# Geometric Analysis Seminar

The geometric analysis seminar is held on Tuesdays at 11am in 210 Deady Hall.

### Fall Quarter, 2017

- October 10,
**Nikolai Saveliev** (University of Miami)

Index theory on manifolds with periodic ends
**Abstract**: We extend the Atiyah, Patodi, and Singer index theorem for Dirac operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. The index is expressed in terms of a new periodic eta-invariant that equals the classical eta-invariant in the cylindrical setting. We use this theorem to study Riemannian metrics of positive scalar curvature on some even-dimensional manifolfds, as well as the Seiberg-Witten invariants of 4-manifolds with integral homology of S^1×S^3. This is a joint work with Jianfeng Lin, Tom Mrowka, and Daniel Ruberman.

- October 17,
**Micah Warren** (UO)

Continuum Nash Bargaining Solutions
**Abstract**: Nash`s classical bargaining solution suggests that n players should maximize a product of utility functions. We consider a special case: Suppose that the players are chosen from a continuum, distribution μμ and suppose they are to divide up a resource νν that is also on a continuum, whose utility to each player is the inverse of exponential of a cost function. The maximization problem becomes an optimal type transport problem, where the target density is the minimizer to the functional F(β)=Hν(β)+W2(μ,β) where H is the entropy and W is the Wasserstein distance. One may recognize this problem from a single time step in the Jordan-Kinderlehrer-Otto scheme. Thanks to optimal transport theory, the solution may be described as by a potential that solves a fourth order nonlinear elliptic PDE.

- October 24,
**Peng Lu** (UO)

New proofs of Perelman`s theorem on shrinking Breathers in Ricci flow
- October 31,
**Shaosai Huang** (Stony Brook)
- November 7,
**Peter Gilkey** (UO)
- November 14,
**Jim Isenberg** (UO)
- November 17,
**Richard Bamler**
- November 28,
**Christine Escher**

**Previous Schedule:** 2016 Fall – 2017 Spring, 2015 Fall – 2016 Spring, 2015 Spring, 2015 Winter, 2014 Fall, 2014 Spring, 2014 Winter, 2012 Winter, 2011 Fall, 2010 Spring, 2010 Winter