# Past Events

We study the distribution of the maximum gap size in one-dimensional hard-core models. First, we sequentially pack rods of length 1 into an interval of length L at random, subject to the hard-core constraint that rods do not overlap. We find that in a saturated packing, with high probability…

We will kick off our reading of Guillemin and Sternberg's monumental set of lecture notes about "Semiclassical Analysis", with a discussion of the textbook's introduction, and some additional motivating examples. Among these will be another "proof" of the Weyl law, as well as a "Weyl law" for…

Abstract

It has long been known how many integers are the sum of two squares, one of which is the square of a prime. However researchershave been frustrated in obtaining a good error term in this seemingly innocuous problem. Recently we discovered the reasons for this difficulty: …

We will show how to differentiate computer programs (lambda-expressions, Turing machines, etc) by encoding them in a new system called linear logic that endows the space of programs/proofs with the structure of a differential k-algebra. We will discuss this theory from the perspective of the…

I will describe some connections between arithmetic geometry of abelian varieties, non-archimedean/tropical geometry, and combinatorics. For a principally polarized abelian variety, we show an identity relating the Faltings height and the Néron--Tate height (of a symmetric effective divisor…

The functional equation of the Estermann function (the additive twist of zeta(s)^2) is morally equivalent to the Voronoi summation formula. This can be used, among other things, to study the correlations of the divisor counting function d(n). Motivated by the divisor correlation problem in the…

The singularity formation problem is a central question in fluid dynamics, and it is still widely open for several fundamental models, including the 3d incompressible Euler equations. In this talk, I will first review the singularity formation problem, describing how particle transport poses the…

Suppose you take a 1 x L strip of paper, twist it around in space, and tape the (short) ends together to make a paper Moebius band. In this talk I'll prove that you must have L > sqrt(3) and also that there is a unique limit that emerges if you have examples with L tending to sqrt(3). B.…

Abstract: Carleson proved in 1966 that the Fourier series of any square integrablefunction converges pointwise to the function, by establishing boundednessof the maximally modulated Hilbert transform from L^2 into weak L^2. Thistalk is about a generalization of his result, where the Hilbert…