Monday, June 3, 2024 - 11:00 in V2-210/216
Statistical mechanics of the focusing nonlinear Schrödinger equation
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Leonardo Tolomeo from University of Edinburgh
| Abstract: |
In this talk, we discuss a number of results related to (non-)construction of the Gibbs measures
for focusing nonlinear Schrödinger equations.
The program was initiated by Lebowitz-Rose-Speer (1988), who built the focusing Φp measure
in dimension 1 by introducing a suitable mass cutoff. A number of open questions were raised
in this work, namely the existence of certain phase transitions and if the construction can
be repeated in higher dimension.
In this talk, we show the solution to most of those questions. After surveying various results,
we will discuss the general strategy for tackling these problems, and the main techniques
developed to find the answer.
This talk is based on joint works with T. Oh (Edinburgh), M. Okamoto (Osaka), H. Weber
(Münster) and J. Forlano (Edinburgh).
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