Previous Conferences & Workshops

TBA

In this talk I will discuss various connections between the dynamics of integrable Hamiltonian flows, gradient flows, and combinatorial geometry. A key system is the Toda lattice  which describes the dynamics of interacting particles on the line. I...

Consider a closed surface M of genus greater than or equal to 2. For negatively curved metrics on M and their corresponding geodesic flow, we can study the topological entropy, the Liouville entropy, and the mean root curvature. In 2004, Manning...

TBD

Let $M(n,m)$ denote the real $m\times n$ matrices. A continuous function $f\colon M(n,m)\to \R$ is called {\it Morrey quasi-convex} if  $$\int_{\R^n}(f(A+\nabla\vf(x))-f(A))\,dx\ge 0$$ for each smooth, compactly supported $\vf\colon\R^n\to\R^m$ and...

The notion of singular support has its origin in the theory of partial differential equations, and was introduced to the world of constructible sheaves by M. Kashiwara and P. Schapira in the 1970s. It is a basic invariant (like the support), and...

In 1962, Yudovich established the well-posedness of the two-dimensional incompressible Euler equations for solutions with bounded vorticity. However, uniqueness within the broader class of solutions with L^p vorticity remains a key unresolved...

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new strings...

Large sieve inequalities are a fundamental tool used to investigate prime numbers and exponential sums. In this lecture I will explain my work that resolves a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann hypothesis)...