报告题目：A new complete proof of the random Brouwer fixed point theorem and its implied consequences of unification

报 告 人：涂强 讲师（岭南师范学院）

报告时间：2026年8月4日（星期二）上午9：00-9：40

报告地点：数学科学学院115（大报告厅）  

校内联系人： 朱传喜 教授   联系方式：84708351-8420

报告摘要：We first establish a general random Sperner lemma by presenting a completely new approach for the theory of $L^{0}$-simplicial subdivisions of  $L^{0}$-simplexes. Based on this, we are able to achieve a new complete proof of the random Brouwer fixed theorem in random Euclidean spaces, which can provide a solid foundation for various contemporary applications of interest. Afterward, we unify the works currently available and closely related to the random Brouwer fixed theorem: we first prove that the stochastic Brouwer fixed point theorem occurring elsewhere in stochastic analysis is equivalent to a special  case of our random Brouwer fixed theorem, and then prove a general random Borsuk theorem and its equivalence with the random Brouwer fixed theorem.

报告人简介：涂强，男，博士毕业于中南大学，现任岭南师范学院数学与统计学院讲师。研究方向为泛函分析（空间理论），现主要从事随机泛函分析框架下稳定紧性理论与不动点理论的研究, 相关成果先后发表在《J.Fixed Point Theory Appl.》《Banach J. Math. Anal.》《J. Nonlinear Convex Anal.》《New York J. Math.》等 SCI 期刊上。