# Upcoming Events

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

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 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…

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…

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…

Yang--Mills gauge theory with gauge group SU(2) has played a significant role in the study of the topology of 3- and 4-manifolds. However, there is not much known about applications of gauge theory with other gauge groups in the study of low dimensional manifolds. In this talk, I will discuss a…

I will present fast practical algorithms for approximate semidefinite programming (SDP) based on regularization by the von Neumann entropy. These approaches are based on a dual formulation of the regularized problem, and dual updates are computed using randomized trace estimators.…

Abstract: In 1970, Erdos and Sarkozy wrote a joint paper studying sequences of integers a1 < a2 < . . . having what they called property P, meaning that no a_i divides the sum of two larger a_j , a_k. In the paper, it was stated that the authors believed that a subset A ⊂ [n]…

A system of linear equations is Sidorenko over F_p if any subset of F_p^n contains at least as many solutions to it as a random set of the same density, asymptotically as n->infty. A system of linear equations is common over F_p if any 2-coloring of F_p^n gives at least as many monochromatic…