Schedule and Abstracts

2024 schedule below.

All times in CENTRAL TIME

ABSTRACTS

Abstracts can be found here!

Below is the schedule for the short talk sessions. In the next section, you may find abstracts for each talk.

Friday, Session 1 (LBC, 201), 4-4:50 pm:

“A discrete-time stage-structured host-parasitoid model with the combination of  pest control strategies.” Jenita Jahangir, University of Louisiana at Lafayette.

“Evolution of predator to resist toxicant effects in a predator-prey system.” Neerob Basak, University of Louisiana at Lafayette.

Friday, Session 2 (LBC 202), 4-4:50 pm:

“Classification of Irreducible Unipotent Numerical Monoids into Symmetric and Pseudo-Symmetric.” Naufil Sakran, Tulane University

“Day One with the Lean4 Theorem Prover” Brandon Sisler, University of South Alabama

Saturday, Session 1 (Jones, 102), 9:30-10:30 am:

“A Predator-Prey Model with Seasonal Breeding” Narendra Pant, University of Louisiana at Lafayette

“Bistability in models of Hepatitis B virus dynamics” Nazia Afrin, University of Louisiana at Lafayette

“A Discrete-Time Trajectory-Based Stabilization Approach” Jackson Knox, Louisiana State University

Saturday, Session 2 (Jones 204), 9:30-10:30 am:

“Embedding Graphs on the Square Grid.” Daniel Hodgins, University of South Alabama

“Cycles-Related Γ-Harmonious Graphs” Gyaneshwar Agrahari, Louisiana State University

“The Algebraic Structure of Hyperbolic Graph Braid Groups” Huong Vo, Louisiana State University

Saturday, Session 3 (Jones 204), 2:00-2:20 pm:

“Quasistatic peridynamics, existence of unique solution in the presence of damage” Nuwanthi Samarawickrama, Louisiana State University.

Saturday, Session 4 (Jones 102), 2:00-2:20 pm:

“The Marvelous world of modular form.” Kalani Thalagoda, Tulane University 

“A discrete-time stage-structured host-parasitoid model with the combination of  pest control strategies." 

Jenita Jahangir, University of Louisiana at Lafayette. 

Abstract: We propose a discrete-time host-parasitoid model with stage structure in both species. For this model, we establish conditions for the existence and global stability of the extinction and parasitoid-free equilibria as well as conditions for the existence and local stability of an interior equilibrium and system persistence. We study the model numerically to examine how pesticide spraying may interact with natural enemies (parasitoids) to control the pest (host) species. We then extend the model to an impulsive difference system that incorporates both periodic pesticide spraying and augmentation of the natural enemies to suppress the pest population. For this system, we determine when the pest-eradication periodic solution is globally attracting. We also examine how varying the control measures (pesticide concentration, natural enemy augmentation, and the frequency of applications) may lead to different pest outbreaks or persistence outcomes when eradication does not occur.

“A Predator-Prey Model with Seasonal Breeding” 

Narendra Pant, University of Louisiana at Lafayette

Abstract: We extend the predator-prey model developed by Ackleh et. al (2019) to include seasonal reproduction. We model the prey reproduction as a 2-periodic function, that is, repeating every two seasons: a breeding season and a non-breeding season. We analyze the dynamics resulting model and demonstrate that if both the prey’s inherent reproduction rate and the predator’s invasion reproduction rate are greater than one, the system is permanent and attains an interior 2-cycle which remains stable in a local sense. We then compare how seasonality affects prey population density with and without predator involvement. We find that while seasonality generally reduces prey density over a full period when predators are absent, it can be beneficial within certain parameter ranges when predators are present.

“Bistability in models of Hepatitis B virus dynamics” 

Nazia Afrin, University of Louisiana at Lafayette

Abstract: Despite effective vaccines and improved treatment strategies, hepatitis B virus (HBV) is a major global health concern with 1.5 million newly infected cases each year. It’s an infection of the liver caused by the Hepatitis B virus. In this preliminary study, we formulate and analyze a within-host model that describes the progression of acute HBV in liver cells (hepatocytes). We derive the basic reproduction number R0 and investigate the stability of the equilibria via threshold analysis. Analytical and numerical results show that the model exhibits complex bifurcation dynamics such as backward bifurcation. Finally, we discuss the epidemiological implications of bistable dynamics.

“Quasistatic peridynamics, existence of unique solution in the presence of damage” 

Nuwanthi Samarawickrama, Louisiana State University

Abstract: We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model with the presence of damage are established.We show uniqueness of quasistatic evolution for load paths.

“Evolution of predator to resist toxicant effects in a predator-prey system.” 

Neerob Basak, University of Louisiana at Lafayette.

Abstract: We extend the predator-prey model developed by Ackleh et al. (2019) to study the evolution of the predator to resist toxicant effects. Assuming a trade-off between toxicant resistance and the ability of the predator to capture prey, we model the predator’s evolution to resist the effect of toxicants. In this paper, we examine two cases: (1) lethal effects where the toxicant resistance directly affects the trait-dependent survival probability of the predator and (2) sublethal effects where the toxicant resistance impacts the conversion growth rate. For both cases, we establish the existence and stability conditions of the predator-prey system with the evolutionary trait where predators evolve to resist toxicants. We also establish persistence results under some conditions on the model parameters.

