Speaker: Ramesh Mete（Indian Institute of Science）

Time: 10:00-11:00 a.m., May 29, 2024, GMT+8

Venue: Online: Zoom: 878 6963 6072    Password: 665065

Abstract: 

The dHYM equation is a special type of complex Hessian equations which has connection to mirror symmetry in string theory. Recently, in the smooth setting it is shown that there exists a smooth solution of the “super-critical” dHYM equation on compact K\”ahler manifolds if and only if certain Nakai-Moishezon type criterion holds. In this talk, we will focus when the NM-type criterion fails – which is the so-called “unstable” case. We will show the existence and uniqueness of solutions of the “weak” dHYM equation, where the wedge product is replaced by the non-pluripolar product. We will also discuss the convergence of the (dHYM) cotangent flow in the unstable case. Based on a joint work with Prof. Ved Datar (IISc, Bengaluru) and Prof. Jian Song (Rutgers University).

Source: School of Mathematical Sciences, PKU