Mirror of submanifolds and special holonomy
数学专题报告
报告题目(Title)：Mirror of submanifolds and special holonomy
报告人(Speaker)：Kotaro Kawai 研究员 (BIMSA)
地点(Place)：后主楼1220
时间(Time)：9月15日下午16:00 - 17:00
邀请人(Inviter)：彦文娇
报告摘要
The Strominger-Yau-Zaslow conjecture suggests that it will be important to consider the special Lagrangian torus fibration for the study of mirror symmetry. I will first introduce the real Fourier-Mukai transform, which gives the explicit ``mirror" correspondence on the trivial torus fibration. By this method, we can define notions for Hermitian connections on a Hermitian line bundle arising from submanifolds, such as the "mirror" volume. I will also explain that the "mirror" of a calibrated submanifold in a $G_2$-manifold is also defined, and it indeed has similar properties to a calibrated submanifold (and a $G_2$-instanton). I will state some recent results and problems about minimal connections, which are ciritical points of the "mirror" volume. A part of this talk is based on the joint work with Hikaru Yamamoto.
