Time  Location  Organizers 

Tuesdays at 11am  Zoom (contact organizers for details)  Ioan Bejenaru and Mohandas Pillai 
Date  Speaker  Title + Abstract 

October 18  Sebastian Herr Bielefeld University 
Global wellposedness of the Zakharov System below the ground state The Zakharov system is a quadratically coupled system of a Schrödinger and a wave equation, which is related to the focussing cubic Schrödinger equation. We consider the associated Cauchy problem in the energycritical dimension d=4 and prove that it is globally wellposed in the full (nonradial) energy space for any initial data with energy and wave mass below the ground state threshold. The result is based on a uniform Strichartz estimate for the Schrödinger equation with potentials solving the wave equation. A key ingredient in the nonradial setting is a bilinear Fourier extension estimate. This is joint work with Timothy Candy and Kenji Nakanishi. 
November 4 4 PM APM 6402 Note the unusual day, time, location 
Dallas Albritton Princeton 
Title and Abstract 
November 15  Kihyun Kim IHES 
Rigidity of longterm dynamics for the selfdual ChernSimonsSchrödinger equation within equivariance We consider the long time dynamics for the selfdual ChernSimonsSchrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the selfduality and nonlocality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy solutions to (CSS) decomposes into at most one(!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finitetime blowup solutions even have a universal blowup speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the selfduality and nonlocality of the problem. 
November 17 34 PM APM 7218 Note the unusual day, time, location 
Jan Slovak Masaryk U 
Nearly invariant calculus for a few CR (and all parabolic) geometries . 
November 29  Manuel Del Pino University of Bath 
DYNAMICS OF CONCENTRATED VORTICITIES IN 2D AND 3D EULER FLOWS A classical problem that traces back to Helmholtz and Kirchhoff is the understanding of the dynamics of solutions to the Euler equations of an inviscid incompressible fluid when the vorticity of the solution is initially concentrated near isolated points in 2d or vortex lines in 3d. We discuss some recent results on these solutions' existence and asymptotic behavior. We describe, with precise asymptotics, interacting vortices, and traveling helices, and extension of these results for the 2d generalized SQG. This is research in collaboration with J. Dávila, A. Fernández, M. Musso, and J. Wei. 
December 6  Benoit Pausader Brown University 

December 6 34 PM APM 5402 Note the unusual time, location 
Nordine Mir Texas A&M University at Qatar 
Finite jet determination of CR maps into realalgebraic sets We present recent results about finite jet determination of CR maps of positive codimension from realanalytic CR manifolds into realalgebraic subsets in complex space, or more generally Nash subsets. One instance of such results is the unique jet determination of germs of CR maps from minimal realanalytic CR submanifolds in $\C^N$ into Nash subsets in $\C^{N'}$ of D'Angelo finite type, for arbitrary $N,N'\geq 2$. This is joint work with B. Lamel. 
Date  Speaker  Title + Abstract 

Date  Speaker  Title + Abstract 
