A key problem in computer proofs based on solutions from copositive optimization, is checking whether or not a given quadratic form is completely positive or not. In this talk we describe […]
A low autocorrelation binary sequence of length $\ell$ is an $\ell$-tuple of $+1$s and $-1$s that does not strongly resemble any translate of itself. Such sequences are used in communications […]
In this talk, I'll attempt to give a friendly introduction to tropical linear series and explore their relationship to matroid theory. Along the way, we'll stop to admire the beautiful view […]
Inspired by the categorification program for a numerical invariant of three-manifolds, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the […]
Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some […]
One of the key objects used in Ngo's proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk, we'll discuss forthcoming work, […]
Many aggregation problems ask us to turn individual judgments into a single collective outcome. In this talk, we model each voter’s input as a relation on a set of alternatives, […]
Given a polynomial defined over a field $K$, you can build an extension of $K_\infty / K$ by adjoining inverse images of some point $\alpha \in K$. The behavior of […]
Kloosterman sums are explicit exponential sums which occur in several contexts in number theory and arithmetic geometry. Bessel functions encode a great deal of representation-theoretic information about finite groups of […]
The unique minimal generating set for a semigroup of lattice points in an n-dimensional polyhedral cone is called its Hilbert basis. In the case when the cone is spanned by […]
Extremal graph theory asks how many edges a graph can have while avoiding a given substructure. We will begin with a brief, accessible introduction to this area, before turning to […]
The Jones Polynomial is an important invariant of knots with applications in physics, quantum computation and more. In this talk I will introduce a family of generalizations of the Jones […]
