»ã±¨±êÌâ (Title)£ºIntegrable Systems in Noncommutative Spaces £¨·Ç»¥»»¿Õ¼äÖеĿɻýϵͳ£©

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

»ã±¨¹¦·ò (Time)£º2024Äê1ÔÂ8ÈÕ 10:30-12:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÕÅÐÛʦ ½ÌÊÚ

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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.