- Nam Le, Indiana University Bloomington
- Hessian eigenvalues and hyperbolic polynomials
- 09/29/2022
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Olga Turanova (turanova@msu.edu)
Hessian eigenvalues are natural nonlinear analogues of the classical Dirichlet eigenvalues. The Hessian eigenvalues and their corresponding eigenfunctions are expected to share many analytic and geometric properties (such as uniqueness, stability, max-min principle, global smoothness, Brunn-Minkowski inequality, etc) as their Dirichlet counterparts. In this talk, I will discuss these issues and some recent progresses in various geometric settings. The focus will be mostly on the case of the Monge-Ampere eigenfunctions and related degenerate equations. I will also explain the unexpected role of hyperbolic polynomials in our analysis. I will not assume any familiarity with these concepts.
