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, […]
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 […]
For a lattice L in the plane, we define the affiliated deep hole lattice H(L) to be spanned by a shortest vector of L and the furthest removed vector from […]
