报告题目 (Title)：Exact Solutions of Anti-Self-Dual Yang-Mills Equations （反自对偶Yang-Mills方程的精确解）
报告人 (Speaker)：Masashi Hamanaka 教授（名古屋大学）
报告时间 (Time)：2023年12月28日(周四) 10:30-12:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：张大军 教授
主办部门：永利数学系
报告摘要：
I Anti-self-dual Yang-Mills (ASDYM) equations are extremely important equations in the intersection of quantum field theory (QFT), geometry and integrable systems. In particular, instantons, special solutions of them have played crucial roles in revealing nonperturbative aspects of QFT and have given a new insight into the study of the four-dimensional geometry [Donaldson]. Furthermore, it is well known as the Ward conjecture that the ASDYM equations can be reduced to many classical integrable systems, such as the KdV eq. and Toda eq. [Ward, Mason-Woodhouse,...]. Therefore integrability aspects of ASDYM eqs. are worth investigating to make a unified formulation of integrable systems in diverse dimensions. In this talk, we review the basics of the ASDYM eqs. from the viewpoint of integrable systems, and construct exact solutions by using some techniques among Bäcklund transformations, Darboux transformations, Penrose-Ward transformations, and ADHM constructions etc.
