Speaker: Kai Fong Ernest Chong, SUTD, Singapore
Title: Stress algebras on simplicial complexes
Abstract:
The g-theorem is a momentous result in topological combinatorics that characterizes the f-vectors of simplicial polytopes. The closely related g-conjecture asserts that the g-theorem can be extended to all simplicial homology spheres. A key breakthrough, due to Kalai, relates the g-conjecture to the notion of stresses on graphs. In this talk, I will introduce the stress algebra, which is defined on arbitrary simplicial complexes, and whose existence solves a fundamental problem on generalized stresses. I will explain the role of the stress algebra in a possible approach for proving the g-conjecture, and I will describe its connections to tropical intersection theory and McMullen's polytope algebra. This is joint work with Tiong Seng Tay.