# Mathematics Colloquium

#### Conformal Metrics of Prescribed Gauss Curvature

Speaker: Michael Struwe, ETH Zurich

Location: Warren Weaver Hall 1302

Date: Monday, October 8, 2012, 3:45 p.m.

Synopsis:

Given a Riemann surface $$\left ( M,g_0 \right )$$, viewed as a two-dimensional Riemannian manifold with background metric $$g_0$$, a classical problem in differential geometry is to determine what smooth functions $$f$$ on $$M$$ arise as the Gauss curvature of a conformal metric on $$M$$. When $$M = S^2$$ this is the famous Nirenberg problem. In fact, even when $$\left ( M,g_0 \right )$$ is closed and has genus greater than 1, this question so far has not been completely settled. In my talk I will present some new results for this problem.