Past Events

For each $p\in(1,\infty)$, a p-energy form $(\mathcal{E}_p,\mathcal{F}_p)$, a natural $L^p$-analog of the standard Dirichlet form for $p=2$, was constructed on the (two-dimensional standard) Sierpinski gasket $K$ by Herman--Peirone--Strichartz...

The class number one problem is one of the central subjects in algebraic number theory that turns back to the time of Gauss. This problem has led to the classical embedding problem which asks whether or not any number field K can be embedded in a...

A classic theorem of Quillen established an equivalence of homotopy theory between (certain) DG Lie algebras and DG coalgebras. Both are models for (simply-connected) rational homotopy theory. A generalization of Quillen's result by Hinich provided a...

Biodiversity loss worldwide coincides with an increase in epidemics. This loss of species and reassembly of species communities is thought to be connected to disease transmission via two, opposing, theories: (1) the dilution effect predicts that high...

The questions of how healthy colonic crypts maintain their size under the rapid cell turnover in intestinal epithelium, and how homeostasis is disrupted by driver mutations, are central to understanding colorectal tumorigenesis. We propose a three...

Let $(M^n,g)$ be compact Riemannian manifold, it is a classical result that if $(M^n,g)$ has Ricci curvature bigger than the standard sphere, its volume and diameter are smaller than those of the sphere. If $(M^n,g)$ only has scalar curvature bigger...

For a population model that encodes parent-child relations, an ordered representation is a partial or complete labelling of individuals, in order of their descendants’ long-term success in some sense, with respect to which the ancestral structure is...

How many ways are there to write a given permutation as a product of m transpositions (i_1, j_1) (i_2, j_2) \dots (i_m, j_m)? For example, there are three ways to write (1,2,3) as a product of two transpositions: (1,2)(1,3), (1,3)(2,3) and (2,3)(1,2)...

In 2000, Shiu proved that there are infinitely many primes whose last digit is 1 such that the next prime also ends in a 1. However, it is an open problem to show that there are infinitely many primes ending in 1 such that the next prime ends in 3...

The Deligne-Mumford compactification, $\overline{M_{0,n}}$, of the moduli space of $n$ distinct ordered points on $\mathbb{P}^1$, has many well understood geometric and topological properties. For example, it is a smooth projective variety over its...