arises as embedded inside a larger quadrat ic algebra characterizing $n$D superintegrable models with non-central ter ms. This is shown both in classical and quantum mechanics through suitable (symplectic or differential) realisations of the Racah and additional gen erators. I will also present an explicit construction of the complete symm etry algebras for two families of $n$-dimensional maximally superintegrabl e models\, the Smorodinsky-Winternitz system and the generalized Kepler-Co ulomb system. For both families\, the underlying symmetry algebras are hi gher-rank quadratic algebras containing the Racah algebra $R(n)$ as subalg ebra. High-order algebraic relations among the generators of the full quad ratic algebras are also obtained both in the classical and quantum framewo rks. However\, these approaches rely on explicit realizations as different ial operators. I will also briefly discuss how an algebraic construction o f the symmetry algebra of the generic superintegrable systems on the 2-sph ere can be generated from an underlying Lie algebra connected with intertw ining operators.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Luc Vinet (Université de Montréal) DTSTART:20201110T203000Z DTEND:20201110T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/16 DESCRIPTION:Title: Sklyanin algebras\, Askey-Wilson polynomials and Heun operat ors\nby Luc Vinet (Université de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nI will discuss the connections betw een Askey-Wilson polynomials\, Heun operators and degenerate Sklyanin alg ebras of dimensions three and four. The q-para Racah polynomials will be s een to realize a basis for the finite dimensional representations of the l atter. The Heun-Askey-Wilson operator will also emerge in this context.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Meng Cheng (Yale University) DTSTART:20210126T203000Z DTEND:20210126T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/17 DESCRIPTION:Title: Fractonic topological phases\nby Meng Cheng (Yale Univer sity) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nRece ntly a new type of gapped phases was discovered in (3+1) dimensions\, whos e unusual properties appear to defy a conventional QFT description. Notabl y\, they support quasiparticles with reduced mobility\, sometimes complete ly immobile\, and have an exponentially large number of locally indistingu ishable ground states on a three torus. In this talk I will review basic f acts about fracton models\, and discuss recent progress in understanding g eneral structures of fractonic phases.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Marie Stephan (Université Lyon 1) DTSTART:20210202T203000Z DTEND:20210202T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/18 DESCRIPTION:Title: Fermionic limit shapes\nby Jean-Marie Stephan (Universit é Lyon 1) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\ nI study a 1d translational invariant free fermions model in imaginary tim e\, with nearest neighbor and next-nearest neighbor hopping terms\, for va rious types of boundary conditions. This type of model typically arises w hen trying to solve 2d classical models such as dimer models\, or Ising mo dels\, through the transfer matrix formalism. In the absence of the next- nearest neighbor perturbation our fermion model is known to give rise to p hases separation and so-called arctic curves\, which have been studied ext ensively both in the physics and mathematical literature. The perturbatio n considered here turns out to not be always positive\, that is\, the corr esponding statistical mechanical model does not always have positive Boltz mann weights. I discuss the conditions under which this is the case\, and what sense to make of it when not.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Jerzy Lewandowski (University of Warsaw) DTSTART:20210209T203000Z DTEND:20210209T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/19 DESCRIPTION:Title: Non-singular global Kerr-NUT-(A)dS spacetimes\nby Jerzy Lewandowski (University of Warsaw) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nThe outstanding issue of a non-singular extension of the Kerr-NUT-(anti) de Sitter solutions to Einstein's equations is sol ved completely. The Misner's method of obtaining the extension for Taub-N UT spacetime is generalized in a non-singular manner. The Killing vectors that define non-singular spaces of non-null orbits are derived and applie d. The global structure of spacetime is discussed. The non-singular conf ormal geometry of the infinities is derived. The Killing horizons are pre sent.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/19/ END:VEVENT BEGIN:VEVENT SUMMARY:James Moran (Université de Montréal) DTSTART:20210309T203000Z DTEND:20210309T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/22 DESCRIPTION:Title: Non-linear ladder operators and coherent states for the 2:1 oscillator\nby James Moran (Université de Montréal) as part of CRM-S éminaire Physique Mathématique\n\n\nAbstract\nThe 2:1 two-dimensional an isotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of non-commutative binomial theorems as well as solving recurrence rel ations. The states generated are good candidates for the natural generalis ation of the su(2) coherent states of the two-dimensional isotropic oscill ator. The two-dimensional non-linear generalised ladder operators lead to several chains of states which are connected in a non trivial way. The unc ertainty relations of the defining chain of states are calculated and it i s found that they admit a resolution of the identity and the spatial distr ibution of the wavefunction produces Lissajous figures in correspondence w ith the classical 2:1 oscillator.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Turbiner (UNAM\, Stony Brook University and CRM) DTSTART:20210223T203000Z DTEND:20210223T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/24 DESCRIPTION:Title: Anharmonic oscillator: a solution\nby Alexander Turbiner (UNAM\, Stony Brook University and CRM) as part of CRM-Séminaire Physiqu e Mathématique\n\n\nAbstract\nAnharmonic oscillator (quantum pendulum) is one of the oldest\, non-solvable exactly problems in quantum physics. Fo r 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 coupling regime) and the semiclassical expansion in powers of $\\hbar$ for energies coincide. It is due to the fact that the dynamics in $x$-space and in $( gx)$-space corresponds to the same energy spectrum with effective coupling constant $(\\hbar g^2)$. Two equations\, which govern the dynamics in th ose two spaces\, the Riccati-Bloch (RB) and the Generalized Bloch (GB) equ ations\, 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 true semi classical expansion in powers of $\\hbar$ for the GB equation\, which corr esponds to a loop expansion for the density matrix in the path integral fo rmalism. Matching these two expansions leads to a extremely compact\, uni form approximation of the wavefunction in $x$-space with unprecedented acc uracy $\\sim 10^{-6}$ locally and unprecedented accuracy $\\sim 10^{-9}-10 ^{-10}$ in energy for any $g^2 \\geq 0$.