Members Seminar

In this talk, I will give two vignettes on the theme of sparse matrices in sparse analysis. The first vignette covers work from compressive sensing in which we want to design sparse matrices (i.e., matrices with few non-zero entries) that we use to...

Symplectic capacities are measurements of symplectic size. They are often defined as the lengths of certain periodic trajectories of dynamical systems, and so they connect symplectic embedding problems with dynamics. I will explain joint work...

A fundamental task in (unsupervised) analysis of data is to detect and estimate interesting "structure" hidden in it. In low dimensions, this task has been explored for over 100 years with dozens of developed methods. In this talk I'll focus on...

Schur polynomials are the characters of finite-dimensional irreducible representations of the general linear group. We will discuss both continuous and discrete concavity property of Schur polynomials. There will be one theorem and eight conjectures...

Deligne's "Weil II" paper includes a far-reaching conjecture to the effect that for a smooth variety on a finite field of characteristic p, for any prime l distinct from p, l-adic representations of the etale fundamental group do not occur in...

Invariant theory is a fundamental subject in mathematics, and is potentially applicable whenever there is symmetry at hand (group actions). In recent years, new problems and conjectures inspired by complexity have come to light. In this talk, I will...

In the early 1930's, the Ergodic theorems of von Neumann and Birkhoff put Boltzmann's Ergodic Hypothesis in mathematical terms, and the natural question was born: is ergodicity the "general case" among conservative dynamical systems? Oxtoby and Ulam...

The goal is to describe how techniques from symplectic dynamics can be used to study orbit travel in three dimensions, for systems like the restricted 3-body problem from celestial mechanics. The pseudo-holomorphic curve theory initiated by Hofer...

I will discuss some geometric inequalities that hold on Riemannian 2-disks and 2-spheres.

For example, I will prove that on any Riemannian 2-sphere there M exist at least three simple periodic geodesics of length at most 20d, where d is the diameter...

Positive geometries are real semialgebraic sets inside complex varieties characterized by the existence of a meromorphic top-form called the canonical form. The defining property of positive geometries and their canonical forms is that the residue...