Abstract: In this talk, first, I will introduce general inverse $\sigma_k$ equations in Kähler geometry. Some classical examples are the complex Monge–Ampère equation, the J-equation, the complex Hessian equation, and the deformed Hermitian–Yang–Mills equation. Second, by introducing some new real algebraic geometry techniques, we can consider more complicated general inverse $\sigma_k$ equations. Last, analytically, we study the solvability of these complicated general inverse $\sigma_k$ equations.

Brief biography: Chao-Ming Lin is currently a Zassenhaus Assistant Professor at the Ohio State University under the mentorship of Bo Guan. He obtained his Ph.D. at University of California-Irvine in 2023 under the supervision of Zhiqin Lu and Xiangwen Zhang. His research focuses on differential geometry, geometric analysis, and real algebraic geometry.

Zoom: https://us02web.zoom.us/j/89270398293?pwd=UnhVbWZSbHdCd255RE9PcitERFFXZz09