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Knap (Technical University of Munich) DTSTART:20210216T203000Z DTEND:20210216T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/25 DESCRIPTION:Title: Hilbert Space Fragmentation\nby Michael Knap (Technical University of Munich) as part of CRM-Séminaire Physique Mathématique\n\n \nAbstract\nStrong interactions and frustration often lead to dynamically constrained excitations of quantum matter. Examples include spin-ice compo unds whose spin moments are aligned to fulfill a local ice rule\, frustrat ed quantum magnets with dimerized excitations\, and fracton phases with ex citations that are only mobile in certain directions if at all. Here\, we will discuss that the combination of charge and dipole conservation\, a ch aracteristic of fractonic quantum matter\, leads to an extensive fragmenta tion of the Hilbert space\, which in turn can lead to a breakdown of therm alization. We characterize such a Hilbert space fragmentation by introduci ng `statistically localized integrals of motion' (SLIOM)\, whose eigenvalu es label the connected components of the Hilbert space. SLIOMs are not spa tially localized in the operator sense\, but appear localized to sub-exten sive regions in space when their expectation value is taken in typical sta tes with a finite density of particles. Furthermore\, we discuss that ther e exist perturbations which destroy these integrals of motion in the bulk of the system\, while keeping them on the boundary. This results in statis tically localized strong zero modes\, leading to infinitely long-lived edg e magnetizations along with a thermalizing bulk\, constituting the first e xample of such strong edge modes in a non-integrable model. We also discus s that in a particular example\, these edge modes lead to the appearance o f topological string order in a certain subset of highly excited eigen sta tes. A variant of these models can be realized in Rydberg quantum simulato rs.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Prof. Johan van de Leur (Utrecht University) DTSTART:20210316T193000Z DTEND:20210316T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/26 DESCRIPTION:Title: Polynomial solutions of KP and Gelfand-Dickey hierarchies\nby Prof. Johan van de Leur (Utrecht University) as part of CRM-Séminai re Physique Mathématique\n\n\nAbstract\nIt is a wellknown result of M. S ato that all Schur functions are solutions of the KP hierarchy and that a general solution can be expressed  as a possibly infinite linear combinat ion of these Schur functions. However\, not all linear combinations are s olutions of this KP hierarchy. In this talk I will address the topic of p olynomial solutions of various hierarchies. In particular\, I will give a simple formula that describes all polynomial solutions for both the KP an d Gelfand-Dickey hierarchies.  This is based on joint work with Victor Ka c.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Del Monte (CRM) DTSTART:20210323T193000Z DTEND:20210323T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/27 DESCRIPTION:Title: Isomonodromic tau functions on Riemann Surfaces through free fermions and four-dimensional QFTs\nby Fabrizio Del Monte (CRM) as pa rt of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nUsing arguments from two-dimensional Conformal Field Theory\, Gamayun Iorgov and Lisovyy provided in 2012 an explicit expression for the tau function of the sixth\ nPainlevé equation as a Fourier transform of Virasoro conformal blocks of a free fermion CFT\, which has an explicit combinatorial (convergent) exp ansion as the so-called\ndual partition function of a corresponding four-d imensional supersymmetric Quantum Field Theory. This "Kiev formula" has be en later generalized to more general isomonodromic problems on the sphere\ , with both regular and irregular punctures\, and the combinatorial expans ion has been shown to arise from the minor expansion of an associated Fred holm determinant\, in terms of which the tau function can be formulated.\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\, where new features arise due to the nontriviality of the moduli space of flat conne ctions. I will consider in detail the example of the punctured torus\, for which I will show that the tau function can be written as a free fermion conformal block from two-dimensional CFT\, and as a Fredholm determinant o f Cauchy operators\, whose minor expansion reproduces the conformal block itself.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Bertola (Concordia University) DTSTART:20210330T193000Z DTEND:20210330T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/28 DESCRIPTION:Title: Padé approximants on Riemann surfaces and KP tau functions< /a>\nby Marco Bertola (Concordia University) as part of CRM-Séminaire Phy sique Mathématique\n\n\nAbstract\nThe talk has two relatively distinct bu t connected goals\; the first is to define the notion of Padé approximati on of Weyl-Stieltjes transforms on an arbitrary compact Riemann surface of higher genus. The data consists of a contour in the Riemann surface and a measure on it\, together with the additional datum of a local coordinate near a point and a divisor of degree g. The denominators of the resultin g Padé–like approximation also satisfy an orthogonality relation and ar e sections of appropriate line bundles. A Riemann–Hilbert problem for a square matrix of rank two is shown to characterize these orthogonal secti ons\, in a similar fashion to the ordinary orthogonal polynomial case.   \n\nThe second part extends this idea to explore its connection to integr able systems. The same data can be used to define a pairing between two s equences of line bundles. The locus in the deformation space where the pa iring becomes degenerate for fixed degree coincides with the zeros of a “tau” function. We show how this tau function satisfies the Kadomtsev –Petviashvili hierarchy with respect to either deformation parameters\, and a certain modification of the 2–Toda hierarchy when considering the whole sequence of tau functions. We also show how this construction is re lated to the Krichever construction of algebro–geometric solutions.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Natasha Rozhkovskaya (Kansas State University) DTSTART:20210406T193000Z DTEND:20210406T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/29 DESCRIPTION:Title: Polynomial tau-functions of the KP and BKP bilinear identit ies\nby Natasha Rozhkovskaya (Kansas State University) as part of CRM- Séminaire Physique Mathématique\n\n\nAbstract\nThe KP hierarchy of evolu tion equations of soliton type was introduced by M.Sato. The ideas were further developed by the members of Kyoto school and other researchers\,   discovering many new examples of soliton type hierarchies and studying their  solutions  by  the methods of mathematical physics\, algebraic geometry and representation theory. In particular\,  tau functions of bi linear identities that correspond to these hierarchies  provide  familie s  of  solutions of the original evolution equations.   