Abstract: Motivated by the classical hyperbolic polynomials and Caffarelli–Nirenberg–Spruck theory, we introduce Gårding and ideal Gårding polynomials to capture the ellipticity and convexity features that appear in fully nonlinear PDEs. I will discuss some interesting properties and their connections to real stable and  Lorentzian polynomials.  Applications in fully nonlinear PDEs and combinatorics will be discussed, including a new Liouville type Theorem, Rayleigh inequalities and log-concavity for matroids and graphs. This talk is based on joint works with Hao Fang and Jinyang Wu.

Bio: Biao Ma is currently an Assistant Professor at East China Normal University. He received his Ph.D. from the University of Iowa in 2022 and was a Postdoctoral Fellow at the Beijing International Center for Mathematical Research (BICMR) from 2022 to 2025. His research focuses on geometric analysis.

Zoom: link       Meeting ID:834 6727 7014      Password:440423