## Colloquium

To receive schedule updates by email, contact the Colloquium Chair, Prof. Marius Beceanu.

The colloquium usually meets on Friday at 3:00 pm in room ES-143.

The colloquium is partially supported from the Simons grant #584738 (Cristian Lenart)

John Meier (Lafayette College)

Topology at Infinity and Robots on Graphs

Friday, January 25, 2019

3:00 p.m. in ES-143

Abstract: The topology at infinity for an infinite, locally finite cell complex is the topology that persists in the complement of any finite subcomplex. For example, a graph is connected at infinity (more commonly called one-ended) if there is a single connected, unbounded component in the complement of any finite subgraph. We will focus on the properties of being connected at infinity and simply connected at infinity, in the context of infinite groups. The primary examples will come from braid groups on graphs, also thought of as robot motion planning where the robots move on fixed tracks.

Leonardo Mihalcea (Virginia Tech)

TBA

Friday, February 8, 2019

3:00 p.m. in ES-143

Michael Lesnick (University at Albany)

Quantifying Genetic Innovation: Mathematical Foundations for the Topological Study of Reticulate Evolution

Friday, February 22, 2019

3:00 p.m. in ES-143

Matthew Zaremsky (University at Albany)

Discrete Morse theory on Vietoris-Rips complexes

Friday, March 29, 2019

3:00 p.m. in ES-143

Abstract: Discrete Morse theory is a powerful tool for leveraging "local" topological information about a cell complex to make "global" topological conclusions. One incarnation is Forman's discrete Morse theory, which is popular in topological data analysis (TDA). Another is Bestvina-Brady discrete Morse theory, which has proven to be a fundamental tool in geometric group theory (GGT). In this talk I will discuss a new generalization that encompasses both, and explain how one can view Forman's theory as a special case of Bestvina-Brady's. I will also discuss some applications, both to TDA and to GGT, involving Vietoris-Rips complexes of metric spaces.

**Maheshwari Colloquium:** Ken Ono (Emory University)

TBD

Friday, April 12, 2019