Math Colloquium Series-Convexity at infinity and the Plateau problem in asymptotically locally hyperbolic manifolds.

There exists a long history of leveraging convexity at infinity to solve the asymptotic Plateau problem: finding area minimizing surfaces with prescribed boundary at infinity. In this talk, we discuss the connection between negative curvature and convexity, and explicate a construction of globally convex sets in asymptotically locally hyperbolic manifolds, a class of manifolds which arise in general relativity and AdS/CFT.