Department of Mathematics, National Tsing Hua University

參考連結
https://sites.google.com/view/sgsnthu/home
 

Abstract:
General inverse $sigma_k$ equations arise in many areas, including PDE, differential geometry, and complex geometry. In this talk, I will begin by introducing general inverse $sigma_k$ equations in Kähler geometry, highlighting classical examples such as the complex Monge–Ampère equation, the J-equation, the complex Hessian equation, and the deformed Hermitian–Yang–Mills equation. Next, by applying new techniques from real algebraic geometry, we are able to consider a more general format of these equations. Finally, from an analytic perspective, we will examine the solvability of these more complicated equations.