Past Events
It turns out you can take the determinant of some linear operators between infinite dimensional spaces (whoa). It turns out the Laplacian on a surface is one of those operators, and the determinant measures something geometric about the underlying space (Whoa!). It turns out that you can…
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…
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]…
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.…
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…
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: …