Slope Conditions for Some Complex Hessian Equations
Time: 2022-03-25
Published By: Wenqiong Li
Speaker(s): Ved Datar(Indian Institute of Science)
Time: 10:00-11:00 March 30, 2022
Venue: Online
Abstract：
Yau's work on the Calabi conjecture, together with the Nakai-Moizeshon criteria relates existence of smooth solutions of complex Monge-Ampere equations to the positivity of some intersection numbers. I will first review some recent works of many authors, on extending this correspondence to other complex Hessian equations. I will then describe some ongoing work with Ramesh Mete and Jian Song on solvability of these equations if the positivity conditions fail and if one allows the solutions to be singular. I will illustrate our main ideas by focusing on the $J$ equation and the deformed Hermitian-Yang-Mills equations on surfaces.
Speaker:
Ved Datar is currently an assistant professor at the Indian Institute of Science in Bangalore, India. He obtained his Bachelors degree in Mathematics and Computer Science from the Chennai Mathematical Insititute, and completed his PhD from Rutgers University under the guidance of Prof. Jian Song. He was a visiting instructor at University of Notre Dame of the academic year 2014-15, and an RTG postdoc at UC Berkeley from 2015-18. His research interests center around existence and degenerations of canonical Kahler metrics, and the relationship with algebro-geometric or topological obstructions.
Zoom:
Link: https://us02web.zoom.us/j/85320344180?pwd=ODkrbExuOGRhL0F4VXlzejRQeDBidz09
ID: 853 2034 4180
Password: 324494
Yau's work on the Calabi conjecture, together with the Nakai-Moizeshon criteria relates existence of smooth solutions of complex Monge-Ampere equations to the positivity of some intersection numbers. I will first review some recent works of many authors, on extending this correspondence to other complex Hessian equations. I will then describe some ongoing work with Ramesh Mete and Jian Song on solvability of these equations if the positivity conditions fail and if one allows the solutions to be singular. I will illustrate our main ideas by focusing on the $J$ equation and the deformed Hermitian-Yang-Mills equations on surfaces.
Speaker:
Ved Datar is currently an assistant professor at the Indian Institute of Science in Bangalore, India. He obtained his Bachelors degree in Mathematics and Computer Science from the Chennai Mathematical Insititute, and completed his PhD from Rutgers University under the guidance of Prof. Jian Song. He was a visiting instructor at University of Notre Dame of the academic year 2014-15, and an RTG postdoc at UC Berkeley from 2015-18. His research interests center around existence and degenerations of canonical Kahler metrics, and the relationship with algebro-geometric or topological obstructions.
Zoom:
Link: https://us02web.zoom.us/j/85320344180?pwd=ODkrbExuOGRhL0F4VXlzejRQeDBidz09
ID: 853 2034 4180
Password: 324494
