Algebra / Number Theory / Combinatorics Seminar

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 […]

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 […]

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, […]

A numerical semigroup is a subset S of the natural numbers that is closed under addition.  One of the primary attributes of interest in commutative algebra are the relations (or […]

Biquandle brackets are skein invariants of biquandle-colored knots, with skein coefficients that are functions of the colors at a crossing. Biquandle power brackets take this idea a step further with […]

A classic problem in graph theory is to find the chromatic number of a given graph: that is, to find the smallest number of colors needed to assign every vertex […]

Beilinson gave a resolution of the diagonal for complex projective space, which gives a strong, full exceptional collection of line bundles as a generating set for the derived category of coherent sheaves. Bayer-Popescu-Sturmfels generalized Beilinson's resolution of the diagonal by giving a cellular resolution of the diagonal for a proper subclass of smooth toric varieties […]