Date: Thursday, December 3, 2020.
Time: 3:30 PM.
Zoom Meeting Link: https://us02web.zoom.us/j/85923312360?pwd=aFk5R2Z1alJ6dEV0UlBHQkV2aU84dz09
Meeting ID: 859 2331 2360
Passcode: 392843
Graph complexes: At the intersection of algebra, topology and combinatorics
Anurag Singh
Chennai Mathematical Institute.
03-12-20

---

Abstract

There are many properties of graphs that are inherited by subsets of vertices and hence give rise to a simplicial complex structure. The study of these simplicial complexes has helped answer many combinatorial questions about graphs. For example, Lovász, in his seminal work, gave a lower bound for the chromatic number in terms of the topological connectivity of the neighborhood complex. Another well-known example is that of the independence complex which captures the combinatorics of independent sets of graphs. The topological study of these complexes has helped answer questions about domination number, independent transversal, etc. The commutative algebra counterpart of this complex is the edge ideal of a graph, an object of independent interest.

In this talk, I will begin with a brief overview of independence complexes and their properties and also explain some of the important results in the literature. The main focus of the talk would be on certain new complexes that generalize independence complexes. With the help of examples, I will describe their structure, homotopy type, and certain applications to graph theory. The talk is based on joint projects with Priyavrat Deshpande and Samir Shukla.