Department of Mathematical Sciences
Antonio J. Torres, Smith College
Thursday, March 5th, 2026
12:00PM-12:50PM
Ollin Hall 218
Speaker: Antonio J. Torres, Smith College
Title: From Tverberg’s Theorem to Nerve Complexes and Graphs
Abstract: Tverberg’s theorem is a fundamental result in discrete geometry that describes when a point set can be partitioned into subsets whose convex hulls share a common intersection. In this talk, we study, in a general setting, the intersection patterns arising from partitions of point sets through the language of nerves, which combinatorially encode the intersection structure of their convex hulls.
We discuss the realizability problem for these nerves, namely, which simplicial complexes can appear as nerves and under what conditions. We also introduce Tverberg partition graphs and, more generally, graphs naturally associated with arbitrary simplicial complexes.
Finally, we present several structural properties of these objects.