In this talk we will compare    constructions of   polynomial tau-function of the  KP and the BKP bilinear identities  based on representation theory methods. \n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Mickael Nahon (Université Savoie Mont Blanc (1/3)) DTSTART:20210321T150000Z DTEND:20210321T170000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/30 DESCRIPTION:Title: Degenerate free discontinuity problems and quantitative spec tral inequalities\nby Mickael Nahon (Université Savoie Mont Blanc (1/ 3)) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nWe stu dy a semilinear eigenvalue problem involving the Laplace operator with Rob in boundary conditions among sets of fixed measure in R n. In particular\ , consider a solid D with a constant volumetric heat source and a thin lay er of insulator on its surface\, and let T(D) be the mean temperature 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 translation an d D∗ is the ball with same measure as D. This will be obtained through a shape optimisation problem involving both free discontinuity and free bo undary phenomena.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Hanna Kim (University of Illinois (2/3)) DTSTART:20210321T150000Z DTEND:20210321T170000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/31 DESCRIPTION:Title: Maximization of the second Laplacian eigenvalue on the spher e\nby Hanna Kim (University of Illinois (2/3)) as part of CRM-Séminai re Physique Mathématique\n\n\nAbstract\nThe second nonzero eigenvalue of the Laplacian on S m becomes maximal as the surface degenerates to two dis joint spheres\, by a result of Nadirashvili for which Petrides later gave another proof. This talk builds on recent developments on the hyperbolic center of mass to simplify the proof\, yielding also the analogous result in higher dimensions.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Perez-Ayala (University of Notre Dame (3/3)) DTSTART:20210321T150000Z DTEND:20210321T170000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/32 DESCRIPTION:Title: Extremal Eigenvalues of the Conformal Laplacian\nby Samu el Perez-Ayala (University of Notre Dame (3/3)) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nI will report on joint work with Mat hew J. Gursky in which we consider the problem of extremizing eigenvalues of the conformal laplacian in fixed conformal classes. I will explain th e connection of these extremal metrics to constant curvature metrics (Yama be metrics)\, to the existence of harmonic maps into spheres\, and to noda l solutions of a Yamabe type equation (first noticed by Ammann-Humbert).\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Garneau-Desroches (Université de Montréal) DTSTART:20210413T193000Z DTEND:20210413T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/33 DESCRIPTION:Title: Ladder operators and coherent states for rational extensions of the Rosen-Morse system\nby Simon Garneau-Desroches (Université de Montréal) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract \nThe quantum (hyperbolic) Rosen-Morse system is known for a long time to be exactly solvable from its shape invariance property in supersymmetric q uantum mechanics (SUSY QM). Nevertheless\, the construction of ladder oper ators for this system has appeared to be more complex than it is for other one-dimensional shape invariant systems. Recently\, an analogy with class ical mechanics has led to the realization of the Rosen-Morse ladder operat ors (Delisle-Doray & Hussin\, 2020). I will present a simplified construct ion of these ladder operators from operators involved in the system’s sh ape invariant supersymmetric transformation. From this new construction ar e obtained ladder operators for rational extensions of the Rosen-Morse sys tem. Coherent states for such rational extensions are constructed. I will discuss their properties with respect to those of the coherent states of t he (non-extended) Rosen-Morse system.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Buckingham (University of Cincinnati) DTSTART:20210420T193000Z DTEND:20210420T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/34 DESCRIPTION:Title: Nonintersecting Brownian bridges on the unit circle with dri ft and generalized Hastings-McLeod functions.\nby Robert Buckingham (U niversity of Cincinnati) as part of CRM-Séminaire Physique Mathématique\ n\n\nAbstract\nNonintersecting Brownian bridges on the unit circle form a determinantalstochastic process exhibiting random matrix statistics for la rge numbers ofwalkers. We investigate the effect of adding a drift term to walkers on the circle conditioned to start and end at the same position.   We use Riemann-Hilbert analysis of a family of discrete orthogonal poly nomials with a complex weight to compute the asymptotic distribution of to tal winding numbers in the scaling regime in which the expected total wind ing is finite.\nFurthermore\, we show that an appropriate double scaling o f the drift and return time leads to a generalization of the tacnode proce ss expressed in terms of generalized Hastings-McLeod functions.  We furth er investigate the large-degree asymptotic behavior of the generalized Has tings-McLeod functions\, which have arisen in a variety of integrable prob ability contexts.\nThis is joint work with Karl Liechty (DePaul University ) and Kurt Schmidt (University of Cincinnati).\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Shai Chester (Weizmann Institute for Science) DTSTART:20210427T193000Z DTEND:20210427T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/35 DESCRIPTION:Title: Monopole operators in Quantum Electrodynamics\nby Shai C hester (Weizmann Institute for Science) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nQuantum electrodynamics in 2+1 dimensions wi th N flavors of matter is at the forefront of theoretical physics\, as it describes new exotic phases of matter that are currently being investigate d experimentally\, and also is at the center of a recently proposed "web o f dualities" between 3d quantum field theories that challenges our very no tion of QFT. The key players in both of these applications are monopole op erators\, which unlike most local operators cannot be described using fiel ds from the Lagrangian. I will discuss recent results on the representatio n theory of monopole operators\, and how their scaling dimensions can be c omputed perturbatively using the large N or 4-epsilon expansions\, and non -perturbatively using lattice simulations or the conformal bootstrap.