报告1题目：Best constant and extremal function for a class Hardy-Mazya-Sobolev inequality

报告人：麻希南

报告摘要：We derive an differential identity for a class p-Laplace equation, and then classify all positive finite energy cylindrically symmetric solutions of the p-Laplacian equation with the help of some a prior estimates. This is joint work with Daowen Lin.

报告时间：11月22日上午9:00—10:00

报告地点：数学楼207

报告人简介：麻希南，中国科学技术大学数学科学学院教授，中法数学中心常务副主任，长江学者，国家杰出青年基金获得者。

报告2题目：Dynamical degrees

报告摘要：Dynamical degrees are fundamental invariants of a rational self-map of an algebraic variety, and arise in many problems in algebraic dynamics (existence of periodic orbits, of invariant fibrations, in the computation of the topological entropy, etc.).We shall give a gentle introduction to this notion and describe some recent results on their behaviour.

报告人：Charles Favre主任研究员

单位：Centre national de la recherche scientifique & École Polytechnique（法国国家科学研究中心、巴黎综合理工大学）

报告时间：11月22日14:00—14:50

报告地点：数学楼108

报告人简介：

I’m CNRS-research director based at the Ecole Polytechnique. I got my Phd in 2000 under the direction of Nessim Sibony in Orsay, and worked at the Institut de Mathématiques de Jussieu until 2006. I spent two sabbatical years at IMPA (Rio-Brazil) and then UBC (Vancouver-Canada). I am the author of over 50 research papers and 2 books. I was the chair of my department for 6 years until 2022.

报告3题目：On the ergodicity of the frame flow

报告摘要：The geodesic flow of compact Riemannian manifolds with negative sectional curvature is hyperbolic, thus ergodic with respect to the Liouville measure on the unit tangent bundle. However, its natural lift to the orthonormal frame bundle - called the frame flow - is only partially hyperbolic, and is not always ergodic, e.g. when the manifold is Kähler or quaternion-Kähler. In the 80's, Brin and Gromov proved the ergodicity of the frame flow when the dimension $n$ of the manifold is odd and different from 7, and conjectured that ergodicity should hold whenever the sectional curvature is at least 0,25 pinched. Some partial results were obtained by Brin-Karcher ('84) and Burns-Pollicott ('03), under quite strong pinching assumptions of the order of 0,86 and 0,98. In this talk I will report on some recent developments towards the Brin-Gromov conjecture, where the required pinching is approximately 0,27 - 0,29 for $n=4k+2$ and 0,57 - 0,6 for $n=4k$. The talk is based on joint work with Mihajlo Cekic (ETH, Zürich), Thibault Lefeuvre (Sorbonne Université) and Uwe Semmelmann (Stuttgart University).

报告人：Andrei Moroianu 主任研究员

报告时间：11月22日14:50—15:40

报告地点：数学楼108

单位：Centre national de la recherche scientifique & Université Paris-Saclay（法国国家科学研究中心、巴黎-萨克雷大学）

报告人简介：Andrei Moroianu graduated at the Ecole Normale Supérieure in Paris in 1995 and got his PhD from the Ecole Polytechnique in 1996. He works for the CNRS since 1997, and his research topic is differential geometry. Since 2017 he is based at the Paris-Saclay University. He was awarded the Peccot Lecture at the Collège de France in 1998 and he held lectures at the Ecole Polytechnique from 2004 to 2016. Since 2021 he gives the Differential Geometry lecture to the China-France Mathematics Talents Class in the University of Science and Technology of China.

报告4题目：Counting points on curves

报告摘要：We shall discuss effectivity, uniformity for bounds on rational points on curves defined over a number field.

报告人：Sinnou David

报告时间：11月22日15:40—16:30

报告地点：数学楼108

报告人简介：Sorbonne Université（索邦大学）教授