Math Candidate Lecture: Hyperbolicity in Cube complexes: an Introduction to CAT(0) Geometry, Dr. Rose Morris-Wright

Rose Morris-Wright (University of California at Los Angeles)

Hyperbolicity in Cube complexes: an Introduction to CAT(0) Geometry

Abstract: The study of hyperbolic surfaces is a fascinating and counterintuitive contrast to classical Euclidean geometry, and provides many powerful tools and theorems with applications in a broad range of mathematics and physics. Yet classical hyperbolic geometry relies heavily on ideas from calculus and thus can these tools can only be applied to surfaces and other spaces where calculus is well defined. In this talk, I will introduce CAT(0) geometry. This is a way of extending many of most powerful results from hyperbolic geometry to spaces where calculus is not possible. CAT(0) cube complexes are one powerful example of such spaces that can be constructed using ideas from combinatorics and graph theory. These spaces have applications in many fields, from group theory to robotics. I will focus on how the properties of CAT(0) spaces imitate those of hyperbolic surfaces. No background in hyperbolic geometry is assumed.