报告题目 (Title)：Integrable Systems in Noncommutative Spaces （非交换空间中的可积系统）

报告人 (Speaker)：Masashi Hamanaka 教授（名古屋大学）

报告时间 (Time)：2024年1月8日 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：理学院数学系

报告摘要：

Integrable systems and soliton theories in noncommutative (NC) spaces have been discussed intensively for the last twenty years. There are three merits to extend to the noncommutative spaces. The first one is that singularities could be resolved in general and as the result, new physical objects appear, such as U(1) instantons. The second one is that gauge theories (e.g. Yang-Mills theory) in noncommutative spaces are equivalent to gauge theories in the background of magnetic fields (B-fields). By considering NC Ward conjecture, NC integrable systems also belong to gauge theories and have physical meanings. The third one is that NC formulations lead to easier descriptions than commutative ones. This is due to resolutions of singularity in some cases, and in other cases to the fact that quasideterminant formulations make any proofs much simpler than commutative ones. This would suggest that quasideterminants might be more essential to formulate integrable systems.

In this talk, we would make an introductory discussion on soliton solutions, conservation laws, soliton scatterings etc. in noncommutative spaces, focusing on NC KdV, KP and ASDYM equations, in order to understand the merits of NC theories.