Past Events

This is the second talk of a series in Persistent homology

A quantum cluster algebra is a subalgebra of an ambient skew field of rational functions in finitely many indeterminates. The quantum cluster algebra is generated by a (usually infinite) recursively defined collection called the cluster variables...

Informally, the essential dimension of a finite group is the minimal number of parameters required to describe any of its actions. It has connections to Galois cohomology and several open problems in algebra. I will discuss how one can use techniques...

By a "rational triangle" we mean a plane triangle whose sides are rational numbers. By Heron's formula, there exists such a triangle of area sqrt(a) if and only if a > 0 and x y z (x + y + z) = a for some rationals x, y, z. In a 1749 letter to...

Start with n particles at the origin in the square grid Z2, and let each particle in turn perform simple random walk until reaching an unoccupied site. Lawler, Bramson and Griffeath proved that with high probability the resulting random set of n...

An alternating permutation w=a1⋯an of 1,2,…,n is a permutation such that ai>ai+1 if and only if i is odd. If En (called an Euler number) denotes the number of alternating permutations of 1,2,…,n, then ∑n≥0Enxnn!=secx+tanx. We will discuss such topics...

A substantial part of extremal combinatorics studies relations existing between densities with which given combinatorial structures (fixed size ``templates'') may appear in unknown (and presumably very large) structures of the same type. Using basic...

Let $K$ be a field of characteristic $p>0$ and let $f(t_1,\ldots ,t_d)$ be a power series in $d$ variables with coefficients in $K$. We discuss a recent generalization of both Derksen's recent analogue of the Skolem-Mahler-Lech theorem in positive...