Analysis

The Analysis seminar meets on Wednesdays at 12:00 in room 70 of the Ross Building.
2019 Dec 18

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

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

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
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.
2020 Jan 01

Analysis Seminar: Cyril Tintarev (Uppsala, visiting Technion) "Weak convergence methods: Cocompactness and structured defect of compactness" )

12:00pm to 1:00pm

Location: 

Ross 70
Profile decomposition theorem is a refinement of the Banach-Alaoglu (weak compactness) theorem in presence of a given set of quasi-isometries. We define a class of co-compact embeddings of Banach spaces that yields a clear structure for bounded divergent sequences. This is a generalization, on the functional-analytic level, of the concentration compactness principle of Lions. Applications include Sobolev, Jawerts  Strichartz and Moser-Trudinger embeddings.
2019 Dec 18

Analysis Seminar: Moshe Goldberg (Technion) "Extending the Spectral Radius to Finite-Dimensional Power-Associative Algebras"

12:00pm to 1:00pm

Location: 

Ross 70

Title: Extending the Spectral Radius to Finite-Dimensional Power-Associative Algebras
Abstract: The purpose of this talk is to introduce a new concept, the \textit{radius} of elements in arbitrary finite-dimensional power-associative algebras over the field of real or complex numbers. It is an extension of the well known notion of the spectral radius.
As examples, we shall discuss this new radius in the setting of matrix algebras, where it indeed reduces to the spectral radius, and then in the Cayley-Dickson algebras, where it is something quite different.
2019 Nov 20

Analysis Seminar: Genadi Levin "The Cauchy transform that vanishes outside a compact"

12:00pm to 1:00pm

Location: 

Ross 70

Title: The Cauchy transform that vanishes outside a compact.
Abstract: The Cauchy transform of a complex finite compactly supported measure on the plane is its convolution with the Cauchy kernel.
The classical F. and M. Riesz theorem asserts that if the Cauchy transform of a measure $\mu$ on the unit circle
vanishes off the closed unit disk then $\mu$ is absolutely continuous w.r.t. the arc measure on the unit circle.
Motivated by an application in holomorphic dynamics we present a certain generalization of this Riesz theorem
2019 Dec 11

Analysis Seminar: Matania Ben-Artzi (HUJI) "Spline functions, the biharmonic operator and approximate eigenvalues"

12:00pm to 1:00pm

Location: 

Ross 70
Title: Spline functions, the biharmonic operator and approximate
eigenvalues.
Abstract: The biharmonic operator plays a central role in a wide array of physical models, such as elasticity theory and the streamfunction formulation of the Navier-Stokes equations.In this talk a full discrete elliptic calculus is presented. The primary object of this calculus is a high-order compact discrete biharmonic operator (DBO).

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