Markov chains have become widely-used to generate random political districting plans. These random districting plans can be used to form a baseline for comparison, and any proposed districting plans that […]
"A Tale of Two Cities" is a novel told in three books/parts. Here we describe three projects related both to published work and ongoing pieces: PROJECT 1: In the world […]
Given a degree d polynomial f(x) in Q, consider the subset S_f of Q consisting of rational numbers t for which the translated polynomial f(x) - t factors completely in […]
The Mahler measure of a polynomial is the modulus of its leading term multiplied by the moduli of all roots outside the unit circle. The Mahler measure of an algebraic […]
Young diagrams are all possible arrangements of n boxes into rows and columns, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n, […]
Let L be a full-rank lattice in R^n and write L+ for the semigroup of all vectors with nonnegative coordinates in L. We call a basis X for L positive […]
Many knot invariants are defined from features of knot projections such as arcs or crossings. Gauss diagrams provide an alternative combinatorial scheme for representing knots. In this talk we will […]
There are two different measures of how far a given Euclidean lattice is from being orthogonal -- the orthogonality defect and the average coherence. The first of these comes from […]
Consider rational polynomials in multiple variables that are linear with respect to some of the variables. In this talk we discuss the problem of finding a zero of such polynomials […]
In this talk we will consider some notions of `robustness' of graph/hypergraph properties. We will survey some existing results and will try to emphasize the following new result (joint with Adva Mond and Kaarel Haenni): The binomial random digraph $D_{n,p}$ typically contains the minimum between the minimum out- and in-degrees many edge-disjoint Hamilton cycles, given […]
Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p, this […]
Given votes for candidates, what is the best way to determine the winner of the election, if some of the votes have been corrupted or miscounted? As we saw in Florida in 2000, where a difference of 537 votes determined the president of the United States, the electoral college system does not seem to be […]
