Past Events
An exact Lagrangian L in a cotangent bundle T*Q is a nearby fibre if it agrees with a cotangent fibre at infinity and it is disjoint from another cotangent fibre. The projection from T*Q to Q induces a map from L/\partial L to Q. We will show that this map is null-homotopic after…
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…
Abstract: The circular law states that the spectral measure of a square matrix with i.i.d. entries of mean zero must converge to the uniform distribution on the unit disk in the complex plane. This result is analogous to the semicircular law for Wigner matrices, but the spectral instability of…
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…