Recent Research Talks in the UTC Department of Mathematics Colloquium Series

Since 1999, the department has sponsored the Colloquium Series. This provides both UTC math faculty as well as guest speakers the opportunity to highlight their most recent research in the field of mathematics.

Past Colloquium Series Presenters & Abstracts

2026-2027 Academic Year

Mohandas Pillai

Date/Time: Fri., Sept. 18 at 3:30 p.m.
Location: Lupton 393
Title: Near soliton dynamics for the critical, two-equivariant Schrodinger map problem
Abstract: I will talk about work in progress with Ioan Bejenaru (UCSD), Daniel Tataru (UC Berkeley) regarding the critical, 2-equivariant Schrödinger map problem into the two-sphere. I will start with a result we proved in 2024, regarding the global existence of topological degree 2 solutions with energy close to that of the ground state solitons, along with a stability result for a more regular set of initial data. This motivates the question of the existence of infinite time relaxation in addition to infinite time singularity forming solutions. I will speak about work in progress regarding those questions.

Brian Choi

Date/Time: Fri., Sept. 25 at 3:30 p.m.
Location: Lupton 393
Title: Long-time continuum limits for twisted Schrodinger lattices
Abstract: This talk explores the long-time justification of Hamiltonian PDEs from a numerical analysis perspective, guided by complete integrability. Focusing on the discrete nonlinear Schrödinger equation with a phase twist, we synthesize Birkhoff coordinates and modified energies to establish polynomial-in-time bounds for the nonlinear approximation error, effectively bypassing the limitations of the Grönwall inequality.

Thien Le

Date/Time: Fri., Oct. 2 at 3:30 p.m.
Location: Lupton 393
Title: Coming Soon
Abstract: High-resolution temporal network data provide an increasingly detailed picture of how interactions change over time. Yet translating this wealth of information into reliable models of spreading processes remains challenging. We investigate this challenge using empirical contact networks from diverse real-world settings and compare spreading processes across different temporal resolutions. Our results show that hourly resolution often produces dynamics comparable to finer-resolution data, while daily observations can substantially distort spreading behavior. These findings provide practical guidance on collecting dynamic network data to study spreading processes.

Ayca Cetinkaya

Date/Time: Fri., Oct. 23 at 3:30 p.m.
Location: Lupton 393
Title: Building bridges between differential equations: The idea of transmutation
Abstract: In this work, we study a family of transformation operators for a specific differential operator with an integrable potential. We establish the existence of the transmutation kernel by using the method of successive approximations. We derive explicit integral representations for these operators on specified function spaces and analyze their properties.

Jin Wang

Date/Time: Fri., Oct. 30 at 3:30 p.m.
Location: Lupton 393
Title: Fluid-structure interaction: Modeling, simulation, and applications
Abstract: The interaction between fluid flows and immersed solid structures leads to nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. There are many numerical techniques currently available for computing fluid-structure interaction, but we will focus on methods of the immersed boundary type in this presentation. Starting from the original immersed boundary method, we will discuss a few improvements of the method as well as their applications. Following that, we will describe an extension of this computational approach to deal with immersed structures that occupy a nonzero volume and that satisfy detailed constitutive laws. We will illustrate the application of these methods through several numerical examples.

Will Erickson

Date/Time: Fri., Nov. 13 at 3:30 p.m.
Location: Lupton 393
Title: Random shuffles with a fixed shape
Abstract: A shuffle is a rearrangement of the integers 1,...,n, and its "shape" is a partition of n which measures the longest unions of increasing subsequences. This notion of "shape," as a global statistic on shuffles, is nearly 100 years old, and is a linchpin of modern algebraic combinatorics; before this year, however, the local effect of shape on shuffles had not yet been studied. That is, for a random shuffle with some fixed shape, what is the probability that the number i occupies position j? In this talk, we share our solution to this problem for three families of shapes ("hooks," "two-row," and "rectangles"), focusing on the surprising visual patterns revealed by the probability formulas. The main souvenir of the talk will be a glimpse of the remarkable RSK correspondence (where the "K" is Donald Knuth), which is the key tool in our technique. The audience should also be prepared for the unexpected appearance of a famous integral from Calculus II. We conclude with several open questions, some of which would make good research problems for interested undergraduates

