Algebra / Number Theory / Combinatorics Seminar

Given a finite quandle $X$, a set $S \subset \mathrm{Hom}(X,X)$ of quandle endomoprhisms, and an oriented knot or link $L$, we construct a quiver-valued invariant of oriented knots and links. […]

In 1846, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.  This was forgotten about for nearly 100 years […]

Combinatorial neural codes are 0/1 vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is […]

The Bateman—Horn Conjecture is a far-reaching statement about the distribution of the prime numbers.  It implies many known results, such as the Green—Tao theorem, and a variety of famous conjectures, […]

Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980's with the development of computer algebra systems like Mathematica, AG has been leveraged in areas of STEM as diverse as statistics, robotic kinematics, computer science/geometric modeling, and mirror symmetry. Part one of my talk will be a […]

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 […]