Geometry of spheres with conical singularities

Event time: 
Tuesday, March 3, 2020 - 6:00pm
LOM 206
Yuchen Liu
Speaker affiliation: 
Yale University
Event description: 
The classical Descartes’ theorem states that the total angular defect of a convex polyhedron is 4\pi. Such a polyhedron can be viewed as a flat surface homeomorphic to a sphere with cone singularities at vertices. We will explore the situation in both spherical geometry and hyperbolic geometry, use the Gauss-Bonnet theorem, and culminate the concept of stability.