TBA

Speaker: 

Le Hai Khoi

Institution: 

Nanyang Technological University, Singapore

Time: 

Friday, February 15, 2019 - 3:00pm to 3:50pm

Host: 

Location: 

RH440R

This is a joint Nonlinear PDEs seminar with Analysis seminar

Bergman-Einstein metrics on Strongly pseudoconvex domains in a complex space.

Speaker: 

Xiaojun Huang

Institution: 

Rutgers University

Time: 

Friday, November 16, 2018 - 3:00pm to 3:50pm

Host: 

Location: 

RH440R

I will give a proof of S.Y.  Cheng's conjecture  that a bounded strongly pseudoconvex domain in C^n has  its Bergman metric being Einstein if and only if it is holomorphically equivalent to the ball.

Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite-gap tori of the 2D cubic NLS

Speaker: 

Zaher Hani

Institution: 

University of Michigan

Time: 

Tuesday, November 27, 2018 - 3:00pm

Location: 

RH 306

 We consider a family of quasiperiodic solutions of the nonlinear Schrodinger equation on the 2-torus, namely the family of finite-gap solutions (tori). These solutions are inherited by the 2D equation from its completely integrable 1D counterpart (NLS on the circle) by considering solutions that only depend on one variable. Despite being linearly stable, we prove that these tori (under some genericness conditions) are nonlinearly unstable in the following strong sense: there exists solutions that start very close to those tori in certain Sobolev spaces, but eventually become larger than any given factor at later times. This is the first instance where (unstable) long-time nonlinear dynamics near (linearly stable) quasiperiodic tori is studied and constructed. (joint work with M. Guardia (UPC, Barcelona), E. Haus (University of Naples), M. Procesi (Roma Tre), and A. Maspero (SISSA))

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