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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/) )
MATH-IHES (TBA) math
Ziyang Gao ( IMJ-PRG ) Application of Functional Transcendence to Counting Rational Points of Curves

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/) )
MATH-IHES (TBA) math
Pierre Colmez ( IMJ-PRG ) Sur le programme de Langlands p-adique

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/) )
MATH-IHES (TBA) math
Barry Mazur ( Harvard University ) New Rational Points of Algebraic Curves over Extension Fields

Monday 8 July 2019, 14:30 at IHES, Amphithéâtre Léon Motchane
( Cours de l'IHES )
MATH-IHES (TBA) hep-th
Alexander Goncharov ( Yale University & IHES ) Quantum Geometry of Moduli Spaces of Local Systems and Representation Theory (3/4)
Abstract: Lectures 1-3 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 semi-simple adjoint group G, we define and quantize moduli spaces Loc(G,S) G-local 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 W-algebras sitting at the punctures of S, we get another local system on the same spa. We conjecture there exists a natural non-degenerate pairing between these local systems, providing conformal blocks for Liouville / Toda theories. In Lecture 4 we discuss spectral description of non-commutative local systems on S, providing a non-commutative 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 )
MATH-IHES (TBA) math
Alexander Goncharov ( Yale University & IHES ) Quantum Geometry of Moduli Spaces of Local Systems and Representation Theory (4/4)
Abstract: Lectures 1-3 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 semi-simple adjoint group G, we define and quantize moduli spaces Loc(G,S) G-local 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 W-algebras sitting at the punctures of S, we get another local system on the same spa. We conjecture there exists a natural non-degenerate pairing between these local systems, providing conformal blocks for Liouville / Toda theories. In Lecture 4 we discuss spectral description of non-commutative local systems on S, providing a non-commutative cluster structure of the latter. It is based on our joint work with Maxim Kontsevich.

Tuesday 23 July 2019, 14:00 at LPTHE, library LPTHE-PPH (Particle Physics at LPTHE) hep-ph
Cen Zhang ( IHEP Beijing ) TBA

Friday 26 July 2019, 14:00 at LPTHE, library LPTHE-PPH (Particle Physics at LPTHE) hep-ph
Florian Domingo ( Bonn U. ) TBA

Monday 9 September 2019, 10:45 at LPTMC, Jussieu, tower 13-12, room 5-23 SEM-LPTMC (Séminaire du Laboratoire de Physique Théorique de la Matière Condensée) cond-mat.mes-hall
Ivan Dornic ( SPEC Saclay & LPTMC ) A tale of Pfaffian persistence tails told by a Painlevé VI transcendent
Abstract: We identify the persistence probability for the spin located at the origin of a half-space magnetized Glauber-Ising chain as a Fredholm Pfaffian gap probability generating function with a sech-kernel. This is then recast as a tau-function for a certain Painlevé VI transcendent --- a sort of exact Kramers' formula for the associated explicitely time-dependent 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 Gauss-Bonnet in terms of the intrinsic curvature of the underlying surface. Since the same sech-kernel with an underlying Pfaffian structure shows up in a variety of Gaussian first-passage problems, our Painlevé VI characterization appears as a universal probability distribution akin to the famous Painlevé II Tracy-Widom laws. Its tail behavior in the magnetization-symmetric 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 super-universal persistence exponent for the coarsening of a non-conserved scalar order parameter in two space dimensions.

Monday 23 September 2019, 10:45 at LPTMC, Jussieu, tower 13-12, room 5-23 SEM-LPTMC (Séminaire du Laboratoire de Physique Théorique de la Matière Condensée) cond-mat.mes-hall
Juliette Mignot ( IPSL-LOCEAN Jussieu ) Changement climatique et mesures concrètes prises par des labos (provisoire)

Wednesday 2 October 2019, 14:15 at IPHT, Salle Claude Itzykson, Bât. 774 IPHT-MAT (Séminaire de matrices, cordes et géométries aléatoires) hep-th
Elias Kiritsis ( APC ) (TBA)
Abstract: (TBA)

seminars from series at institute
in subject with field matching

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