## Colloquium

To receive schedule updates by email, contact the Colloquium Chair, Prof. Marius Beceanu.

The colloquium usually meets on Friday at 3:00 pm in room ES-143.

The colloquium is partially supported from the Simons grant #584738 (Cristian Lenart)

Sun-Yung Alice Chang (Princeton University)

On a fourth-order PDE and applications to problems in conformal geometry

Friday, September 14, 2018

3:00 p.m. in LC 25

Abstract: In this talk, I will report the study of a 4-th order linear operator P_4 with leading symbol the bi-Laplace operator discovered by Paneitz in 1983. It turns out P_4 is a special case of the general class of GJMS operators with "conformal invariant" properties. I will report some recent progress on the study of P_4 and its associated curvature Q_4 on general n-dimensional manifolds with emphasis on the case when n = 4. I will also discuss some matching 3-order boundary operator of P_4 on manifolds with boundary and some geometric applications.

Justin Curry (University at Albany)

"How Many Directions Determine a Shape?" and other Tales of Topological Transforms

Friday, October 12, 2018

3:00 p.m. in ES-143

Abstract: Given a nice subset X of Euclidean space a theorem of Schapira says that knowing the Euler characteristic of every hyperplane slice of X uniquely determines the embedding of X. However, one can ask to what extent knowing the topology of finitely many slices of X suffices to determine X. In this talk I will present joint work with Sayan Mukherjee (Duke) and Katharine Turner (ANU) that provides the first finite bound for embedded simplicial complexes with lower bounds on curvature. See arxiv:1805.09782 for a pre-print. I will also consider the non-injectivity of these topological transforms when only one direction is given and provide a partial characterization of the fiber of the persistence map.

Benoit Pausader (Brown University)

Global stability for the Einstein-Klein-Gordon equation

Friday, October 26, 2018

3:00 p.m. in ES-143

Abstract: We consider small perturbations of the Minkowski space for the Einstein-Klein-Gordon equation with initial data with slow decay and show some form of modified scattering. This reduces to a small data/Global existence for a coupled system of quasilinear wave and Klein-Gordon equations. The nonlinear stability was studied earlier by Q.Wang and Lefloch-Ma, but the case of slowly decaying data leads to some additional complications.

This is joint work with A. Ionescu.

Hyun Kwon (University at Albany)

The corona problem and related questions

Friday, November 2, 2018

3:00 p.m. in ES-143

Abstract: The corona problem has been posed by Kakutani in 1941 and was later proved by Carleson in 1962. While Carleson's original proof is quite elegant, the machinery involved is quite complicated. To solve various versions of the corona problem, people have been using the technique first introduced by Hormander and popularized by Wolff. It will be shown how this technique can be applied to solve other problems such as determining when two Cowen-Douglas operators are similar and getting a degree bound for the polynomials that show up as a result of Hilbert's Nullstellensatz. The talk is based on a series of papers with R. G. Douglas, K. Ji, A. Netyanun, J. Sarkar, S. Treil, and T. T. Trent.

Kristin Bennett (Rensselaer Polytechnic Institute)

TBA

Friday, November 16, 2018

3:00 p.m. in ES-143

John Meier (Lafayette College)

TBA

Friday, January 25, 2019

3:00 p.m. in ES-143

Leonardo Mihalcea (Virginia Tech)

TBA

Friday, February 8, 2019

3:00 p.m. in ES-143

**Maheshwari Colloquium:** Ken Ono (Emory University)

TBD

Friday, April 12, 2019