Talk #1 (9:30am-10:45am): Catalina Quincosis Martínez, Department of Pure Mathematics, University of Waterloo
Title: One way to tell a simple polytope from its graph
Abstract: The Perles conjecture is a question about reconstruction and representation of convex polytopes. In this talk, we will focus on the result for simple polytopes, presenting a short and algorithmic proof due to Gil Kalai. The reconstruction of a simple polytope from its graph was first done by Blind and Mani, and recent work has been aimed at finding a polynomial-time algorithm to accomplish it.
Talk #2 (11:00am-12:15pm): Paul Mcauley, Department of Pure Mathematics, University of Waterloo
Title: Lifting the Metric into the Tangent Space
Abstract: For a Riemannian manifold (M,g), we will look at splitting the tangent space of TM into two parts, the vertical space and the horizontal space. We will then look at a metric on TM induced by g which makes the vertical and horizontal spaces orthogonal. We will also investigate the Levi-Civita connection of this metric.