2025-2026 Academic Year

Vladimir Vladicic

Date/Time: Fri., Sept. 5 at 2:30PM
Location: Lupton 393
Title: Inverse spectral problems: From Ambarzumian’s theorem to theorem of uniqueness
Abstract: Inverse spectral theory its roots back to classical results such as Borg’s two spectra theorem and Ambarzumian’s theorem, which provide foundational insights into how the spectrum of a Sturm-Liouville operators determines its potential.
In his famous paper ”Uber eine Frage der Eigenwerttheeorie” from (1929) Ambarzumian describes the exceptional case in wich the spectrum of boundary value problem generated with Sturm-Liouville operator under Neumann boundary conditions uniquely determines potential. In general, the specification of the spectrum does not uniquely determined potential.
Borg(1946) proved Theorem of uniqueness from two spectra of the boundary value problem defined with Sturm-Liouville operator under Robin boundary conditions.
In addition to this result, many mathematicians contributed to the determination potential functions or proved the uniqueness of the potential based on other spectral characteristics like spectral function, spectral data or Weyl function and we can say that inverse problem for Sturm-Liouville differential operators is fully solved.
One of the most important direction for further research was BVPs generated with a Sturm-Liouville type differential equation with a constant delay and one of the first resulat was given by Freiling and Yurko (2012) and they proved Ambarzumian type theorem for differential operators defined with Sturm-Liouville equation with constant delay under Dirichlet-Neumann boundary conditions from two spectra. Compared with Ambarzumian’s theorem it could be expected that Borg-type inverse problem for this BVP will be more complicated than in the case of classical Sturm-Liouville operator. In several papers authors solve Borg-type inverse spectral problems for this class of the boundary value problems and they give complete answer for which value of the delay Theorem of uniqueness from two spectra is true or not true.
There has recently been increasing interest in boundary value problems generated by Sturm–Liouville operators with more than one constant delay. In the case with two constant delays an attempt was made to answer the question of how many spectra are needed for Ambarzumian’s theorem to be correct, but until now we don’t have answer. Also, we don’t have complete
answer when potential function is unique ordered.
The focus of this research is on the boundary value problems generated with differential equation Sturm-Liouville-type two constant delay. The Ambarzumian type theorem for operator with two constant delays from four spectra will be proven and a partial answer to the question of when the Theorem of uniqueness is true and when it is not will be given.

Ayca Cetinkaya

Date/Time: Fri., Sept. 12 at 2:30 p.m.
Location: Lupton 393
Title: From difference to differential equations: Eigenvalue problems via Prufer transformation
Abstract: In this talk, I will present a parallel approach for eigenvalue problems in both discrete and continuous settings. Starting from second-order difference equations and then moving to second-order differential equations, I will show how the Pr¨ufer transformation translates these problems into systems of first-order linear equations. This transformation not only reveals the underlying structure but also provides a natural framework for both analytical insights and numerical techniques for eigenvalue estimation.

Ziwei Ma

Date/Time: Fri., Sept. 19 at 3:20 p.m.
Location: Lupton 393
Title: Some work on "wrong skewness" problem in stochastic frontier model
Abstract: The stochastic frontier model (SFM) is an econometric approach used to estimate production or cost efficiency by separating random noise from inefficiency in observed output. The main idea of SFM is to distinguish between random shocks and systematic inefficiency, which makes SFM is one of the most powerful tools for efficiency analysis. While like most other models, it has limitations, like being sensitive to the distributional assumptions and bias efficiency estimates by misspecification of the production function. But the "wrong skewness" problem will lead to the whole result being invalid. In this talk, some recent work on handling the "wrong skewness" problem will be presented, including generalized models of random noise, estimation algorithm improvement. In the end, several further directions of further improvement will be discussed.

Thien Le

Date/Time: Fri., Oct. 3 at 3:20 p.m.
Location: Lupton 393
Title: Universally consistent tests for the graph of a Gaussian graphical model
Abstract: The Gaussian graphical model is widely used to capture the joint distribution of multiple random variables, with its induced graph offering both interpretability and improved estimation efficiency. They play a central role in applications such as inferring gene networks in genomics, mapping brain connectivity in neuroscience, and modeling dependencies among financial assets. Although estimation methods are well developed, tests for whether a proposed graph is adequate remain limited. This talk introduces new goodness-of-fit tests that are computationally simple yet theoretically rigorous. We propose a simple plug-in test and an enhanced version that achieves universal consistency, both following a Gumbel distribution under the null. Simulations confirm the procedures have the correct size under the null and strong power under alternatives. An application to COVID-19 data illustrates their value in selecting graph structures for efficient estimation.

