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, allowing pairwise comparisons to include strict preferences, ties, or incomparability. This perspective gives a common framework for median procedures and scoring methods, including several familiar […]
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, joint with Victor Ginzburg, which describes the coordinate ring of the group scheme of universal centralizers in terms of the root datum of G using Demazure (or divided […]
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 specified subsets. The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K. From the proof of […]
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 series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk, we review the original series invariants […]
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 […]
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 […]
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 […]
Hecke algebras play a central role in both number theory and representation theory. While some Hecke algebras have explicit descriptions in terms of generators and relations, others are understood through […]
The classical Siegel's lemma (1929) asserts the existence of a nontrivial integer solution to an underdetermined integer homogeneous linear system, whose "size" is small as compared to the size of […]
This is a talk in two parts covering two projects that the speaker mentored over the summer of 2025. The first project deals with the study of polytopes that arise […]
We will examine the multiplicative structure of two skein algebras--- the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang […]
Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the […]
