Lorentzian, Affine, and Hyperbolic Differential Geometry - in Memory of Todd Drumm

April 7, 2025 - April 9, 2025


Caleb Ashley
Boston College
Charles Frances
University of Strasbourg
William Goldman
University of Maryland
Jill McGowan
Howard University
Karin Melnick
University of Luxembourg

This workshop is devoted to the mathematical legacy of Todd Drumm. The primary topics are affine manifolds, constant-curvature Lorentzian geometry, and links with hyperbolic geometry, as well as the geometry of the bidisk.

Since Margulis' discovery in 1983 of properly discontinuous, affine actions of nonabelian free groups on 3-dimensional Minkowski space, the corresponding Margulis space-times were the focus of robust research activity in affine and Lorentzian differential geometry. This activity includes Drumm's construction of fundamental domains bounded by crooked planes; the characterization of proper actions via the continuous Margulis invariant of Goldman, Labourie, and Margulis; and the tameness of Margulis space-times proved by Choi, Danciger, Guéritaud, and Kassel. From the same era that gave rise to Margulis space-times, famous conjectures in affine geometry such as the Auslander Conjecture have seen substantial but limited progress and remain very much open.

Closely related to affine geometry and hyperbolic geometry are constant-curvature Lorentzian structures, convex projective stuctures, and others. The workshop will bring together leading experts in these areas to build on past achievements and discuss current developments and future challenges. Todd Drumm received his Ph.D. from the University of Maryland in 1990. He was a professor at Howard University from 2008 until his sudden passing in March 2020.