2020
May
27

# Analysis

- 2020 May 20
- 2020 May 06
- 2020 Apr 22
- 2020 Apr 01
- 2020 Mar 25
- 2020 Mar 18
# Analysis Seminar: Cancelled

12:00pm to 1:00pm## Location:

Ross 70Abstract:Weprove eigenfunction and quasimode estimates on compact Riemannian manifolds for Schr\”odingeroperators, $H_V=-\Delta_g+V$ involving critically singular potentials $V$ which weassume tobe in $L^{n/2}$ and/or the Kato class ${\mathcal K}$. Our proof is basedon modifying the oscillatory integral/resolvent approachthat was used to study the case where $V \equiv 0$ using recently developedtechniques by many authorsto study variable coefficient analogs of the uniform Sobolev estimates ofKenig, Ruiz and the speaker.

- 2020 Jan 15
# Dvoretzky Lectures: Mean Field Limits for Coulomb Dynamics

## Lecturer:

Sylvia Serfaty12:00pm to 2:00pm## Location:

Ross 70We consider a system of N points evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We show a convergence result as N tends to infinity to the expected limiting evolution equation. This was previously an open question in general dimension, rendered difficult by the singular nature of the interaction. We will also discuss briefly similar results in the context of models of superfluidity and superconductivity. - 2020 Jan 15
# Analysis Seminar Dvoretsky Lecture: Sylvia Serfaty (NYU Courant) - Mean Field Limits for Coulomb Dynamics

12:00pm to 1:00pm## Location:

Ross 70We consider a system of N points evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We show a convergence result as N tends to infinity to the expected limiting evolution equation. This was previously an open question in general dimension, rendered difficult by the singular nature of the interaction. We will also discuss briefly similar results in the context of models of superfluidity and superconductivity. - 2020 Jan 08
# Special Analysis Seminar: Andrew Ahn (MIT) "Largest Singular Values of Products of \beta-Ensembles"

2:00pm to 3:00pm## Location:

221BTitle:Largest Singular Values of Products of \beta-Ensembles