Thursday, October 10, 2013, at 4 p.m. at MSB 203

Title: From Pythagoras to Einstein:  Geometry and the Large-Scale Structure of the Universe

Thursday, October 24, 2013 at 4 p.m. at PBP131

Title: A Minkowski Inequality and a Penrose Inequality

Abstract: The Minkowski inequality is a classical inequality in differential geometry. The Penrose inequality is an inequality in general relativity, as a natural consequence of Cosmic Censorship. In my talk, I shall explain how these inequalities are intimately related, and how insights from different perspectives lead to discovering universality of surface geometry.

Thursday, October 17, 2013 at 4 p.m. at BPB 131

Title: Ancient Solutions to Geometric Flows

Abstract: We will discuss ancient solutions  to non-linear parabolic equations, such as the semi-linear heat equation, the Ricci flow on surfaces, the Yamabe flow and the mean curvature flow.  We will address the problem of classification of ancient  solutions,  the existence and classification of solitons as well as the construction  or other ancient non-soliton solutions.

Thursday, November 7, 2013 at 4 p.m. at MSB 203

Title: Sobolev Spaces, Lipschitz Homotopy Groups and Sub-Riemannian Manifolds

Thursday, November 14, 2013 at 4 p.m. at MSB 203

Title: Canonical Metrics on Algebraic Varieties

Abstract: The Uniformization Theorem says that every compact Riemann surface has a metric with constant curvature. The generalization to higher dimensional smooth projective manifolds is still not known (even conjecturally). I will discuss some recent advances due to Donaldson, Chen, Sun, Tian, as well as some applications to the theory of solitons.