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Mattia Cafasso (Université d'Angers) DTSTART:20210504T193000Z DTEND:20210504T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/36 DESCRIPTION:Title: Tau functions as Widom constants\nby Mattia Cafasso (Uni versité d'Angers) as part of CRM-Séminaire Physique Mathématique\n\n\nA bstract\nWidom constants originally appeared in the study of the asymptoti cs of block Toeplitz determinants\, and have been used to generalize the s trong 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 identification i s interesting\, both from a theoretical point of view and in applications. \nThe results I will speak about have been obtained in collaboration wit h Chaozhong Wu\, Di Yang\, Ann Du Crest\, Oleg Lisovyy and Pavlo Gavrylenk o.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry Korotkin (Concordia University) DTSTART:20210511T193000Z DTEND:20210511T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/37 DESCRIPTION:Title: Generating function of monodromy symplectomorphism\, isomono dromic tau-function and its WKB expansion\nby Dmitry Korotkin (Concord ia University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstr act\nWe discuss three closely related problems. First\, we consider the S L(n) character variety of the Riemann surface of genus g with n punctures and show how to invert the Goldman Poisson structure on its symplectic lea f in terms of Fock-Goncharov coordinates.  A version of this result for t he extended character variety proposed by L.Jeffrey in 1994 is presented.     \n\nSecond\, we apply this formalism to study the generating functio n of the monodromy symplectomorphism for the Fuchsian system on the Riema nn sphere. In our framework the symplectic potential on the (extended) ch aracter variety is expressed via Fock-Goncharov coordinates. This generat ing function can be naturally identified with the Jimbo-Miwa tau-function\ , which allows to fix the dependence of the tau-function on monodromy data . As a by-product we obtain a new hamiltonian formulation of Schlesinger system which involves quadratic Poisson brackets with dynamical r-matrix.   \n\nThird\, we study the WKB expansion of the generating function\; t hese calculations are based on WKB expansion of Fock-Goncharov coordinates in terms of certain Abelian integrals\, known as Voros symbols.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Tamara Grava (Scuola Internazionale Superiore di Studi Avanzati) DTSTART:20210518T193000Z DTEND:20210518T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/38 DESCRIPTION:Title: Correlation functions for unitary invariant ensembles and Hu rwitz numbers\nby Tamara Grava (Scuola Internazionale Superiore di Stu di Avanzati) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstrac t\nWe  provide effective formulae for generating functions of multipoint correlators  for unitary invariants ensembles.As an application we show t hat  the multipoint correlators  of  the Laguerre and the Jacobi ensemb les are obtained in terms of Hahn polynomials and  Wilson polynomials gen eralising earlier formula for one-point correlators. Finally we provide a n enumerative interpretation of the topological expansion of these multipo int correlators. \nThis is a joint work with M. Gisonni and G. Ruzza.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Semeon Artamonov (Berkeley) DTSTART:20210525T193000Z DTEND:20210525T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/39 DESCRIPTION:by Semeon Artamonov (Berkeley) as part of CRM-Séminaire Physi que Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Claeys (UC Louvain) DTSTART:20210601T193000Z DTEND:20210601T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/40 DESCRIPTION:Title: Airy kernel determinants\, the KdV equation\, and conditiona l point processes\nby Tom Claeys (UC Louvain) as part of CRM-Séminair e Physique Mathématique\n\n\nAbstract\nA family of unbounded solutions to the Korteweg-de Vries equation arose recently in the context of the Karda r-Parisi-Zhang equation. These solutions can be constructed as log-deriva tives of deformed Airy kernel Fredholm determinants\, and are also related to an integro-differential Painlevé II equation. In my talk\, I will wi ll give an overview of these developments\, and I will discuss in more det ail the initial data of this family of solutions and the connection with c onditional Airy point processes.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Bothner (University of Bristol) DTSTART:20210608T193000Z DTEND:20210608T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/41 DESCRIPTION:Title: Momenta spacing distributions in anharmonic oscillators\ nby Thomas Bothner (University of Bristol) as part of CRM-Séminaire Physi que Mathématique\n\n\nAbstract\nThis talk will highlight new results for the edge momentum distribution function of a noninteracting fermionic quan tum many-body system when confined to an anharmonic trap at finite tempera ture. Based on arXiv:2101.03557\, joint with M. Cafasso and S. Tarricon e.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Rufus Boyack (Université de Montréal) DTSTART:20210914T193000Z DTEND:20210914T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/42 DESCRIPTION:Title: Critical properties of quantum spin liquid phase transitions described by gauged Gross-Neveu quantum field theories\nby Rufus Boya ck (Université de Montréal) as part of CRM-Séminaire Physique Mathémat ique\n\n\nAbstract\nAn important class of quantum phase transitions (QPTs) from an underlying Dirac spin liquid to either a magnetically-ordered pha se or a topological spin liquid can be described by gauged Gross Neveu (GN ) quantum field theories. In particular\, recent sign-problem-free quantu m Monte Carlo simulations of lattice quantum electrodynamics (QED) with N flavours of fermions on the square lattice have found evidence of continuo us QPTs between a critical deconfined phase at small gauge coupling and co nfined antiferromagnetic or valence-bond-solid phases at large gauge coupl ing. Here I outline the explicit QED-GN models for these transitions and p resent results for their critical exponents using epsilon and large-N exp ansions at the stable critical points. Another important aspect of lattice QED is the presence of monopole operators. I will present results for min imal-charge monopole scaling dimensions to sub-leading order in 1/N for tr ansitions from a DSL to two different topological spin liquids. These resu lts agree with operators predicted to be equal due to a conjectured dualit y between three-dimensional QED-GN and the CP1 model.