Reconstruction of Convex Geometric Shapes and Monge-Ampère Equations
Prof. Gaoyong Zhang, NYU - Courant
Abstract: Can a convex geometric shape be fully reconstructed from its local measurements? This fundamental question drives a number of geometric problems known as Minkowski-type problems. For example, a convex polytope can be recovered from its facet areas and unit normals, and a smooth closed convex hypersurface can be reconstructed from its Gauss curvature.
Solving these shape recovering problems relies on both analytical and geometrical tools. In the smooth setting, they translate into Monge-Ampère-type partial differential equations. When dealing with general, non-smooth shapes, they lead to singular Monge-Ampère and convex geometric measure equations.
This talk will introduce several of the Minkowski-type problems through accessible examples. We will talk about their analytical equations, recent developments, and open problems in the field.
Tea and refreshments available from 3:00-3:25 p.m. in the Assmus Conference Room (CU 212).
