Algebra / Number Theory / Combinatorics Seminar

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 use Gauss diagrams to enhance the biquandle counting invariant for classical and virual knots using biquandle arrow weights, a new algebraic structure without a clear […]

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 the study of sphere packing while the second is motivated by frame theory, but both of them have applications in digital communications, especially in coding […]

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 that are bounded with respect to a height function. For a system of such polynomials satisfying certain technical conditions we prove the existence of a […]

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 […]

Discrete Calculus studies discrete structures, such as sequences and graphs, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate […]

It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It […]

We prove, in this joint work with Maksym Radziwill, a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann Hypothesis) concerning the bias of cubic Gauss sums. This explains […]

In a remarkable series of papers Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers, and independently Olga Kharlampovich and […]

Public key quantum money is a replacement for paper money which has cryptographic guarantees against counterfeiting. We propose a new idea for public key quantum money. In the abstract sense, […]