Search Research Symposium Abstracts math

Amitsur subgroup of Fano threefolds

The Amitsur subgroup of a smooth Fano G-variety measures the obstruction to G-linearization of line bundles on it. It is an equivariant birational invariant. The Amitsur subgroup of such varieties has been studied in cases of dimensions 1 and 2 in algebraically closed setting. A natural next step is to classify it for Fano varieties of dimension 3. In this [Read More...]

Presenter: Shreya Sharma, University of South Carolina
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 18, 2025; 10:35 am

Boolean Matrix Rank via Monomial Ideals

Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to approximate a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying structure in the data. When interpreting a binary matrix as the adjacency matrix of a bipartite graph, BMF is [Read More...]

Presenter: Juliann Geraci, University of Nebraska - Lincoln
Authors: Alexandra Seceleanu (University of Nebraska - Lincoln), Alexander B. Kunin (Creighton University), (), ()
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 16, 2025; 3:55 pm

Cohomological support varieties and monomial ideals

Given a ring R and an R-module M, the cohomological support variety of M is a geometric object that encodes homological information about M. Even restricting to the case when M=R, we can obtain information about the singularities of R, such as whether R is complete intersection. In this talk, we will consider the problem of whether R has an embedded [Read More...]

Presenter: Eloísa Grifo, University of Nebraska-Lincoln
Authors: Benjamin Briggs (Imperial College London), Josh Pollitz (Syracuse University)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 16, 2025; 4:20 pm

Combinatorial bounds on the Castelnuovo-Mumford regularity of toric surfaces

In 1996, L'vovsky showed the Castelnuovo-Mumford regularity of the coordinate ring of a monomial curve is bounded by the sum of its semigroup's two largest gaps. We explore analogous results for toric surfaces embedded by incomplete linear systems, and show that for certain classes the regularity is controlled by the combinatorics of the associated [Read More...]

Presenter: Sean Grate, Auburn University
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 17, 2025; 10:10 am

Fixed quotients of polynomial rings and Stanley–Reisner rings

We will discuss homological properties of the fixed quotient of an algebra with group action. This is a natural invariant theoretic object and a module over the ring of invariants. We first study the action of the symmetric group on the polynomial ring, giving results and conjectures on the minimal free resolution of its fixed quotient. We will then [Read More...]

Presenter: Alexandra Pevzner, Northeastern University
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 18, 2025; 10:10 am

Homomorphisms of maximal Cohen-Macaulay modules over the cone of an elliptic curve

Consider the ring R=k[[x,y,z]]/(f) where f=x^3+y^3+z^3 with an algebraically closed field k and char(k) neq 3. In a 2002 paper, Laza, Popescu and Pfister used Atiyah's classification of vector bundles over elliptic curves to obtain a description of the maximal Cohen-Macaulay modules (MCM) over R. In particular, the matrix factorizations corresponding to rank [Read More...]

Presenter: Bhargavi Parthasarathy, Syracuse University
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 18, 2025; 9:45 am

Invariant Theory and the Graph Reconstruction Conjecture

Given an unlabelled graph, a card of the graph is defined to be the induced subgraph formed by deleting a single vertex. The deck of the graph is defined as the multiset of all its cards. The Graph Reconstruction Conjecture, by Kelly and Ulam, asks if one can determine, up to isomorphism, a graph from its deck. We approach this conjecture from an [Read More...]

Presenter: Jenny Kenkel, Grinnell College
Authors: Emilie Dufresne (University of York), Nelly Villamizar (Swansea University), Gabriela Jeronimo (University of Buenos Aires), Haydee Lindo (Harvey Mudd College)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 17, 2025; 11:20 am

Minimal Degree Varieties in Weighted Projective Spaces

Classically, the degree of a variety embedded nondegenerately in projective space is bounded below by one more than the codimension. Such varieties were classified by Bertini and Del Pezzo, and are important geometric objects appearing in the study of sygygies and free resolutions. We extend this classical theory to the setting of weighted projective spaces, [Read More...]

Presenter: Maya Banks, Fields Institute
Authors: Ritvik Ramkumar (Cornell University)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 16, 2025; 3:05 pm

Permutation Action on Chow Rings of Matroids

Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincar'e duality and the Hard Lefschetz theorem. We lift these to statements about this [Read More...]

Presenter: Anastasia Nathanson, University of Minnesota
Authors: Robert Angarone (University of Minnesota), Victor Reiner (University of Minnesota)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 17, 2025; 10:35 am

Poincare series over almost complete intersection rings

We study Poincare series of modules over almost complete intersection rings defined by n+1 quadrics in n variables, starting first with a particular example and then moving to the generic case. We also study the Gorenstein rings that are linked to such almost complete intersections. In particular we show that both such rings are Golod and provide explicit [Read More...]

Presenter: Rachel Diethorn, Oberlin College
Authors: Sema Gunturkun (University of Essex), Alexis Hardesty (Texas Women's University), Pinar Mete (Balikesir University), Liana Sega (University of Missouri Kansas City)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 17, 2025; 9:45 am

Resolutions Over Numerical Semigroup Rings via Apery Specialization

Each numerical semigroup $S$ with smallest positive element m corresponds to an integer point in a polyhedral cone $C_m$, known as the Kunz cone. The faces of $C_m$ form a stratification of numerical semigroups that has been shown to respect a number of algebraic properties of $S$, including the combinatorial structure of the minimal free resolution of the [Read More...]

Presenter: Aleksandra Sobieska, Marshall University
Authors: Tara Gomes (University of Minnesota -- Twin Cities), Christopher O'Neill (San Diego State University), Eduardo Torres Dávila (University of Minnesota -- Twin Cities)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 18, 2025; 11:00 am

Toward an Infinite-dimensional Multigraded Grothendieck-Riemann-Roch Theorem

Inspired by work of Knutson, Miller, and Sturmfels, and with the goal of defining Grothendieck and Schubert polynomials for infinite matrix Schubert varieties, we introduce a new category of multigraded “BDF modules” (containing the syzygies of infinite matrix Schubert varieties, which need not be finitely generated) over a new type of multigraded [Read More...]

Presenter: Nathaniel Gallup, Northeastern University
Authors: Anna Chlopecki (Purdue)
Symposium Year: 2025
Session: Homological Methods in Commutative Algebra
Presentation Time: May 16, 2025; 3:30 pm