Informal Geometric Analysis Seminar
Winter 2018
Organizers: G. Liu, V. Tosatti, B. Weinkove, S. Zelditch
The seminar meets on Thursdays from 3.00pm to 4.00pm in
Lunt 107.
Schedule

January 10
Oran Gannot  Black Holes

January 17
Perry Kleinhenz  Energy decay for the damped wave equation with Hölder continuous damping

January 24
Abe Rabinowitz  HermanKluk Semiclassical Approximation

January 31
Sisi Shen  KählerRicci flow on blowups along submanifolds  Reference

February 7
Mitchell Faulk (Columbia)  CalabiYau metrics on asymptotically conical manifolds with prescribed decay rates  Reference  Abstract
Yau's solution to Calabi's conjecture involves solving a complex Monge Ampere equation for a scalarvalued function on the manifold. A paper by Conlon and Hein states that in the case that the manifold is asymptotically conical, there still exist solutions to this equation, but the existence (and uniqueness) depends on the decay rate of the prescribed Ricci form appearing in the equation. In this talk, we discuss these existence results and focus on a small improvement with respect to the decay rate of solutions in the case that the Fredholm index of the Laplacian is the first negative value.

February 21
Eric Zaslow  Dimer models, quantum integrable systems, mirror symmetry, limit shapes and Mahler entropy  Abstract
In this sprawling and probably overambitious talk, I will state one theorem (because I'm supposed to) and then cite difficult work by other people to try demonstrate the interconnectivity of the topics of the title. The theorem is joint with David Treumann and Harold Williams.

February 28
Steve Zelditch  Nodal intersections and geometric control  Abstract
Suppose that a Riemannian surface has an isometric involution across an axis H (fixed point set), e.g. the equator of a sphere. Half of the eigenfunctions are even, half odd under the involution. The odd ones vanish on the axis, which is a union of geodesics. BourgainRudnick asked: is this the only kind of curve on which an infinite sequence of eigenfunctions can vanish? Toth and I posed a related problem: what if the L^{2} norms of the restrictions tend to zero. The main result: the only curves (or hypersurfaces, in higher dimensions) on which a positive proportion of eigenfunctions can vanish is 'very like' an axis of symmetry. The precise condition involves the dynamics of the geodesic flow. I will also explain how the proof combines with a recent result of DyatlovJin on the fractal uncertainty principle and control theory to replace 'positive proportion' by 'infinite sequence'.

March 7
Nick McCleerey  Lower bounds for the Calabi functional  References 1  2

April 4
Jianchun Chu  Stability of solutions of complex MongeAmpère equations  Reference
Schedule for the past years:
201213 
201314 
201415 
201516 
201617 
201718 
Fall 2018