Mathematics Colloquium

Feb. 06: Dr. Youssef Raffoul
Title: Analysis of Functional and Neutral Differential Equations Via Lyapunov Functionals
Abstract: We employ Lyapunov-type functions and functionals and obtain sufficient conditions that guarantee the boundedness and the exponential decay of solutions, stability, and exponential stability of the zero solution in nonlinear delay and neutral differential systems. The theory is illustrated with several examples.

Feb. 13: Dr. Reza Bidar
              Title: Estimates for the norm of the derivative of Lie exponential map for connected Lie groups.

Feb. 15 (Thursday): Dr. Alessandra Costantini

         Title: Rees algebras: an algebraic tool to study singularities. 

        Abstract: How many tangent lines does a plane curve have at a given point? And how can we find the implicit equations of a parametric curve? These seemingly unrelated problems from algebraic geometry can be both solved using tools from abstract algebra, through the notion of Rees algebras.

In this talk, I will discuss the fundamental role of Rees algebras in the study of commutative rings and of the singularities of algebraic varieties. I will then give an overview of how one can use methods from algebraic combinatorics to understand the algebraic properties of Rees algebras. 

Feb. 20:  Dr. Thanh Thai Nguyen
      Title: Symbolic Powers: Degree Bounds, Containment Problem, and Beyond

     Abstract: One of the fundamental questions in polynomial interpolation is the following: What is the smallest degree of a homogeneous polynomial that vanishes to order at least m on a given set of points? This question is wide open and the answer to it has many applications and implications in many other fields. Even lower bounds for such degree play a crucial role in many contexts, such as Nagata’s counterexamples to Hilbert’s fourteenth problem, or the Schwarz exponent in complex analysis to name a few.

     A classical result by Zariski and Nagata tells us the set of such polynomials is precisely an algebraic object called the m-th symbolic power of the defining ideal I of the set of points. Symbolic power is one of the central objects which has a long history in commutative algebra. To study the above interpolation question, one can study containment between symbolic powers and ordinary powers of I. My talk will be an introduction to this subject. I will present some recent progresses on studying the lower bounds on the degree and containment problem based on our joint projects with Sankhaneel Bisui, Eloísa Grifo and Huy Tài Hà. I will also discuss some further related research directions.  

Feb. 27: Dr. Alexander Sistko
          Title: An Introduction to Representation Theory over the Field with One Element 

Abstract: To any finite quiver Q, we may associate its category of finite-dimensional representations over the so-called "field with one element" F1. This category acts like a combinatorial degeneration of the more familiar versions over fields, and in particular, it admits a well-defined Hall algebra. In this talk, we discuss recent progress towards understanding this category and its Hall algebra. In particular, we outline a recent result which stratifies finite connected quivers by the asymptotic growth of their nilpotent indecomposable F1-representations. Time permitting, we will also discuss open problems, future directions of research, and other instances of representation theory over F1.   

Mar. 12: Dr. Jim Albert, Emeritus Professor, Department of Mathematics and Statistics, Bowling Green State University (Host: Tessa)
      Title: Sports Analytics and Catcher Framing in Baseball

      Abstract: Sabermetrics, the search for objective truth in baseball, is currently popular among MLB teams.  This talk focuses on how one measures catcher framing, catching a ball in such a way as it looks like the pitch lands within the strike zone.  We review runs expectancy, the runs value of plays and pitches, and how one measures the true strike zone.  Called strikes depend on many variables such as the pitcher, catcher and umpire, and by use of a statistical model, one can measure the effect of the catcher.  By use of this methodology, It is now possible to rank the best catcher framers in baseball.

Mar. 14 (Thursday): Dr.  Jeff Neugebauer, Eastern Kentucky University (Host: Islam)
Title: p-periodic solutions of a q-integral equation with finite delay

Abstract: A Volterra type integral equation with a finite delay is considered on a discrete nonadditive time scale domain q^{N_0}. The existence of periodic solutions of this equation, which we call a q-integral equation, are shown employing the contraction mapping principle and a fixed point theorem due to Krasnosel’skii.

Apr. 02: Dr. Adam Waterbury, Denison University (Host: Matt Wascher)
Title: Large Deviations for Empirical Measures of Self-Interacting Markov Chains 

Abstract: Self-interacting Markov chains arise in a range of models and applications. For example, they can be used to approximate the quasi-stationary distributions of irreducible Markov chains and to model random walks with edge or vertex reinforcement. The term self-interacting Markov chain is something of a misnomer, as such processes interact with their full path history at each time instant, and therefore are non-Markovian. Under conditions on the self-interaction mechanism, we establish a large deviation principle for the empirical measure of self-interacting chains on finite spaces. In this setting, the rate function takes a strikingly different form than the classical Donsker-Varadhan rate function associated with the empirical measure of a Markov chain; the rate function for self-interacting chains is typically non-convex and is given through a dynamical variational formula with an infinite horizon discounted objective function. This is based on joint work with Amarjit Budhiraja and Pavlos Zoubouloglou.

