Seminar| Institute of Mathematical Sciences
Time: Friday, March 27th, 2026,14:00-15:00
Location: IMS, RS408
Speaker: Tao Gui, Beijing International Center for Mathematical Research
Abstract: Combinatorial algebraic geometry (and combinatorial Hodge theory) has emerged as a highly active field of research in recent years. The area draws from three seemingly distinct origins: polytopes, Coxeter groups, and matroids. The central philosophy is that even when the actual geometric varieties do not exist, one can still develop a good cohomology theory by imagining their existence and recovering the beautiful properties of classical Hodge theory. In this talk, I will provide a motivated introduction to this field, focusing on the classical interplay between polytopes and (projective) toric varieties. After reviewing Peter McMullen's celebrated g-conjecture (1971), I will present some of our recent results regarding reflection symmetries on polytopes and toric varieties. This talk will be in a colloquium style, and no specialized background is required to appreciate the main ideas.