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 […]
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 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. […]
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 have their origin in the work of Ramanujan. In this lecture, we will describe a completely new and unexpected role for partitions that also arises […]
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 even number of elements. In this talk, we will discuss these results as well as the following variants: We consider set sizes and pairwise intersection […]
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 […]
Let K be a compact convex set in the Euclidean space R^n. How many lights are needed to illuminate its boundary? A classical conjecture of Boltyanskii (1960) asserts that 2^n lights are sufficient to illuminate any such set K. While this is still open, an earlier observation of Hadwiger (1945) guarantees that if K has […]
Following Kalashnikov, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
Following Kalashnikov, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
