»ã±¨±êÌâ (Title)£ºExact Solutions of Anti-Self-Dual Yang-Mills Equations £¨·´×Ô¶ÔżYang-Mills·½³ÌµÄ¾«È·½â£©

»ã±¨ÈË (Speaker)£ºMasashi Hamanaka ½ÌÊÚ£¨Ãû¹ÅÎÝ´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê12ÔÂ28ÈÕ(ÖÜËÄ) 10:30-12:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÕÅÐÛʦ ½ÌÊÚ

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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 B?cklund transformations, Darboux transformations, Penrose-Ward transformations, and ADHM constructions etc.