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Analysis

The Analysis seminar meets on Wednesdays at 12:00 in room 70 of the Ross Building.
2020 Jun 24

Analysis Seminar: Angkana Rüland (Heidelberg) "Microstructure in Shape-Memory Alloys: Rigidity, Flexibility and Some Numerical Simulations"

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12:00pm to 1:00pm

Location: 

zoom

Title: Microstructure in Shape-Memory Alloys: Rigidity,Flexibility and Some Numerical Simulations

 

Abstract: In this talk I will discuss a striking dichotomy whichoccurs in the mathematical analysis of microstructures in shape-memory alloys:On the one hand, some models for these materials display a very rigid structurewith only very specific microstructures, if one assumes that surface energiesare penalised. On the other hand, without this penalisation, for the samemodels a plethora of very ``wild'' solutions exists.

2020 Jun 03

Analysis Seminar: Victor Ivrii (Toronto) "Complete Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Coefficients Operators and Bethe-Sommerfeld Conjecture in Semiclassical Settings"

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12:00pm to 1:00pm

Location: 

Ross 70
TITLE:

Complete Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Coefficients Operators and Bethe-Sommerfeld Conjecture in Semiclassical Settings

ABSTRACT:
Under certain assumptions, we derive a complete semiclassical asymptotics of aspectral function of the constant coecient scalar operator perturbed by almostperiodic smaller operator. In particular, a com-
plete semiclassical asymptotics of the integrated density of states also holds.
2020 Mar 18

Analysis Seminar: Cancelled

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12:00pm to 1:00pm

Location: 

Ross 70
Abstract:

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.

2019 Dec 18

Special Analysis and Mathematical Physics Seminar: Eliran Subag (Courant) "Spherical spin glass models"

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2:30pm to 3:30pm

Location: 

221B

Title: Spherical spin glass models

  

Abstract: In the 70s, physicists proposed several models fordisordered magnetic alloys called spin glass models. Mathematically, thespherical models are random functions on the sphere in high-dimensions, andmany of the questions physicists are interested in can be phrased aspurely mathematical questions about geometric properties, extreme values,critical points, and Gibbs measures of random functions and the interplaybetween them.

 

2020 Jan 15

Analysis Seminar Dvoretsky Lecture: Sylvia Serfaty (NYU Courant) - Mean Field Limits for Coulomb Dynamics

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12:00pm to 1:00pm

Location: 

Ross 70
We 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

Dvoretzky Lectures: Mean Field Limits for Coulomb Dynamics

Lecturer: 

Sylvia Serfaty
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12:00pm to 2:00pm

Location: 

Ross 70
We 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.

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