Algebra / Number Theory / Combinatorics Seminar

The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K, called a primitive element. In fact, it is […]

Imagine the hands on a clock.  For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way.   […]

For a finite group G, a G-module M, and a field F, an element u in H^d(G,M) is negligible over F if for each field extension L/F and every continuous […]

What are the possible angles between two integer vectors in R^n? If we fix one such possible angle and one integer vector x, is there always another integer vector y […]

In order to understand a topological space X, it is often easier to understand X in terms of an action by a group G. When X is a compact complex […]

Biquandle module enhancements are invariants of knots and links generalizing the classical Alexander module invariant. A quiver categorification of these invariants was introduced in 2020. In this work-in-progress (joint with […]

A modification of the cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels gives a virtual resolution of the diagonal for smooth projective toric varieties and toric Deligne-Mumford stacks which are […]

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 […]

​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 […]

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 […]

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 […]

The classical Noether-Lefschetz Theorem states that a suitably general algebraic surface S of degree d ≥ 4 in complex projective 3-space P3 contains no curves besides complete intersections, that is, […]