Algebra / Number Theory / Combinatorics Seminar

Around 20 years ago, physicists Michael Faux and Jim Gates invented Adinkras as a way to better understand Supersymmetry.  These are bipartite graphs whose vertices represent bosons and fermions and whose edges represent operators which relate the particles.  Recently, Charles Doran, Kevin Iga, Jordan Kostiuk, Greg Landweber and Stefan M\'{e}ndez-Diez determined that Adinkras are a […]

​I will introduce two general problems and explain how they surprisingly connect with each other and with other aspects of mathematics (for a glimpse, Sato—Tate, hypergeometric functions, moduli spaces of sheaves, Catalan numbers, Hall polynomials, etc.)​. The first problem is to count finite-field points on so called "varieties of matrix points''. They are created from […]

In the field of commutative algebra, the principal object of study is (unsurprisingly) commutative algebras. A somewhat unintuitive fact is that results about commutative algebras can be gleaned from an associated non-commutative algebra whose generators are very analytic in nature. This object is called the ring of differential operators, often denoted by D. In a sense gives […]

In this talk, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.  Resolving the lack of phase information is called the phase problem.  We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function.  […]