应数学与统计学院孙红蕊教授的邀请，湖南师范大学数学与统计学院苏治铜 博士将于8月8日至8月12日访问兰州大学，并于8月11日上午作学术报告， 欢迎全校师生参加!

报告题目：A decomposition lemma in convex integration via classical algebraic geometry

时 间：2024年8月11日(星期一) 10:00

地 点：理工楼518教室

摘要： In this talk, we introduce a decomposition lemma in the convex integration scheme. The lemma allows error terms to be expressed using fewer rank-one symmetric matrices than n(n+1)/2 within constructing flexible C^(1,α) solutions to a system of nonlinear PDEs in dimension n ≥ 2, which can be viewed as a kind of truncation of the codimension one local isometric embedding equation in Nash-Kuiper Theorem. This leads to flexible solutions with higher Hölder regularity, and consequently, improved very weak solutions to certain geometric equations.

Our arguments involve applications of several results from algebraic geometry and topology, including theorem on vector fields on spheres, the intersection of projective varieties, and projective duality. We also use an elliptic method that avoids loss of differentiability. Consequently, our improvements on exponent involves the Radon-Hurwitz number, which exhibits an 8-fold periodicity on n that is related to Bott periodicity. This work is inspired by Cao-Székelyhidi'19, and is a joint work with Weijun Zhang.

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报告人简介

苏治铜博士，现任湖南师范大学教师。2022年毕业于美国罗格斯大学纽瓦克分校，师从王晓玮教授。2022至2024年在中山大学从事博士后研究，合作导师为李长征教授。研究方向为微分几何，主要聚焦于Gromov-Witten理论中的量子上同调与黎曼几何中的等距嵌入问题（后者为其博士研究核心课题）。曾在国际数学期刊 Asian Journal of Mathematics 发表研究论文。

甘肃应用数学中心 数学与统计学院

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