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Doyon (King’s College London) DTSTART:20210921T193000Z DTEND:20210921T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/43 DESCRIPTION:Title: The hydrodynamics of many-body integrable systems\nby Be njamin Doyon (King’s College London) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nHydrodynamics is a powerful theory for the em ergent behaviours at large scales of space-time in many-body systems. The theory says that only few degrees of freedom are sufficient in order to de scribe what is observed at such scales\, and it provides equations for the dynamics of these degrees of freedom. Think of the simple water waves eme rging from the motion and interaction of a myriad of water molecules. It i s strongly based on the presence of microscopic conservation laws in the m any-body model\, such as conservation of energy\, momentum and mass. But t he standard equations of hydrodynamics fail to describe one-dimensional in tegrable systems\, including the ultracold atomic gases observed in experi ments. Integrable systems admit an extensive number of conservation laws\, which must be taken into account in the emergent hydrodynamic theory. Rec ently this theory\, dubbed ``generalised hydrodynamics”\, has been devel oped. In this talk\, I will review fundamental aspects of hydrodynamics an d 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 nonequilibrium st eady states and asymptotic of correlation functions\, and if time permit s ome mathematically rigorous results in these directions.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Maloney (McGill University) DTSTART:20210928T193000Z DTEND:20210928T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/44 DESCRIPTION:Title: The Siegel-Weil Formula and Quantum Gravity as an Average\nby Alex Maloney (McGill University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nI will explore the idea that certain theories of gravity are not traditional quantum theories\, but are instead averag es over ensembles of quantum theories.  Remarkably\, this idea can be ex plored quantitatively using ideas from number theory.  I will consider t he average over free boson conformal field theories in two dimensions\, and compute the genus g partition function using the Siegel-Weil formula.   The result is a real analytic Eisenstein series which can be interpr eted as the sum over geometries in a certain exotic - but in a sense exac tly solvable - theory of quantum gravity.  The techniques used are simil ar to those used to study high dimensional sphere packing by averagin g over spaces of lattices\, suggesting an analogy between semi-classical g ravity and a theory of random lattices (or sphere packings) in high dime nsions.  This talk is a review of work done in collaboration with E. Wit ten\, and is intended to be accessible to mathematicians without a special ized physics background.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Costello (Perimeter Institute) DTSTART:20211005T193000Z DTEND:20211005T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/45 DESCRIPTION:Title: Celestial holography and twistors\nby Kevin Costello (Pe rimeter Institute) as part of CRM-Séminaire Physique Mathématique\n\n\nA bstract\nThe celestial holography program aims to describe scattering ampl itudes of gauge theory and gravity in terms of a conformal field theory li ving on the celestial sphere. I will explain an approach to celestial hol ography based on twistors\, which recasts it in a formulation much closer to ordinary holography. I will also discuss the role of gauge anomalies o n twistor space\, and a Green-Schwarz mechanism\, in celestial holography at loop-level. This is joint with Natalie Paquette.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Sung-Sik Lee (McMaster University\, Perimeter Institute) DTSTART:20211012T193000Z DTEND:20211012T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/46 DESCRIPTION:Title: Quantum Renormalization Group\nby Sung-Sik Lee (McMaster University\, Perimeter Institute) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nThe renormalization group (RG) flow describes the change of effective theories as the momentum cutoff is lowered. However\ , it is often hard to compute the exact effective action because operators composed of arbitrary numbers of fields and space derivatives are generat ed under the exact RG flow. This difficulty is alleviated in quantum RG\, which is an exact reformulation of the Wilsonian RG. It significantly re duces 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 coupling s in the subspace are promoted to dynamical variables. In this talk\, 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 function of two leading scaling operators with infinitely many derivatives.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Koroteev (Berkeley) DTSTART:20211026T193000Z DTEND:20211026T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/47 DESCRIPTION:Title: q-Opers\, QQ-systems and Bethe Ansatz\nby Peter Koroteev (Berkeley) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract \nWe introduce the notions of (G\,q)-opers and establish a one-to-one corr espondence 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-sys tem). Additionally we associate to a (G\,q)-oper a class of meromorphic se ctions of a G-bundle\, satisfying certain difference equations\, which we refer to as generalized q-Wronskians. We show that the QQ-systems and thei r extensions emerge as the relations between generalized minors\, thereby putting the Bethe Ansatz equations in the framework of cluster mutations k nown in the theory of double Bruhat cells.\n LOCATION:https://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:20260422T225924Z UID:PhysiqueMathematique/48 DESCRIPTION:Title: Excitations and ergodicity of critical quantum spin chains f rom non-equilibrium classical dynamics\nby Stéphane Vinet\; Gabriel L ongpré (University of Waterloo\; Université de Montréal) as part of CRM -Séminaire Physique Mathématique\n\n\nAbstract\nWe study a quantum spin- 1/2 chain that is dual to the canonical problem of non-equilibrium Kawasak i dynamics of a classical Ising chain coupled to a thermal bath. The Hami ltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic\ , and depends on the Ising couplings normalized by the bath's temperature. We give its exact ground states. Proceeding with uniform couplings\, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime\, the two-magnon branch states show intricate behavior\, especially regarding th eir hybridization with the continuum. We find that that the gapless chain hosts multiple dynamics at low energy as seen through the presence of mul tiple dynamical critical exponents. Finally\, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclu de that the system is non-integrable for generic parameters\, or equivalen tly\, that the corresponding non-equilibrium classical dynamics are ergodi c.