The relationship between Betti tables and clique sums on graphs

Student Algebraic Geometry Seminar
Friday, October 27, 2017 - 10:00
1 hour (actually 50 minutes)
Skiles 114
GA Tech
For any undirected graph, the Stanley-Reisner ideal is generated by monomials correspoding to the graph's "non-edges." It is of interest in algebraic geometry to study the free resolutions and Betti-tables of these ideals (viewed as modules in the natural way.) We consider the relationship between a graph and its induced Betti-table. As a first step, we look at how operations on graphs effect on the Betti-tables. In this talk, I will provide a basic introduction, state our result about clique sums of graphs (with proof), and discuss the next things to do.