Moment generating functions (Laplace transforms) are a means for transforming probability problems into problems involving polynomials. Here I will concentrate on the binomial distribution, and use the mgf to link […]
In this talk we use the unit-graphs and the special unit-digraphs on matrix rings to show that every n x n nonzero matrix over F_q can be written as a […]
We consider sums in which an additive character of a finite field F is applied to a binomial whose individual terms (monomials) become permutations of F when regarded as functions. These Weil […]
The classical Sperner - KKM (Knaster - Kuratowski - Mazurkiewicz) lemma has many applications in combinatorics, algorithms, game theory and mathematical economics. In this talk we consider generalizations of this […]
We begin with a review of the Bateman—Horn conjecture, which sheds light on the intimate relationship between polynomials and prime numbers. In this expository talk, we survey a host of […]
In this talk we will survey recent work on Niebzydowski Tribrackets and Niebrydowski Algebras, algebraic structures related to region colorings the planar complements of knots and trivalent spatial graphs.
Lattice valued vector systems have taken an important role in packing, coding, cryptography, and signal processing problems. In compressed sensing, improvements in sparse recovery methods can be reached with an […]
Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups […]
Given integers $k,l$ and a graph $G$, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges? The systematic study of this very natural […]
An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent […]
Modular forms are ubiquitous in modern number theory. For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat's Last Theorem. In addition […]
Chebotarev's theorem on roots of unity says that every minor of a discrete Fourier transform matrix of prime order is nonzero. We present a generalization of this result that includes […]
