Abstracts

December 17 (Tuesday)

• [09:20 - 9:55] (FR) | [17:20 - 17:55] (JP)
  
  Title: Two reciprocities on Hecke algebras
  H. Miyachi (Osaka)
  
  I would like to talk about two reciprocities on Hecke algebras. One is about (1) Iwahori-Hecke algebras and their Kazhdan-Lusztig left cells. I would like to report that Mackey formula holds for left cells as group elements. The other is about (2) a generalization of Robinson reciprocity in finite groups to Hecke algebras, especially on cyclotomic quiver Hecke algebras. Robinson found a reciprocity on the projective summand multiplicities between induced and restricted simple modules. I would  like to report that its graded analogue holds.

• [10:00 - 10:35] (FR) | [18:00 - 18:35] (JP)
  
  Propagation of global analyticity and unique extension for semilinear wave equations
  C. Laurent (Reims)
  
  In this talk, I will first present some known results of unique continuationfor wave-like equations. I will explain the difficulties of obtaining global results under natural geometrical assumptions. Subsequently, I will present a recent result, in collaboration with Cristobal Loyola, where we prove the unique continuation for semilinear wave equations under the geometric control  assumption. A crucial step is the global propagation of analyticity in time from open sets verifying the geometric control condition. The proof uses control methods associated with Hale-Raugel ideas concerning attractor regularity.
  This is a joint work with Cristobal Loyola (Sorbonne).
  

• [10:40 - 11:15] (FR) | [18:40 - 19:15] (JP)
  
  Cluster algebras and scattering diagrams
  T. Nakanishi (Nagoya)
  
  Cluster algebras were a class of commutative algebras introduced by Fomin and Zelevinsky around 2000. Some important conjectures on cluster algebras were solved by Gross-Hacking-Keel-Kontsevich around 2014 using the scattering diagram method. I will explain the essence of this method.

• [11:20 - 12:00] (FR) | [19:20 - 20:00] (JP)
  
  Actions of tensor categories on operator algebras
  Y. Arano (Nagoya)
  
  Tensor categories and their actions on operator algebras naturally arise from subfactors, which can be considered as a counterpart for the Galois groups for inclusions of operator algebras. In this talk, I will give an overview of such theory and then talk on the recent progress on the classification of inclusions of C*-algebras, especially from the viewpoint of K-theory.

December 18 (Wednesday)

• [9:00 - 9:35] (FR) | [17:00 - 17:35] (JP)
  
  Normal distributions and highest weight unitary representations of the Jacobi group
  H. Ishi (Osaka)
  
  We shall see that rather elementary observations of Laplace transform of some invariant measures lead us to results in two different topics: convolution power of the normal distribution and description of highest weight unitary representations of the Jacobi group.
  

• [9:40 - 10:15] (FR) | [17:40 - 18:15] (JP)
  
  Theoretical and numerical study of the nonlinear Schrödinger equation with defects
  J. Le Quentrec (Reims)
  
  In this work, we investigate the nonlinear Schrödinger equation involving a defect term, which materializes the presence of an impurity along a hypersurface.
  We first adapt the techniques already used in the absence of a defect term to study the local or global well-posedness of our problem, as well as finite time blow-up. This requires to define a well-adapted functional framework that takes into account the singular term and a new viriel identity.
  We then focus on the schemes allowing us to compute numerical solutions. Special attention will be paid to the discretization of the default with finite differences.
  

• [10:20 - 10:55] (FR) | [18:20 - 18:55] (JP)
  
  On the branching functions of affine Lie algebras with respect to the underlying simple Lie algebras
  M. Okado (Osaka)
  
  In this talk, I explain a “kettaina” (weird in Kansai dialect) formula of the branching function for affine Lie algebras. It was found more than 20 years ago through the studies of integrable systems.
  

• [11:00 - 11:35] (FR) | [19:00 - 19:35] (JP):
  
  Link invariants from Yokonuma-Hecke algebras
  L. Poulain d'Andecy (Reims)
  
  A family of link invariants were obtained some 20 years ago from algebras introduced in the 60s by the Japanese mathematician Takeo Yokonuma (in a series of papers written in French!). The construction and a classification of these invariants will be discussed together with some connections with the usual Hecke algebra and the quantum Schur--Weyl duality. This was part of joint works with Nicolas Jacon, Abel Lacabanne and  Emmanuel Wagner.