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg Lisovyy (Université de Tours) DTSTART:20211130T203000Z DTEND:20211130T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/49 DESCRIPTION:Title: Accessory parameters in Heun equations and classical conform al blocks\nby Oleg Lisovyy (Université de Tours) as part of CRM-Sémi naire Physique Mathématique\n\n\nAbstract\nWe will discuss accessory para meters of Floquet type in the Heun equation and some of its confluent vers ions. A conjecture by Zamolodchikov relates them to quasiclassical limit of conformal blocks of the Virasoro algebra. I will explain an extension of this conjectural relation to another class of accessory parameter fun ctions that are defined by inverting all-order Bohr-Sommerfeld periods for the confluent and biconfluent Heun equation.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Frédéric Dupont-Dupuis (Université de Montréal) DTSTART:20220111T203000Z DTEND:20220111T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/50 DESCRIPTION:by Frédéric Dupont-Dupuis (Université de Montréal) as part of CRM-Séminaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Its (Indiana University–Purdue University Indianapolis (IUPUI)) DTSTART:20211116T203000Z DTEND:20211116T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/51 DESCRIPTION:Title: Isomonodrtomy aspects of the tt* equations of cecotti and va fa. Iwasawa factorization and asymptotics\nby Alexander Its (Indiana U niversity–Purdue University Indianapolis (IUPUI)) as part of CRM-Sémina ire Physique Mathématique\n\n\nAbstract\nThe talk is concerned with the g lobal asymptotic analysis of the tt* - Toda equation\, 2(wi)tt = 􀀀e2(w i+1􀀀wi) + e2(wi􀀀wi+1)\; where\, for all i\, wi = wi+n+1 (periodicity )\,wi = wi(jtj) (radial condi- tion)\, and wi + w􀀀i􀀀1 = 0 (\\anti-sy mmetry"). The problem has been intensively studied since the early 90s wo rk of Cecotti and Vafa. In these work a prominent role of the tt*- equati ons in the classi\ncation of su- persymmetric \neld theories had been reve aled and a series of important conjectures about their solutions has been formulated. Assuming n = 3 (the \nrst case beyond the known Painleve III situa- tion)\, we study the question using a combination of methods from p.d.e.\, isomonodromic deformations (Riemann-Hilbert method)\, and loop gr oups (Iwasawa factorization). We place these global solutions into the br oader context of solutions which are smooth near 0. For such solutions\, we compute explicitly the Stokes data and connection matrix of the as- soc iated meromorphic system\, in the resonant cases as well as in the non-res onant case. This allows us to give a complete picture of the monodromy da ta\, holomorphic data\, and asymptotic data of the global solutions and pr ove some of Cecotti-Vafa conjectures. In the talk\, the above mentioned r esults will be presented in detail with an outline of the key steps in the ir derivation. Also\, the relation to 1998 work of Tracy and Widom on the tt*-Toda equation will be discussed. This is a joint work with Martin Gu est and Chang-Shou Lin\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Ken McLaughlin (Colorado State University) DTSTART:20211109T203000Z DTEND:20211109T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/52 DESCRIPTION:Title: Some intuition and some asymptotic analysis: from two solit ons to a continuum limit of solitons\nby Ken McLaughlin (Colorado Stat e University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstra ct\nWe will work our way from 2-solitons interactions through to a gas of solitons\, and conclude with the description of a single soliton interacti ng with this soliton gas. Intuition will be developed in the completely t ractable examples of a single soliton\, and a pair of solitons locked in a mild battle before turning to dense limits.\n LOCATION:https://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:20260422T225924Z UID:PhysiqueMathematique/53 DESCRIPTION:Title: Réductions d'une équation de sine-Gordon en 2+1 dimensions \nby Robert Conte (ENS Paris-Saclay\, The university of Hong Kong) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\n(Joint work w ith Michel Grundland). \n\nWe establish all the reductions of the system of two coupled 2+1-dimensional sine-Gordon equations introduced by Konopel chenko and Rogers to ordinary di erential equations (ODE). There is only one such reduction\, to an ODE of Chazy\, algebraic transform of the sixth Painlevé equation. Various degeneracies also lead to the fiffth\, third and second Painlevé equations and to elliptic functions.\n LOCATION:https://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:20260422T225924Z UID:PhysiqueMathematique/54 DESCRIPTION:Title: Integrable systems from a Newton polygon\nby Bertrand Ey nard (Institut de Physique Théorique\, CEA (Commissariat à l'Energie Ato mique et aux Energies Alternative)) as part of CRM-Séminaire Physique Mat hématique\n\n\nAbstract\nLet $P(x\,y)\\in \\mathbb C[x\,y]$ a bivariate p olynomial\, written $P(x\,y)=\\sum_{(i\,j)\\in N}P_{i\,j} x^i y^j$. The p olytope $N\\subset \\mathbb Z\\times \\mathbb Z$ is called the Newton's po lytope and its convex envelope is the Newton's polygon. The locus of solu tions $P(x\,y)=0$ in $\\mathbb C\\times \\mathbb C$ is a plane curve (an i mmersed Riemann surface). Its geometry can be produced from the combinato rics of the Newton's polygon. This allows to construct a Baker-Akhiezer f unction and a Lax pair associated to $P(x\,y)$\, in other words an integra ble system. In fact there are several integrable systems that can be asso ciated to P. The easiest is the isospectral system\, following the Kriche ver's reconstruction method\, and the others can be seen as "quantum" defo rmations. In particular we can get an isomonodromic system and other defo rmations. We shall illustrate on the elliptic curve $P(x\,y)=y^2-x^3+g_2 x+x_3$.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Parez (Université de Montréal) DTSTART:20220118T203000Z DTEND:20220118T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/55 DESCRIPTION:by Gilles Parez (Université de Montréal) as part of CRM-Sém inaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuan Miao (University of Amsterdam) DTSTART:20220125T203000Z DTEND:20220125T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/56 DESCRIPTION:by Yuan Miao (University of Amsterdam) as part of CRM-Séminai re Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Clément Berthière (Université de Montréal) DTSTART:20220201T203000Z DTEND:20220201T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/57 DESCRIPTION:Title: Entanglement of skeletal regions\nby Clément Berthière (Université de Montréal) as part of CRM-Séminaire Physique Mathématiq ue\n\n\nAbstract\nThe entanglement entropy encodes key properties of quant um many-body systems. It is usually calculated for a subregion of finite volume (or area in 2d). In this talk\, I will discuss entanglement proper ties of subsystems possessing no volume\, dubbed « skeletal » (e.g. a line in 2d/3d). I will show that skeletal entanglement displays new beha vior compared to its bulk counterpart\, and leads to distinct universal qu antities. We discovered signatures including skeletal topological entangl ement entropy\, novel bulk and boundary cusp terms\, and strict area-law s caling for metals. I will focus on quantum systems with emergent Lorentz and scale invariance\, with an incursion into non-relativistic Lifshitz fi eld theories.