Mohandas Pillai

Date/Time: Fri., Oct. 17 at 3:30 p.m.
Location: Lupton 393
Title: On the existence and asymptotics of solitions on intersecting 3-branes
Abstract: This work in progress considers a system of 7 Lie(SU(2))-valued nonlinear PDEs in 6 Lie(SU(2)) unknowns which arose from certain string theory considerations in a physics work of Cottrell, Hashimoto and the speaker from 2014 (CHP 14). The aforementioned work presented some computations that would suggest that there exists a two parameter collection of soliton solutions to the aforementioned system of equations. However, a mathematically rigorous proof of existence of these solutions was not given. Denoting the two soliton parameters by (a,v), the aforementioned work also presented the leading order behavior of the supposed solitons as a approaches zero. On the other hand, based on a work of Mintun, Polchinski, and Sun from 2014, it was conjectured that the supposed soliton solutions should degenerate as a approaches infinity. However, no precise large a asymptotics or heuristics regarding how exactly these solitons should degenerate were given in CHP 14. A later work of Cottrell, Hashimoto, Pettengill, and the speaker (CHPP 14) studied a problem in supergravity whose solutions are supposed to correspond to the solitons of (CHP 14). The work (CHPP 14) presented some heuristics regarding approximate solutions to a linearization of a nonlinear PDE. On the other hand, no rigorously proven asymptotics of the solutions to the nonlinear problem were presented, and no precise details of how exactly the solitons of (CHP 14) are supposed to degenerate as a approaches infinity were presented. These works then leave open the problem of rigorously establishing the existence and the large a asymptotics of the soliton solutions of (CHP 14). The current work of the speaker is making progress towards solving these problems. In particular, one objective of the current work is to obtain, with proof, the large a asymptotics of the solitons from (CHP 14), thereby rigorously proving a precise form of the conjecture of (CHP 14) regarding the large a asymptotics.

Xiunan Wang

Date/Time: Fri., Oct. 24 at 2:30 p.m.
Location: Lupton 393
Title: Impact of water flow on schistosomiasis transmission: Insights from a reaction-advection-diffusion model
Abstract: Water flow plays a crucial role in disease transmission; however, it is often overlooked in traditional models of schistosomiasis. In this presentation, we use a reaction-advection-diffusion model to capture the complexities of water flow, seasonality, and spatial variation in schistosomiasis dynamics. We obtain the threshold-type result in terms of he basic reproduction ratio and show how faster water flows can actually help reduce the spread of the disease, offering a clear explanation for why schistosomiasis is more revalent in areas with slow-moving waters. Our findings emphasize the importance of incorporating these factors into disease modeling and suggest new strategies for controlling chistosomiasis in regions where it remains a significant public health threat.

Brian Choi

Date/Time: Fri., Nov. 7 at 2:30 p.m.
Location: Lupton 393
Title: Excitation thresholds and breather dynamics in multi-dimensional nonlocal lattices
Abstract: This talk surveys new results on discrete breathers in multi-dimensional lattices with long-range (nonlocal) coupling. Using a variational framework and concentration–compactness, I obtain an exact threshold condition that ties together the lattice dimension, the strength of the nonlinearity, and the nonlocality, yielding a sharp mass-threshold dichotomy: no positive threshold in the mass-subcritical regime and a strictly positive threshold at and above criticality. In the anti-continuum limit, I show uniqueness of ground states and derive analytic formulas that quantify the excitation threshold. Then, I establish sharp spatial decay of ground states and identify a qualitative change in dispersive ime decay at α=1, corroborated by numerics. The results extend the nearest-neighbor DNLS theory to genuinely nonlocal lattices and clarify when ocalization persists versus when dispersive dynamics dominate.

Wilhelm Treschow

Date/Time: Fri., Nov. 14 at 3:30 p.m.
Location: Lupton 393
Title: Inverse scattering theory for embedded eigenvalues: A Marchenko approach
Abstract: In this talk I will explore an approach to apply inverse scattering theory of Schrödinger operators to reconstruct the potential from the scattering data at embedded eigenvalues. I begin with an overview of embedded eigenvalues and why they are delicate (lying inside the continuous spectrum), as well as my previous results on the persistence of such eigenvalues under perturbations of the potential. This previous work led to a natural inverse question: Given certain information of the embedded eigenvalue, what can we say about the potential? In an attempt to answer this question, I will proceed with providing a motivating example and then outline a simpler one-dimensional setting and review the essentials of inverse scattering on the line, deriving the Levitan-Gelfand-Marchenko integral equation. I then explain the additional difficulties associated with the presence of embedded eigenvalues in a slightly more general setting and how we are aiming to resolve those issues

