Past Events
The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. We show that there exists a constant 1.94 < a < 1.9449 such that Q(n) = ((1 + o(1))ne^(-a))^n. The constant a is characterized as the solution to a convex…
Proving the asymptotic expansion of the heat kernel; proving Gauss Bonnet
To capture singularities under mean curvature flow one wants to understand all ancient solutions. In addition to shrinkers and translators one also encounters ancient ovals, namely compact noncollapsed solutions that are not self-similar. In this talk, I will explain that any bubble-sheet oval…
The method of moments is a classical technique for showing weak convergence and follows a simple recipe: for any natural number m, compute the mth moments of the random variables of interest, and prove they tend to the mth moment of the claimed limit (this works for…
A central heuristic in arithmetic combinatorics concerns an incongruence between additive and multiplicative structure in integers. This is encapsulated in a famous conjecture of Erdős–Szemerédi, which states that any finite set of integers either produces many sums or many products. While this…
Inspired by the work of Lalonde-McDuff-Polterovich, we describe how the C^0 and C^1 flux conjectures relate to new instances of the strong Arnol’d conjecture and make new progress on…
We prove that applying a permutation after each step of a random walk on a tree can only increase its speed. I will discuss related results and open problems.
In this talk, I will discuss the way in which algebraic geometry can shed some light on a central problem in statistics. Along the way, I'll discuss how one can use maximum likelihood to recommend Netflix shows. My talk will also feature pictures of my dog in his Halloween costume.…