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Delacretaz (University of Chicago) DTSTART:20220215T203000Z DTEND:20220215T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/58 DESCRIPTION:Title: Nonlinear bosonization of Fermi liquids\nby Luca Delacre taz (University of Chicago) as part of CRM-Séminaire Physique Mathématiq ue\n\n\nAbstract\nLandau's theory of Fermi liquids is a cornerstone of con densed matter physics. I will show how to formulate Fermi liquid theory a s an effective field theory of bosonic degrees of freedom\, using the math ematical formalism of coadjoint orbits. While at the linear level\, this theory reduces to multidimensional bosonization\, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response and certain other aspe cts of Fermi liquid theory phenomenology that are not captured by current bosonization approaches. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior\, and pr ovides a new angle to approach non-Fermi liquids. (Based on upcoming work with: Yi-Hsien Du\, Umang Mehta\, and Dam Thanh Son).\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Cenke Xu (University of California\, Santa Barbara) DTSTART:20220308T203000Z DTEND:20220308T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/59 DESCRIPTION:Title: Phases and Phase Transitions with Fractal Symmetries: Models and Experimental Platform\nby Cenke Xu (University of California\, Sa nta Barbara) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstrac t\nIn recent years\, generalizations of the notion of symmetry have signif icantly broadened our view on states of matter. We will discuss some recen t progress of understanding and realizing the "fractal symmetry"\, where t he symmetric charge i.e. the generator of the symmetry is defined on a fra ctal subset of the system with a noninteger or more generally irrational H ausdorff dimension. We will introduce a series of models with exotic fract al symmetries\, which can in general be deduced from a "Pascal Triangle" ( also called Yang Hui Triangle in ancient China) symmetry. We will discuss their various features including quantum phase transitions. We will also d iscuss the potential realization of these phases and phase transitions in experimental systems\, such as the highly tunable platform of Rydberg atom s.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafael Nepomechie (University of Miami) DTSTART:20220322T193000Z DTEND:20220322T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/60 DESCRIPTION:Title: Bethe ansatz and quantum computing\nby Rafael Nepomechie (University of Miami) as part of CRM-Séminaire Physique Mathématique\n\ n\nAbstract\nWe begin with a brief review of the Heisenberg quantum spin c hain and its remarkable solution found by Bethe. We then review a probabil istic algorithm for preparing exact eigenstates of this model on a quantum computer. An exact formula for the success probability is presented\, and the computation of correlation functions is discussed. A generalization o f the algorithm to open chains with boundaries is also noted.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Terwilliger (University of Wisconsin-Madison) DTSTART:20220208T203000Z DTEND:20220208T213000Z DTSTAMP:20260422T225924Z 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 algebra $O_q$ is a quantized enveloping algebra for the Onsager Lie algebra $O$. Recently Baseilhac\, Koizumi\, and Shigechi introduced an algebra $\\mathc al O_q$ 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 moti vate this description\, we first consider a toy model\, involving the posi tive part $U^+_q$ of $U_q(\\widehat{\\mathfrak{sl}}_2)$ and its alternatin g central extension $\\mathcal U^+_q$. We will see that $O_q$ is related to $\\mathcal O_q$ in essentially the same way as $U^+_q$ is related to $\ \mathcal U^+_q$. We finish with an open problem.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Crampe (Université de Tours) DTSTART:20220222T203000Z DTEND:20220222T213000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/62 DESCRIPTION:Title: Absorption or emission of solitons\nby Nicolas Crampe (U niversité de Tours) as part of CRM-Séminaire Physique Mathématique\n\n\ nAbstract\nI will present how to obtain integrable differential equations with particular boundary conditions which admit solutions where the solito n can be absorbed or emitted by the boundary. After an introduction to cl assical integrable systems with boundary conditions and solitonic solution s\, I will explain how an algebraic question lead to consider time-depende nt boundary conditions. In this case\, special solutions have been comput ed where the number of solitons is not preserved.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Bouchard (University of Alberta) DTSTART:20220315T193000Z DTEND:20220315T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/63 DESCRIPTION:Title: Transalgebraic Spectral Curves\, Quantum Curves\, and Atlan tes Hurwitz Numbers\nby Vincent Bouchard (University of Alberta) as pa rt of CRM-Séminaire Physique Mathématique\n\n\nAbstract\nPhysics is a gr eat source of ideas for pure mathematics. The topological recursion of Che khov-Eynard-Orantin (CEO) is an example of this approach: it was originall y developed to solve matrix models in physics\, but was then abstracted aw ay from its physics origins. The result is a mathematical formalism that h as found numerous applications in various areas of mathematics\, particula rly in enumerative geometry. \n\nThe Topological Recursion/Quantum Curve ( TR/QC) correspondence\, which also originated in the context of matrix mod els\, states that the CEO topological recursion (and its higher analog)\, which associates a sequence of differentials to a spectral curve\, can be used to reconstruct the WKB asymptotic solution of a differential equation 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 transalgeb raic spectral curves\; those are curves with exponential singularities\, w hich can be obtained as limits of sequences of algebraic spectral curves. To this end\, we construct a generalization of topological recursion that is consistent with limits of sequences of algebraic curves\; it includes c ontributions from the exponential singularities. The prototypical example is the spectral curve which is known to give rise to r-spin Hurwitz number s via the usual topological recursion\; we show that\, for the same spectr al curve\, our natural generalization of the topological recursion instead computes atlantes Hurwitz numbers\, and reconstructs the WKB solution of the appropriate quantum curve. This is particularly interesting given that atlantes Hurwitz numbers had so far evaded topological recursion methods. \n\nThis is joint work with Reinier Kramer and Quinten Weller.