Past Events

In Manak's talk, we learned what a deformation functor is. We will explore this notion more in depth and look at some examples. Deformation functors allow us to make the idea of a "formal moduli problem" more precise. Time permitting, we will discuss...

Let A and B be compact sets in ℝd. One of the fundamental problems in geometric measure theory is to study the relations between the Hausdorff dimensions of A, B, and A∩f(B), where f runs through a set of transformations. This type of question has...

Random band matrices provide a simple model for studying the metal-insulator transition of random operators, the prominent example of which is the Anderson model. According to the famous sqrt(N) conjecture, N x N random matrices with non-zero entries...

I will talk about the `minimal spanning arborescence', a directed version of the Minimal spanning tree. I will explain how this naturally leads to a new type of stochastic process which we call `loop contracting random walk'. I will show how this can...

In this talk, we will discuss the classical problem, known as Falconer's distance problem, of quantifying the minimum amount of pairwise distances associated with a given Borel set in Euclidean space. For the last 25 years, methods in harmonic...

Advances in microscopy can now provide snapshot images of individual RNA molecules within a nucleus. Decoding the underlying spatiotemporal dynamics is important for understanding gene expression, but challenging due to the static, heterogeneous, and...

We discuss the role of long Dirichlet polynomials in number theory. We first survey some applications of mean values of long Dirichlet polynomials over primes in the theory of the Riemann zeta function which includes central limit theorems and pair...

Modern physics involves beautiful and intricate mathematics, and entirely new mathematical structures often emerge from physical theories. An example of this is the concept of Airy structures, which was first introduced by Kontsevich and Soibelman in...

Waldhausen’s S_\bullet-construction gives a way to define the algebraic K-theory space of a category with cofibrations. Specifically, the K-theory space of a category with cofibrations C can be defined as the loop space of the realization of the...

Until quite recently, many points of connection between mathematics and theoretical physics focused on so-called "twists" of supersymmetric field theories. Such twists are holomorphic or topological field theories that are amenable to rigorous...