Algebra / Number Theory / Combinatorics Seminar

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 this distributions probabilities directly to the binomial theorem.  The mgf is also a key ingredient in Chernoff bounds, which give upper bounds on the tail […]

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 sum of two SL_n-matrices when n>1. We compute the eigenvalues of these graphs in terms of Kloosterman sums and study their spectral properties; and prove […]

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 sums characterize the nonlinearity of power permutations of interest in cryptography.  They also tell us about the correlation of linear recursive sequences over finite fields that are used […]