Southwest Local Algebra Meeting

University of Texas at Arlington, 28 February – 1 March 2026

Program

Saturday 28 February

12.30–1.00 pm  Check-in and coffee/snacks
1.00–1.50 pm  Poster session
2.00–2.50 pm  Talk 1
3.00–3.50 pm  Talk 2
4.00–4.50 pm  Poster session
5.00–5.50 pm  Talk 3
6.30 pm  Social gathering

Sunday 1 March

8.30–9.00 am  Continental breakfast
9.00–9.50 am  Talk 4
10.00–10.50 am  Poster session
11.00–11.50 am  Talk 5
12.00–12.50 pm  Talk 6

Registration

To ease planning and reporting we request that all participants fill out the registration form before the end of January 2026. Early registrants have priority for support, and you must register by 16 January 2026 to be considered for support.

Sponsors and support

The meeting is supported by the National Security Agency and by the Department of Mathematics at UR Arlington.

Organizers

Tatheer Ajani  (University of Texas at Arlington)

Lars Winther Christensen  (Texas Tech University)

Luigi Ferraro  (University of Texas at Rio Grande Valley)

David Jorgensen  (University of Texas at Arlington)

Registered participants

Speakers

Lea Beneish  (University of North Texas)

Towards Artin’s conjecture on \(p\)-adic forms in low degree

Let \(F\) be a homogeneous polynomial of degree \(n\) in at least \(d^2 +1\) variables over the \(p\)-adic numbers, \(\mathbb{Q}_p\) . Artin conjectured that such \(F\) always have nontrivial zeros in any \(p\)-adic field. Although this has been shown to be false in general, the conjecture is still widely believed to be true for prime degree forms. This conjecture holds for \(d=2\) and \(d=3\) due to Hasse and Lewis, respectively. By the work of Ax and Kochen, the conjecture is also known to hold whenever the characteristic of the residue field is sufficiently large. In this talk, we will explore recent progress for low degree forms towards making bounds on the size of the residue field effective. A wide range of techniques are needed, including Bertini theorems, point counting on curves over finite fields, and computation. This is joint work with Christopher Keyes.

Jason McCullough  (Iowa State University)

Quadratic and Koszul licci ideals

Let \(S\) be a standard graded polynomial ring over a field \(K\). Let \(R = S/I\), where \(I\) is a graded ideal of \(S\). \(R\) is called Koszul if \(K\) has a linear free resolution over \(R\). If \(R\) is Koszul, then \(I\) is generated by linear and quadratic elements, but the converse fails. An ideal \(J\) of \(S\) is linked to \(I\) if there is a complete intersection \(C\) such that \(J = C:I\) and \(I = C:J\). The ideal \(I\) is called licci if there are a finite number of ideals, each linked to the previous by some complete intersection, such that the first ideal is \(I\) and the last is a complete intersection. All such ideals are Cohen-Macaulay.

Huneke, Polini, and Ulrich previously asked whether the licci property of an ideal may be detected from its graded Betti table. While recent examples due to Boocher show that the answer is no, we give a strong positive answer in the case of quadratic ideals. In particular, we show how to identify the Hilbert function of a quadratic licci ideal with a partition of its codimension. Further we give a complete characterization of Koszul licci ideals, in terms of Betti tables, Hilbert functions, and defining equations, showing that they are at most 2 links away from a complete intersection. This is joint work with Paolo Mantero and Matthew Mastroeni.

Greg Muller  (University of Oklahoma)

Friezes of Dynkin type

A "frieze" is an infinite configuration of positive integers satisfying certain determinantal identities. The first examples were studied by Coxeter and later Conway, who showed they were miraculously periodic and counted by the Catalan numbers. In this talk, I will describe friezes whose shape is determined by a tree, and review the recent results on periodicity, finiteness, and enumeration. Remarkably, all of these results are fueled by a connection to cluster algebras, a type of combinatorial commutative algebra which has been an area of explosive research for the last 25 years.

Andrew Soto Levins  (Texas Tech University)

Wenbo Niu  (University of Arkansas)

Prashanth Sridhar  (University of Alabama)

Poster presenters

Benjamin Betts  (University of New Mexico)   Morse resolutions
of monomial ideals in a complete intersection domain

Reid Buchanan  (Oklahoma State University)  
Characteristic-dependent monomial resolutions with few generators

Souvik Dey  (University of Arkansas)  
On self-duality of syzygies of residue field and the fundamental module

Hasitha Geekiyanage  (Texas Tech University)  
Module theory over Bézout domains

Haoxi Hu  (Tulane University)  
Okounkov bodies and family of ideals

Dorian Kalir  (Syracuse University)  
Asymptotics of DG modules over a Koszul complex

Sehwan Kim  (New Mexico State University)  
Prüfer domain as a holomorphy ring

Dipendranath Mahato  (Tulane University)  
Rational symbolic powers of ideals

Paulo Martins  (University of Sao Paulo)  
On modules of finite quasi-injective dimension

Zachary Nason  (University of Nebraska-Lincoln)  
Maximal Cohen-Macaulay DG complexes

Vinh Pham  (Tulane University)  
F-volume of filtrations and p-family of ideals

Kory Pollicove  (Syracuse University)  
Computing derived Hochschild cohomology in positive characteristic

Siddharth Ramakrishnan Cherukara  (University of Oklahoma)  
Atkin-Lehner decompositions for quaternionic modular forms

Naufil Sakran  (Tulane University)  
Enumerating log rational curves on some toric varieties

Pablo Sanchez Ocal  (University of British Columbia and Okinawa Institute of Science and Technology)  
The tableaux algebra (with applications to geometry and crystals)

Nathaniel Vaduthala  (Tulane University)  
Homomorphisms of partial fields

Dalena Vien  (Bryn Mawr College)  
The degree of h-polynomials of edge and cover ideals

Joseph Walker  (University of Texas at Arlington)  
Pinched tensors


SLAM in the past

2025 at Arizona State University   2024 at University of Oklahoma   2023 at University of North Texas

2022 at Baylor University   2020 at Tulane University   2019 at University of Texas at El Paso   2018 at University of Arkansas

2017 at University of New Mexico   2016 at Texas State University   2015 at Oklahoma State University   2014 at Texas A&M University

2013 at University of Arizona   2012 at Texas Tech University   2011 at New Mexico State University   2010 at University of Texas at Arlington