There will be a poster session for graduate students during lunch break (11:50am-2:00pm) on Saturday, April 22. We encourage all participants at the conference to enjoy our catered lunch while discussing mathematics with poster presenters.

Posters should be set up by 11:50am on Saturday. We will have display boards and pins for your posters.

One poster per individual. Any posters left behind will be disposed after the conference.

To be considered for presenting a poster at this conference, you need to submit,
a title and abstract for your poster on the registration form by
**April 1, 2023. **

- Souvik Dey (University of Kansas)
- Monalisa Dutta (University of Kansas)
- Adam LaClair (Purdue University)
- Uyen Le (West Virginia University)
- David Lieberman (University of Nebraska - Lincoln)
- Ritika Nair (University of Kansas)
- Shravan Patankar (University of Illinois at Chicago)

Souvik Dey

(University of Kansas)
**E-mail:**
souvik@ku.edu

**Title: ** No title has been posted

**Abstract: **No abstract has been posted

Monalisa Dutta

(University of Kansas)
**E-mail:**
m819d903@ku.edu

**Title: ** No title has been posted

**Abstract: **No abstract has been posted

Adam LaClair

(Purdue University)
**E-mail:**
alaclair@purdue.edu

**Title: **Invariants of Binomial Edge Ideals via Linear Programs

**Abstract:**In 2009 Herzog et al. and independently Ohtani introduced the
notion of binomial edge ideal---a binomial ideal associated to a simple graph.
Since their introduction there has been much research relating the combinatorial
structure of the underlying graph to the algebraic structure of the associated
ideal. I introduce a novel linear program that combinatorially relates to maximally
packing vertex disjoint paths inside the graph. Algebraically, this linear program,
its LP-relaxation, and dual relate to the binomial grade, F-threshold, log canonical
threshold, and height of the binomial edge ideal. I discuss these connections in
this poster presentation.

Uyen (ENNI) Le

(West Virginia University)
**E-mail:**
hle1@mix.wvu.edu

**Title: **Remarks on a conjecture of Huneke and Wiegand

**Abstract:** Unlike vector spaces over a field, not all modules over a ring
have a basis. Using an operation known as the tensor product, the Huneke-Wiegand
Conjecture (HWC) seeks conditions on a module $M$ over a one-dimensional local
ring such that $M$ has a basis. This research shows (HWC) is affirmative for 2-periodic
(joint work with O. Celikbas, Matsui, and Sadeghi) and 4-periodic modules.

David Lieberman

(University of Nebraska - Lincoln)
**E-mail:**
david.lieberman@huskers.unl.edu

**Title: **Generalizing Bernstein's inequality for D-modules

**Abstract:** Bernstein's inequality is a classic result in the realm of D-modules.
The inequality puts a lower bound on the dimension of a D-module over polynomial
rings. More generally, when the inequality holds modules that achieve this lower
bound enjoy nice properties. Our overall goal is to show the inequality holds in
certain non-polynomial ring settings. This has previously been shown in the case
of Veronese rings. In this poster we present a new proof of the same fact that
we hope may be useful in showing other singular rings satisfy Bernstein's inequality.

Ritika Nair

(University of Kansas)
**E-mail:**
rnair@ku.edu

**Title: **On the Lefschetz property for quotients by monomial ideals containing
squares of variables

**Abstract:** Let $\Delta$ be an (abstract) simplicial complex on $n$ vertices.
One can define the Artinian monomial algebra $A(\Delta) = \Bbbk[x_1, \ldots, x_n]/
\langle x_1^2, \ldots, x_n^2, I_{\Delta} \rangle$, where $\Bbbk$ is a field of
characteristic $ 0$ and $I_{\Delta}$ is the Stanley-Reisner ideal associated to
$\Delta$. For a general linear form $\ell$, $A(\Delta)$ has the Weak Lefschetz
Property (WLP) if the homomorphism induced by multiplication by $\ell$, $\mu_i
: A(\Delta)_i \to A(\Delta)_{i+1}$ has maximal rank for all $i$. In the joint work
with Hailong Dao, we aim to characterize the Weak Lefschetz Property (WLP) of $A(\Delta)$
in terms of the simplicial complex $\Delta$. In particular, we see a complete characterization
of WLP in degree $1$ in terms of the edge graph of $\Delta$. We also look at pseudomanifolds
of small dimension and some interesting results relating WLP with colorability
of triangulation of the pseudomanifold. We also construct a family of Artinian
Gorenstein algebras that fail WLP by combining our results and the standard technique
of Nagata idealization.

Shravan Patankar

(University of Illinois at Chicago)
**E-mail:**
spatan5@uic.edu

**Title: **Coherence of absolute integral closures

**Abstract:**We prove that the absolute integral closure of an equi-characteristic
zero noetherian complete local domain R is not coherent, provided dim(R) ≥ 2. As
a corollary, we give an elementary proof of the mixed characteristic version of
the result due to Asgharzadeh and extend it to dimension 3. Furthermore, we apply
the methods of Aberbach and Hochster used to prove the positive characteristic
version of this result to study F-coherent rings and our work naturally suggests
a mixed characteristic analogue of a result of Smith.

NAME/LAST NAME

(Institution)
**E-mail:**

**Title: **No title has been posted

**Abstract: **
No abstract has been posted