Apr. 16: Math Clinic Presentation of Jungmi McBride( Applied Mathematics Graduate Student)
Title: Difference Equation SIR model for Spread of Disease

Abstract:  In this project, we will investigate linearizing non-linear system and add perturbation to study the equilibrium solution. We will begin this by observing the prey and predator model, SI model, and SIR model.

Apr. 23: Dr. Marina Mancuso (ASU)

Title: Mathematical Modeling of Infectious Diseases

Abstract: This talk will discuss two applications of mechanistic mathematical modeling on infectious disease dynamics. The first part of the talk introduces a mathematical model for COVID-19, specifically designed to assess the impact of vaccine-induced, cross-protective efficacy of COVID-19 transmission in the United States. We present conditions for achieving vaccine-derived herd immunity and results from global sensitivity analysis under different transmissibility and cross-protection scenarios.

The second part of the talk relates to modeling West Nile Virus (WNV), which is the most common vector-borne disease in the continental US.

The model includes time and temperature dependence on demographic and epidemiological processes, and considers time-since-infection structure for vector and host populations. We describe how we connect experimental infection and epidemiological data to infection-age dependent processes, and parameterize the model to human case data. We further show a range of scenario projections under climate change to quantify the increased risk and variability for future WNV prevalence.

This talk will be accessible to graduate students and undergraduate students with familiarity of differential equations.

Jan. 19: Yafan Guo (University of Kentucky)

 Approximate Tolerance Intervals for Semiparametric Regression Models

Jan. 24: Dr. Thilini Jayasinghe (Wittenberg University)

 Regression models using the LINEX loss to predict lower bounds for the number of points for   approximating planar contour shapes and LINEX loss to fit SIR model

Jan. 31: Mr. Yanxi Li (University of Kentucky)

Some Modeling Considerations Involving the Exponentially-Modified Gaussian (EMG) Distribution

Feb. 07:  No Colloquium

Feb. 14:  No Colloquium

Feb. 21:  Paul Eloe (UD)
                Maximum and anti-maximum principles in neighborhoods of simple eigenvalues

Feb. 28:  Dr. David Sivakoff (OSU), Host: Matthew Wascher (UD)

Mar. 07:  Ying-Ju Chen (Tessa), Jun Li, George Todd, Matthew Wascher (Facilitator Aparna Higgins)

                Exploring ChatGPT

Mar. 21: Kyle Helfrich (UD)

               Applications of DNNs

Mar. 28:  Jun Li (UD)

               Isotopy of the Base Class of a Ruled 4-Manifold

In April we have Math Clinic Presentations by Graduate Students (30 mins each)

Apr. 04:  Serge AlHalbi (Math Clinic Presentation)

Apr. 11:  Charles Destefani (Math Clinic Presentation)

Apr. 18:  Soulayma Saba and Charbel Al Bacha (Math Clinic Presentations)

Apr. 20: Special Colloquium by Heshan Aravinda Pathirannehelage

  Discrete Log-Concave Distributions, Properties, and Applications

Apr. 25:  1) Challita Jabbour and 2) Ibrahim Guediri (Math Clinic Presentations)

               3) Special Colloquium at 5:00 PM 

                 Speaker: Richard Buckalew

                From the cell cycle to the redistricting cycle, feedback mechanisms in complex systems lead to emergent dynamics

Apr. 27: Special Colloquium at 3:35 pm in SC 323

Speaker: Nur Saglam

Title: Geography & Botany Problem of Symplectic 4-Manifolds

Apr. 28 (Fri)  Sharmina Yasmin and Mohammed Abdulaziz Almalki (Math Clinic Presentations)

May 08: Special Colloquium at 3:30 in SC 323

Speaker: Tavish Dunn

Bio: Dr. Dunn received his B.S. degree from California Lutheran University. In 2021, he received his PhD in mathematics from Baylor University. For the past two years, he has worked at Oxford College of Emory University as a Visiting Assistant Professor. His research interests are in topology and dynamical systems.

Title: Properties of Generalized Inverse Limits

May 10: Special Colloquium at 3:30 in SC 323

Speaker: Mohammad Reza Bidar

Title: RESEARCH PRESENTATION ON BLOCKING PROBLEMS AND THE DERIVATIVE OF THE EXPONENTIAL MAPS IN CONNECTED LIE GROUPS

May 11: Special Colloquium by Mark Batell from 2:45--3:45 PM in SC 323
            Title: The Descending Chain Condition On Primitive Ideals