Past Events

Given two elliptic curves, the path finding problem asks to find an isogeny (i.e. a group homomorphism) between them, subject to certain degree restrictions. Path finding has uses in number theory as well as applications to cryptography. For...

We will see the definition and some examples of broken toric varieties and balloon animal maps between them. After an overview of some of the many different areas in which they appear, we look at how their geometry can be studied via complexes of...

We consider the Grassmannian G r C ( k , n ) , a manifold parameterized by k -dimensional planes in complex n -dimensional space. The Schubert decomposition of the Grassmannian is perhaps the classic way to split this space into smaller pieces...

Radial projections have been a quickly developing topic in harmonic analysis. The work of Orponen-Shmerkin-Wang connected this topic to a continuum Beck theorem for lines, finding a (lower) bound for the dimension of lines that contain at least two...

For long-range percolation on ℤ with translation-invariant edge kernel J, it is a classical theorem of Aizenman and Newman (1986) that the phase transition is discontinuous when J(x−y) is of order |x−y|−2 and that there is no phase transition at all...

Due to their nonlocal properties, fractional derivatives, such as the Riemann-Liouville or Caputo type, are sometimes used to model memory effects. While their physical interpretation is still not clear, fractional models seem to better describe...

There are two ways to compute moments in families of L-functions: one uses the approximation by Dirichlet polynomials, and the other is based on multiple Dirichlet series. We will introduce the two methods to study the family of real Dirichlet L...

For a fixed $d \in \mathbb{N}$, the non-commutative (nc) universe $\mathbb{M}^d$ is defined as the graded (disjoint) union of $d$-tuples of $n \times n$ (complex) matrices over $n \in \mathbb{N}$. A function $f : \mathbb{M}^d \to \mathbb{M}^1$ is...

The notions of noise sensitivity and stability were recently extended for the voter model, a well-known and studied interactive particle system. In this model, vertices of a graph have opinions that are updated by uniformly selecting edges. We...

A directed variant of the famous Oberwolfach problem, the directed Oberwolfach problem considers the following scenario. Given n people seated at t round tables of size m1,m2…,mt, respectively, such that m1+m2+⋯+mt=n, does there exist a set of n−1...