Algebra / Number Theory / Combinatorics Seminar

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 manifold, we often let G be products of S^1 or \C^* acting in a nice way ("holomorphically") on X. This simplifies several calculations of an […]

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 Yewon Joung from Hanyang University in Seoul) we take the next step by defining invariant quiver representations. As an application we obtain new polynomial knot […]

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 a global quotient of a smooth projective variety by a finite abelian group. In the past year, Hanlon-Hicks-Lazarev gave a minimal resolution of the diagonal […]

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 […]

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, […]

Integer partitions are ubiquitous in mathematics, arising in subjects as disparate as algebraic combinatorics, algebraic geometry, number theory, representation theory, to mathematics physics. Many of the deepest results on partitions […]

The classical oddtown and eventown problems involve a collection of subsets of a finite set with an odd (resp. even) number of elements such that all pairwise intersections contain an […]

Quandles are algebraic structures encoding the motion of knots through space. Quandle cocycle quivers categorify the quandle cocycle invariant. In this talk we will define a quiver representation associated to […]