报告人：程伟
报告地点：数学与统计学院二楼会议室
报告时间：2023年08月31日08:30-09:30
邀请人：冀书关、高忆先
报告摘要：
There are various notions of singular characteristics in the theory of propagation singularities of viscosity solutions. In this talk, we will discuss the variational construction of generalized characteristics and strict singular characteristics. We proved the solution of generalized characteristics can be constructed in an intrinsic way using the idea of minimizing movements and certain process of homogenization. Moreover, the relation between the strict singular characteristics and the EDI-EVI frame of gradient flow was also discussed. In general, these results bridge various different topics. This talk is based on our latest work with Piermarco Cannarsa, Jiahui Hong and Kaizhi Wang.
主讲人简介：
程伟，南京大学数学系教授、博士生导师。目前主要研究领域为Hamilton动力系统，Aubry-Mather理论，Hamilton-Jacobi方程的粘性解理论，变分法与最优控制，平均场博弈论等，取得了丰硕的成果。其中一个代表工作《Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry》发表在在国际顶级数学期刊《Publications mathématiques de l'IHÉS》，该论文研究了一般流形上Hamilton-Jacobi方程粘性解奇性传播，证明了粘性解的割迹与动力学极小不变集Aubry集补集的同伦等价性，以及割迹的局部可缩性。作为应用，解决了完备Riemann流形任意闭子集割迹与奇点集的局部可缩性和局部道路连通性这一长期未决的经典问题。
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