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Semeon Artamonov (Université de Montréal) DTSTART:20220329T193000Z DTEND:20220329T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/64 DESCRIPTION:by Semeon Artamonov (Université de Montréal) as part of CRM- Séminaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Galina Filipuk (University of Warsaw) DTSTART:20220419T193000Z DTEND:20220419T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/66 DESCRIPTION:by Galina Filipuk (University of Warsaw) as part of CRM-Sémin aire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Loic Poulain D'Andecy (Université de Reims) DTSTART:20220426T193000Z DTEND:20220426T203000Z DTSTAMP:20260422T225924Z 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://researchseminars.org/talk/PhysiqueMathematique/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Cliff (Université de Sherbrooke) DTSTART:20220412T193000Z DTEND:20220412T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/68 DESCRIPTION:Title: Moduli spaces of principal 2-group bundles and a categorific ation of the Freed-Quinn line bundle\nby Emily Cliff (Université de S herbrooke) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstract\ nA 2-group is a higher categorical analogue of a group\, while a smooth 2- group is a higher categorical analogue of a Lie group. An important examp le is the string 2-group in the sense of Schommer-Pries. We study the not ion of principal bundles for smooth 2-groups\, and investigate the moduli "space" of such objects. In particular in the case of flat principal bund les for a finite 2-group over a Riemann surface\, we prove that the moduli space gives a categorification of the Freed--Quinn line bundle. This lin e bundle has as its global sections the state space of Chern--Simons theor y for the underlying finite group. We can also use our results to better understand the notion of geometric string structures (as previously studie d by Waldorf and Stolz--Teichner). This is based on joint work with Dan B erwick-Evans\, Laura Murray\, Apurva Nakade\, and Emma Phillips.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Del Monte (Université de Montréal) DTSTART:20220503T193000Z DTEND:20220503T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/69 DESCRIPTION:Title: Supersymmetric partition functions and isomonodromic tau fun ctions\nby Fabrizio Del Monte (Université de Montréal) as part of CR M-Séminaire Physique Mathématique\n\n\nAbstract\nClass S theories are fo ur-dimensional N=2 QFTs that are obtained by wrapping M5-branes on Riemann surfaces with singular points. In recent years a correspondence between c lass S theories and isomonodromic deformations equations (whose simplest e xamples are the six Painlevé equations) is emerging\, where the so-called isomonodromic tau function is identified with the dual partition function of the QFT. The tau functions can be tipycally written as Fredholm determ inants or Pfaffians\, providing a fully nonperturbative approach to study partition functions of class S theories\, relying only on the geometric da ta entering in the string theory construction\, and not on a classical act ion.\n\nAfter reviewing the Fredholm determinant formulation of tau functi ons for spheres with regular singularities\, corresponding to linear quive r gauge theories\, I will show how the description can be extended to tau functions with orthogonal gauge groups\, that are written as Fredholm Pfaf fians\, and to tau functions for tori with regular singularities\, corresp onding to circular quiver gauge theories. I will conclude by showing how t he tau function description allows to study the S-duality transformation o f the resulting gauge theory dual partition function.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/69/ END:VEVENT BEGIN:VEVENT SUMMARY:David Aasen (Microsoft Station Q and KITP) DTSTART:20220510T193000Z DTEND:20220510T203000Z DTSTAMP:20260422T225924Z 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://researchseminars.org/talk/PhysiqueMathematique/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrzej Pokraka (McGill University) DTSTART:20220405T193000Z DTEND:20220405T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/71 DESCRIPTION:Title: The duals of Feynman integrals\nby Andrzej Pokraka (McGi ll University) as part of CRM-Séminaire Physique Mathématique\n\n\nAbstr act\nWe elucidate the vector space (twisted relative cohomology) that is P oincaré dual to the vector space of Feynman integrals (twisted cohomology ) in general spacetime dimension. The pairing between these spaces — an algebraic invariant called the intersection number — extracts integral c oefficients for a minimal basis\, bypassing the generation of integration- by-parts identities. Dual forms turn out to be much simpler than their Fey nman counterparts: they are supported on maximal cuts of various sub-topol ogies (boundaries). Thus\, they provide a systematic approach to generaliz ed unitarity\, the reconstruction of amplitudes from on-shell data. As an application of our formalism\, we derive compact differential equations sa tisfied by arbitrary one-loop integrals in non-integer spacetime dimension and show how to use the intersection number to express a scattering ampli tude in terms of a minimal basis of integrals. We also examine the 4-dimen sional limit of our formalism and provide prescriptions for extracting rat ional terms.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Dimitra Karabali (Lehman College CUNY) DTSTART:20220517T193000Z DTEND:20220517T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/72 DESCRIPTION:by Dimitra Karabali (Lehman College CUNY) as part of CRM-Sémi naire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Juliàn Barragan Amado (Université de Sherbrooke) DTSTART:20220913T193000Z DTEND:20220913T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/73 DESCRIPTION:Title: Quasinormal modes via isomonodromy\nby Juliàn Barragan Amado (Université de Sherbrooke) as part of CRM-Séminaire Physique Math ématique\n\n\nAbstract\nIn this talk\, I will introduce the method of iso monodromic deformations to study the quasinormal modes (QNMs) of a charged scalar field on a Reissner-Nordström anti-de Sitter (RN-AdS5) black hole . Namely\, we need to recast the boundary value problem of the radial sec ond-order ordinary differential equation in terms of an initial value prob lem of an isomonodromic tau function. Then we can obtain asymptotic expan sions for the fundamental QNMs in the small radius and the near extremal b lack hole limit.\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Marquette (University of Queensland) DTSTART:20221004T193000Z DTEND:20221004T203000Z DTSTAMP:20260422T225924Z UID:PhysiqueMathematique/74 DESCRIPTION:by Ian Marquette (University of Queensland) as part of CRM-Sé minaire Physique Mathématique\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/PhysiqueMathematique/74/ END:VEVENT END:VCALENDAR