Academic Workshop on China-France Mathematics Talents Class（CFMTC）中法数学英才班学术报告会
本讲教师：Laurent LAFFORGUE Xiaonan MA Marc ROSSO
01-16中法数学英才班学术报告会 Academic Workshop on China-France Mathematics Talents Class（CFMTC） Date: Wednesday, Janaury 16 Venue: Room 5203, The Fifth Teaching Building, East Campus of USTC, Hefei Time: 2: 00 - 3: 00PM Speaker: Laurent LAFFORGUE（IHES） Title： Grothendieck toposes and the multiple ways to look at them Abstract: The notion of topos was introduced by A. Grothendieck in the early 1960's as the most general context where all basic geometric intuitions still make sense. According to him : "It is the topos theme which is this “bed” or “deep river” where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the “continuous” and that of “discontinuous” or discrete structures". The purpose of the talk will be to give an idea of how rich is this notion. Time: 3: 10 - 4: 10PM Speaker: Xiaonan MA（Paris7) Title: Local index theory: from index to analytic torsion and eta invariant Abstract: “We will review first the heat equation proof of Atiyah-Singer theorem by Bismut and Getzler, and explain how these ideas could be used to study more refine spectral invariants: analytic torsion and eta invariant which have had implications in topology, geometry, mathematical physics and arithmetic.” Time: 4: 30 - 5: 30PM Speaker: Marc ROSSO（Paris7) Title: Quantum groups : from physics to algebra, via low dimensional topology Abstract: Quantum groups appeared as the algebraic structure underlying quantum completely integrable systems. A basic ingredient, the R-matrix, turns out to provide representations of the braid groups (i.e. braided vector spaces), and powerful invariants of knots and 3-dimensional manifolds. Quantum groups were first defined as deformations of enveloping algebras of simple or Kac-Moody Lie algebras, and have lead to far reaching developments in representation theory (canonical bases, connection with Lie theory in finite characteristics when the deformation parameter is a root of unity,…). A new construction of them (as quantum symmetric algebra) is at the heart important progress in the classification of finite dimension Hopf algebras. I will explain the main notions, describe the simplest examples (quantum groups associated with the general linear group), and will illustrate some of the above developments on them.