"A Discrete-Time Trajectory-Based Stabilization Approach"

Jackson Knox, Louisiana State University

Abstract: Continuous-time trajectory-based estimates play a significant role in mathematical control theory, because they can help us prove exponential stability properties in cases that are not necessarily amenable to Lyapunov functions or to other standard control theoretical techniques. These include cases with input delays, where a feedback control for a control system must be computed using time delayed measurements from the system, because current measurements from the system may not be available. Here we present a new class of trajectory-based estimates for discrete-time systems. We use our new estimates to prove an input-to-state stability estimate for a class of discrete-time linear control systems that contain arbitrarily long constant input delays. The control systems use delay-compensating feedback controls that are calculated using a predictor approach, and our input-to-state stability result quantifies the degree of robustness of the delay compensation with respect to uncertainties in coefficient  matrices.

“The Algebraic Structure of Hyperbolic Graph Braid Groups” 

Huong Vo, Louisiana State University

Abstract: Genevois has recently classified which graph braid groups on >= 3 strands are word hyperbolic. In the 3-strand case, he asked whether all such word hyperbolic groups are actually free; this reduced to checking two infinite classes of graphs. We give positive and negative answers to this question: one class of graphs always has free 3-strand braid group, while the braid groups in the other class usually contain surface subgroups. This is part of the VIR course that was taught by Professors Pallavi Dani and Kevin Schreve at Louisiana State University in Fall 2023.

“Day One with the Lean4 Theorem Prover” 

Brandon Sisler, University of South Alabama

Abstract: In our everyday life we often need to keep track of information so that we avoid mistakes later. An accountant uses excel to avoid data errors, a physicist uses the back of an envelope to avoid arithmetic errors, but what can a mathematician use? The answer to this question is Lean4! Lean4 is a theorem proving software, which allows the user to validate their proofs formally and to ensure their correctness. In this talk, we will discuss how this is achieved, how one can access this software and show some examples. This talk is aimed at someone who has never seen a theorem prover before and who is curious to learn about their basic mechanisms.

“Embedding Graphs on the Square Grid.” 

Daniel Hodgins, University of South Alabama

Abstract: Minimizing the lengths of connections in network systems can be useful in the real world when connections are cost prohibitive. In this talk, we define a function called the minimum edge sum to evaluate embeddings of graphs determined by the lengths of the edges in a square grid. In addition, our objective is to find bounds on the minimum edge sum for various classes of graphs. 

“Classification of Irreducible Unipotent Numerical Monoids into Symmetric and Pseudo-Symmetric.” 

Naufil Sakran, Tulane University

Abstract: The talk intends to introduce the generalization of the theory of numerical semigroups to the theory of unipotent numerical semigroups (UNS). Numerical semigroups arise naturally in the field of commutative algebra. It has the advantage of being simple, yet powerful enough to be used in classification problems. Application of these objects ranges from providing tests to determine "especially nice” rings and local domains to algebraic coding theory and singularity theory. The aim of this research is to extend the theory and introduce new tools so that they can be used in broader contexts. In our work, we extend the basic invariants of the classical theory to our proposed unipotent setting, enabling us to define ideals, symmetric and pseudo-symmetric UNS. We show the behavior of ideal theory in the general unipotent setting and use it to classify irreducible UNS into symmetric and pseudo-symmetric UNS. This result indicates that we have a good foundation for future progress. In addition, we lay the foundation for Unipotent Arf semigroups and comment on the commutativity of blowups and Arf closure in our setting.

“Cycles-Related Γ-Harmonious Graphs”  

Gyaneshwar Agrahari, Louisiana State University

Embedding a graph on a topological surface is a well-studied problem. Can we have an analogous concept for embedding groups on graphs? When the group is cyclic, we call such embedding harmonious labeling. Harmonious labeling is one of the most extensively studied labeling schemes in graph theory. We extend its definition from cyclic groups to any finite Abelian groups. Let G=(V,E) be a graph with q edges and $\Gamma$ an Abelian group of order q. We say that G is $\Gamma$-harmonious if there exists an injection $f: V\to\Gamma$ (called$\Gamma$-harmonious labeling) with the property that the induced labels w(e) of all edges, defined as w(xy)=f(x)+f(y) (where the addition is performed in $\Gamma$), are all distinct. We proved results on cycle-related classes of graphs such as wheels, windmills, prisms, and web graphs. We will also propose some open problems related to this labeling. 

“The Marvelous world of modular form.” 

Kalani Thalagoda, Tulane University 

Abstract: If you have encountered modular forms before, lucky you! If not, lucky you! At first sight, modular forms are intimidating objects. Classically, they are complex valued function on the upper-half plane satisfying growth conditions, and symmetry conditions. To grasp their definition, we just need some complex analysis. But their beauty and versality goes far beyond. In this short talk, I hope to give some intuition about application of modular forms to number theory.

“Using Singular Value Decomposition to Compare Fluid Flows from Different Bacterial Models” Janet Jiang, Trinity University.

"Robustness of Multivariate Dispersion Charts Based on Grouped Observations to Normality Assumptions” Nurudeen Ajadi, University of Louisiana at Lafayette.

“Schubert-Polar Conditions on the Grassmannian-(2, l)” Mackenzie Bookamer, Tulane University

“Singular Value Decomposition for Convoluted Chemical Dynamics” Mendis Kasun, Tulane University

“A theorem about p-families of ideals" Vinh Pham, Tulane University

“Inverse PDE problem using Physics-informed Neural Network” Lan Trinh, Tulane University

“Guessing a probability distribution using partial samples” Victor Backston, Tulane University

“Lill’s Method: Origami and Solving Polynomial Equations” Julian Huddell & Maggie Lai, Tulane University