Martin Bridgeman (Mathematics)

Promoted to associate professor with tenure

Ph.D., Princeton University

Faculty member since 1999

Specialization: Hyperbolic geometry; Kleinian groups

Representative publication: “From the boundary of the convex core to the conformal boundary” (Geometra Dedicata, 2003)

“In hyperbolic geometry, a circle of radius 15 feet would have a circumference of about 10 million feet. When people discuss the structure of the universe, they ask, what kind of geometry does the universe have? Locally, it looks Euclidian, which is the geometry you learn in high school, but the problem with trying to understand a vast structure that you’re in, is that you can’t see at large scales. Geometry gives you a structure for wrestling with the notion of what the essence of space is. What does it mean to be three-dimensional, four-dimensional? We can think of space as being little patchworks we see in front of us, but we don’t know what happens very very far away. It might wrap up and be connected, as though you’re gluing the sides to each other. The question is, what kind of spaces are formed by these procedures of gluing-up, and what is it like to live in these spaces? You can think of this in terms of a video game where you go off one side of a square and come back in on the other side, like in Pac-Man or Asteroids. A mathematician would say, you’re playing on the surface of a doughnut.”