报告题目：Cut locus from touching point of view

报告时间：2025年12月5日（周五）16:00-17:00

报告地点：腾讯会议 421-504-580

主办单位：国产自拍

报告摘要：In the study of singularity propagation for viscosity solutions of Hamilton-Jacobi equations, we observe that using smooth functions with certain regularity to touch semiconcave functions can characterize the cut locus of viscosity solutions. We provide a general characterization of the $C^{1,1}$-type regularity of semiconcave functions in the complement of the cut locus and explore the relationship between this regularity and the structure of the cut locus. As a byproduct, we present an elementary proof of Alexandrov's theorem on the almost everywhere twice differentiability of convex functions. This work is based on joint research with Jiahui Hong and Wenxue Wei.

主讲人简介：程伟，南京大学教授，博士生导师，至诚特聘教授。现为南京大学数学学院教学委员会主任，中国数学会常务理事。长期从事Hamilton动力系统、特别是Aubry-Mather理论，Hamilton-Jacobi方程粘性解理论，平均场博弈论和最优输运等领域的交叉研究。在包括Publ. Math. IHÉS在内的国际一流期刊上发表诸多重要成果，产生了较大的国际影响。主持完成多项国家自然科学基金面上项目，目前主持一项国家自然科学基金重点项目（2023-2027）。