Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	胡佳俊，清华大学
Inviter:	刘杰
Title:	Intersection theoretic inequalities via Lorentzian polynomials
Language:	Chinese&English
Time & Venue:	2023.05.27 14:00-15:30 腾讯会议:816-542-609
Abstract:	We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we establish a series of intersection theoretic inequalities, which we call rKT property, with respect to m-positive classes and Schur classes. We also study its convexity variants -- the geometric inequalities for m-convex functions on the sphere and convex bodies. Along the exploration, we prove that any finite subset on the closure of the cone generated by m-positive classes can be endowed with a polymatroid structure by a canonical numerical-dimension type function, extending our previous result for nef classes; and we prove Alexandrov-Fenchel inequalities for valuations of Schur type. We also establish various analogs of sumset estimates (Plunnecke-Ruzsa inequalities) from additive combinatorics in our contexts. This is a joint work with Jian Xiao.