Difference between revisions of "Analysis Seminar"

Analysis Seminar Current Semester

The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.

Analysis Seminar Schedule Spring 2017

date speaker title host(s)
January 17, Math Department Colloquium Fabio Pusateri (Princeton) The Water Waves Problem Angenent
January 24, Joint Analysis/Geometry Seminar Tamás Darvas (Maryland) Existence of constant scalar curvature Kähler metrics and properness of the K-energy Viaclovsky
Monday, January 30, 3:30, VV901 (PDE Seminar) Serguei Denissov (UW Madison) Instability in 2D Euler equation of incompressible inviscid fluid
February 7 Andreas Seeger (UW Madison) The Haar system in Sobolev spaces
February 21 Jongchon Kim (UW Madison) Some remarks on Fourier restriction estimates|
March 7, Mathematics Department Distinguished Lecture Roger Temam (Indiana) TBA Smith
Wednesday, March 8, Joint Applied Math/PDE/Analysis Seminar Roger Temam (Indiana) TBA Smith
March 14 Xianghong Chen (UW Milwaukee) Restricting the Fourier transform to some oscillating curves Seeger
March 21 SPRING BREAK

March 27 (joint PDE/Analysis seminar), 3:30, VV901 Sylvia Serfaty (Courant) TBA Tran
March 28 Brian Cook (Fields Institute) TBA Seeger
April 4 Francesco Di Plinio (Virginia) TBA Seeger

Abstracts

Fabio Pusateri (Princeton)

The Water Waves problem

We will begin by introducing the free boundary Euler equations which are a system of nonlinear PDEs modeling the motion of fluids, such as waves on the surface of the ocean. We will discuss several works done on this system in recent years, and how they fit into the broader context of the study of nonlinear evolution problems. We will then focus on the question of global regularity for water waves, present some of our main results - obtained in collaboration with Ionescu and Deng-Ionescu-Pausader - and sketch some of the main ideas.

Tamás Darvas (Maryland)

Existence of constant scalar curvature Kähler metrics and properness of the K-energy

Given a compact Kähler manifold $(X,\omega)$, we show that if there exists a constant scalar curvature Kähler metric  cohomologous to $\omega$ then Mabuchi's K-energy is J-proper in an appropriate sense, confirming a conjecture of Tian from the nineties. The proof involves a careful study of weak minimizers of the K-energy, and involves a surprising amount of analysis. This is joint work with Robert Berman and Chinh H. Lu.