Existence and uniqueness of Green's function to a nonlinear Yamabe problem

Yanyan Li
Rutgers University
March 6, 2019

Abstract: For a given finite subset S of a compact Riemannian manifold (M; g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and
sufficient condition for the existence and uniqueness of a conformal metric on $M \setminus S$ such that each point of S corresponds to an asymptotically flat end and
that the Schouten tensor of the new conformal metric belongs to the boundary of the given cone.  This is a joint work with Luc Nguyen.

Normalized harmonic map flow

Michael Struwe
ETH Zürich
March 6, 2019

Abstract: Finding non-constant harmonic 3-spheres for a closed target manifold N is a prototype of a super-critical variational problem. In fact, the 
direct method fails, as the infimum of the Dirichlet energy in any homotopy class of maps from the 3-sphere to any closed N is zero; moreover, the 
harmonic map heat flow may blow up in finite time, and even the identity map from the 3-sphere to itself is not stable under this flow. 

Spacetime positive mass theorem

Lan-Hsuan Huang
University of Connecticut; von Neumann Fellow, School of Mathematics
March 5, 2019

Abstract: The spacetime positive mass theorem says that an asymptotically flat initial data set with the dominant energy condition must have a timelike energy-momentum vector, unless the initial data set is in the Minkowski spacetime. We will review backgrounds and recent progress toward this statement.