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Friday 5 July 2019, 14:00 at
IHES,
Centre de conférences Marilyn et James Simons ( "Journée Gretchen & Barry Mazur" (https://indico.math.cnrs.fr/event/4697/) )  MATHIHES (TBA)  math 


Friday 5 July 2019, 15:15 at
IHES,
Centre de conférences Marilyn et James Simons ( "Journée Gretchen & Barry Mazur" (https://indico.math.cnrs.fr/event/4697/) )  MATHIHES (TBA)  math 


Friday 5 July 2019, 16:45 at
IHES,
Centre de conférences Marilyn et James Simons ( "Journée Gretchen & Barry Mazur" (https://indico.math.cnrs.fr/event/4697/) )  MATHIHES (TBA)  math 


Monday 8 July 2019, 14:30 at
IHES,
Amphithéâtre Léon Motchane ( Cours de l'IHES )  MATHIHES (TBA)  hepth 



Abstract:  Lectures 13 are mostly based on our recent work with Linhui Shen. Given a surface S with punctures and special points on the boundary considered modulo isotopy, and a split semisimple adjoint group G, we define and quantize moduli spaces Loc(G,S) Glocal systems on S, generalising character varieties. To achieve this, we introduce a new moduli space P(G, S) closely related to Loc(G,S). We prove that it has a cluster Poisson variety structure, equivariant under the action of a discrete group, containing the mapping class group of S. This generalises results of V. Fock and the author, and I. Le. For any cluster Poisson variety X, we consider the quantum Langlands modular double of the algebra of regular functions on X. If the Planck constant h is either real or unitary, we equip it with a structure of a *algebra, and construct its principal series of representations. Combining this, we get principal series representations of the quantum Langlands modular double of the algebras of regular functions on moduli spaces P(G, S) and Loc(G,S). We discuss applications to representations theory, geometry, and mathematical physics. In particular, when S has no boundary, we get a local system of infinite dimensional vector spaces over the punctured determinant line bundle on the moduli space M(g,n). Assigning to a complex structure on S the coinvariants of oscillatory representations of Walgebras sitting at the punctures of S, we get another local system on the same spa. We conjecture there exists a natural nondegenerate pairing between these local systems, providing conformal blocks for Liouville / Toda theories. In Lecture 4 we discuss spectral description of noncommutative local systems on S, providing a noncommutative cluster structure of the latter. It is based on our joint work with Maxim Kontsevich. 
Wednesday 10 July 2019, 14:30 at
IHES,
Amphithéâtre Léon Motchane ( Cours de l'IHES )  MATHIHES (TBA)  math 



Abstract:  Lectures 13 are mostly based on our recent work with Linhui Shen. Given a surface S with punctures and special points on the boundary considered modulo isotopy, and a split semisimple adjoint group G, we define and quantize moduli spaces Loc(G,S) Glocal systems on S, generalising character varieties. To achieve this, we introduce a new moduli space P(G, S) closely related to Loc(G,S). We prove that it has a cluster Poisson variety structure, equivariant under the action of a discrete group, containing the mapping class group of S. This generalises results of V. Fock and the author, and I. Le. For any cluster Poisson variety X, we consider the quantum Langlands modular double of the algebra of regular functions on X. If the Planck constant h is either real or unitary, we equip it with a structure of a *algebra, and construct its principal series of representations. Combining this, we get principal series representations of the quantum Langlands modular double of the algebras of regular functions on moduli spaces P(G, S) and Loc(G,S). We discuss applications to representations theory, geometry, and mathematical physics. In particular, when S has no boundary, we get a local system of infinite dimensional vector spaces over the punctured determinant line bundle on the moduli space M(g,n). Assigning to a complex structure on S the coinvariants of oscillatory representations of Walgebras sitting at the punctures of S, we get another local system on the same spa. We conjecture there exists a natural nondegenerate pairing between these local systems, providing conformal blocks for Liouville / Toda theories. In Lecture 4 we discuss spectral description of noncommutative local systems on S, providing a noncommutative cluster structure of the latter. It is based on our joint work with Maxim Kontsevich. 
Tuesday 23 July 2019, 14:00 at LPTHE, library  LPTHEPPH (Particle Physics at LPTHE)  hepph 


Friday 26 July 2019, 14:00 at LPTHE, library  LPTHEPPH (Particle Physics at LPTHE)  hepph 


Monday 9 September 2019, 10:45 at LPTMC, Jussieu, tower 1312, room 523  SEMLPTMC (Séminaire du Laboratoire de Physique Théorique de la Matière Condensée)  condmat.meshall 



Abstract:  We identify the persistence probability for the spin located at the origin of a halfspace magnetized GlauberIsing chain as a Fredholm Pfaffian gap probability generating function with a sechkernel. This is then recast as a taufunction for a certain Painlevé VI transcendent  a sort of exact Kramers' formula for the associated explicitely timedependent Hamiltonian  where the persistence exponent emerges as an asymptotic decay rate. By a known yet remarkable correspondence that relates Painlevé equations to Bonnet surfaces, the persistence probability has also a geometric meaning à la GaussBonnet in terms of the intrinsic curvature of the underlying surface. Since the same sechkernel with an underlying Pfaffian structure shows up in a variety of Gaussian firstpassage problems, our Painlevé VI characterization appears as a universal probability distribution akin to the famous Painlevé II TracyWidom laws. Its tail behavior in the magnetizationsymmetric case allows in particular to recover the exact value 3/16 for the persistence exponent of a 2d diffusing random field, as found very recently by Poplavskyi and Schehr (arXiv:1806.11275). Due to its topological origin, this value should constitute the superuniversal persistence exponent for the coarsening of a nonconserved scalar order parameter in two space dimensions. 
Monday 23 September 2019, 10:45 at LPTMC, Jussieu, tower 1312, room 523  SEMLPTMC (Séminaire du Laboratoire de Physique Théorique de la Matière Condensée)  condmat.meshall 


Wednesday 2 October 2019, 14:15 at IPHT, Salle Claude Itzykson, Bât. 774  IPHTMAT (Séminaire de matrices, cordes et géométries aléatoires)  hepth 



Abstract:  (TBA) 

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