Federico Ardila (SFSU)
Title: The combinatorics of CAT(0) cubical complexes and robotic motion planning

Abstract:
A cubical complex is "CAT(0)" if it has non-positive curvature. These objects play an important role in pure mathematics (group theory) and in applications (phylogenetics, robot motion planning, etc.). In particular, as Abrams and Ghrist observed, when one studies the possible states of a discrete robot, one often finds that they naturally form a CAT(0) cube complex. 

Gromov gave a remarkable topological/combinatorial characterization of CAT(0) cube complexes. We give an alternative, purely combinatorial description of them, allowing a number of applications. In particular, for many robots, we can use these tools to find the fastest way to move from one position to another one.

The talk will describe joint work with Tia Baker, Megan Owen, Seth Sullivant, and Rika Yatchak. It will require no previous knowledge of the subject.