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.

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.

Title: Optimal growth of frequently oscillating subharmonic functions.

Abstract: In this talk I will present Nevanlinna-type tight bounds on the minimal possible growth of subharmonic functions with a large zero set.  We use a technique inspired by a paper of Jones and Makarov.

Title: On the spacing of zeros of paraorthogonal polynomials for singular measures
Abstract:

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.

Title:
Limit theorems of optimal transportation and teleportation
Abstract:
I’ll review the fundamental definitions in optimal transport theory and discuss limit theorems along with applications to regularity of flows and, if time permit, a novel application to optimal networks,

Title: The Wiener spectrum and Taylor series with pseudo-random coefficients.
Abstract:

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

Title: On the matrix range of random matrices

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).