报告一：

报告人: 黄飞敏（中国科学院数学与系统科学研究院研究员）

报告题目:Global well-posedness of the boltzmann equation with large amplitude initial date

报告摘要:The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\\infty_xL^1_{v}\\cap L^\\infty_{x,v}$ approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^\\infty$ norm under some smallness condition on $L^1_xL^\\infty_v$ norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in $L^\\infty_{x,v}$ norm with explicit rates of convergence is also studied

报告人简介:黄飞敏研究员，主要研究双曲守恒律方程组和粘性守恒律方程组，解决了等温气体动力学方程组（即绝热指数 \gamma=1 ）带真空的 Cauchy 问题弱解的整体存在性这一长期未解决的数学难题。

报告时间：2019年6月5日（星期三）下午14：00

报告地点：科技楼南楼702

报告二：

报告人: 范辉军（北京大学教授）

报告题目:On gauged linear sigma model

报告摘要:Gauged linear sigma model was a physical model proposed by E. Witten in the early of 90's, which was used by him to explain the mirror symmetry phenomenon. Only up to recent years has this model been seriously considered by mathematicians with the development of Gromov-Witten theory and quantum singularity theory (FJRW theory). In this talk, I will report our progress on this topic.

报告人简介:范辉军教授的研究领域为有关弦理论、量子场理论的数学物理，以及几何分析。2002-2008年,与人合作通过一系列文章构造了量子奇点理论(国际上称为Fan-Jarvis-Ruan-Witten理论)并解决了DE情形的广义Witten猜想。2010-2011年,独自构造了形式薛定谔方程的形变理论,对应着紧复流形的Kodaira-Spencer 理论。除此之外,在几何分析方向的调和映射问题，非正曲率流形Martin 边界的研究和Novikov理论方面取得了一系列重要的结果。

报告时间：2019年6月5日（星期三）下午16：00

报告地点：科技楼南楼702