Past Events

Fix a set V of finitely many points and consider those triangles whose vertices are in V. Consider a geometric space X constructed by taking the union of some of these triangles. How many triangles can X have if no subset of these triangles triangulates a sphere? This question (which…

Abstract: We will introduce the Ising model on a finite lattice and discuss the infinite volume thermodynamic limit. We will prove that the pressure (a.k.a. free energy) converges, and describe the magnetization in the limit in terms of differentiability of the pressure. This will lead us…

We present a proof of the Gromov non-squeezing theorem following the scheme of Gromov’s original proof, with a more modern perspective on some of the techniques involved.

Originating in the study of the Lebesgue and Lorentz spaces, interpolation theory has evolved into a powerful tool with applications through analysis and PDE. In this talk, we will provide a brief introduction to interpolation theory through the theorems of Marcinkiewicz and Riesz-Thorin and…

Fourier analysis is an important tool in additive combinatorics, famously used by Roth to find 3-term arithmetic progressions in dense subsets of the integers. One of the key properties used in his proof is that a Fourier-uniform set A consisting…

Weitzenböck Formula; analytic properties of Dirac operators; functional calculus

We use the free-fermionic six-vertex model to define the double factorial (supersymmetric) Schur functions which generalize the Schur functions, the factorial Schur functions, the double Schur functions, the supersymmetric Schur functions, the factorial supersymmetric…

We show that there exists a quantity, depending only on $C^0$ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$ sense…

Diffusion of new products is a classical problem in Marketing, where it has been extensively studied using compartmental Bass models. These compartmental models implicitly assume that all individuals are homogeneous and connected to each other. To relax these assumptions, one can go back to the…