Hanae El Ouardani

Date/Time: Fri., Jan. 23 at 3:30 p.m.
Location: Lupton 303
Title: Evolving Behavioral Dynamics and Environmental Risk in Cholera Epidemics
Abstract: Cholera, a water-borne infectious disease, continues to be a significant public health problem in numerous low and middle-income countries, where insufficient water and sanitation systems, coupled with pronounced climatic seasonality, facilitate frequent and often severe outbreaks. Therefore, it is crucial to understand how environmental risks and human decision-making mutually increase disease burden in our society. In this work, we develop and analyze a seasonally driven cholera model integrating a human-to-human direct transmission and an aquatic bacterial reservoir, enabling indirect transmission with behavioral dynamics. Seasonal fluctuations in precipitation, temperature, and hydrological conditions are shown via regularly changing transmission and environmental factors, reflecting recurring alterations in bacterial survival and exposure risk throughout the year. Human behavior is integrated through an evolutionary game-theoretic (EGT) framework, wherein individuals decide protective and non-protective strategies and adjust their choices by emulating strategies that provide greater perceived benefits. The interaction between behavior and transmission influences the effective force of infection from the environment and significantly changes the magnitude, duration, and temporal dynamics of outbreaks. We calculate the basic reproduction number as well as the corresponding disease-free equilibria and examine how the interaction between seasonal fluctuations and behavioral adaptation influences long-term dynamics. Our findings indicate that the swift and widespread adoption of protective behaviors, combined with moderate vaccination and prompt treatment, can significantly reduce the average incidence and the magnitude of the seasonal peak. Conversely, elevated prevention costs or inadequate risk perception confine the system in a sustained high-burden state, despite the availability of medical interventions. Our model outcomes emphasize that effective cholera control in seasonal environments requires improvements in water and sanitation infrastructure, alongside policies that align individual incentives with collective benefits, such as subsidies for household water treatment, targeted risk communication, and vaccination strategies informed by behavioral insights. We expect that those results will assist policymakers in formulating a comprehensive strategy to mitigate waterborne illnesses.

Dr. Michelle Cadieux

Date/Time: Wed., Feb. 4 at 3:30 p.m.
Location: Lupton 393
Title: Engaging the masses: Motivating attendance and participation in large classes
Abstract: Engaging students in a large class can be challenging. It’s hard enough just getting students to attend in-person when the new norm is for lectures to be recorded and posted online. This presentation will explore strategies for motivating students to not only attend but come prepared and actively participate. It will highlight how thoughtful course design, clear expectations, and audience participation can build community and turn lectures into something students want to show up for. In addition, we will discuss managing asynchronous online classes which have their own unique struggles with student engagement. We will explore using low-stakes activities that invite students into the learning process and help them feel a sense of belonging and ownership, reminding students that they play a key role in their own academic journey online.

2024-2025 Academic Year

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2023-2024 Academic Year

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2022-2023 Academic Year

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2021-2022 Academic Year

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2020-2021 Academic Year

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2019-2020 Academic Year

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2018-2019 Academic Year

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2017-2018 Academic Year

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2016-2017 Academic Year

Meg Kiessling, Angelique Ramnarine, Tracy Hughes, and Lani Gao

Title: Online Course Development

Abstract: As the first generation of teaching online courses in mathematics, we will share our experience and thoughts in developing online math courses at different levels. Strategies for effective design, course structure and content, technical needs and resources, how to create video lectures, homework, quiz and exams etc. will be shared. Quality Matters standards and direction for future online course development will also be discussed.

Lin Mu

Title: Weak Galerkin Finite Element Methods and Numerical Applications

Abstract: Weak Galerkin FEMs are new numerical methods that were first introduced by Wang and Ye for solving general second order elliptic PDEs. The differential operators are replaced by their weak discrete derivatives, which endows high flexibility. This new method is a discontinuous finite element algorithm, which is parameter free, symmetric, symmetric, and absolutely stable. Furthermore, through the Schur-complement technique, an effective implementation of the WG is developed. Several applications of weak Galerkin methods will be discussed in this talk

Lingju Kong

Title: On a quasilinear biharmonic equation

Abstract: In recent years, fourth order nonlinear differential equations have become increasingly popular due to their possible applications in the fields of image and signal processing, nuclear physics, and engineering. In this paper, we study the existence of positive radial solutions of the boundary value problem of the quasilinear biharmonic equation. Using the function g(t) in the problem, our results are presented in three cases in terms of different value of the expression ∫k(T,s)g(s)ds, where k(T,s) is explicitly defined in the paper. The function g(t) itself may be nonnegative, nonpositive, or sign-changing. For all three cases, explicit lower and upper bounds are obtained for the solutions.

Hong Qin

Title: Network models of cellular aging and their applications

Abstract: Biological aging is a complex phenotype with many genes involved, and is characterized by an exponential increase of mortality rate. A probabilistic gene network model will be presented to demonstrate that cellular aging can be an emergent property of gene networks. Results on empirical network models and simulation-based fitting will be presented. Methods will be presented to infer changes of gene interactions during aging by comparing viability of cells with mutations in gene pairs with special properties. Open mathematical and computational challenges will be discussed.

Billy Jackson

Title: Those who teach the teachers: Knowledge growth for mathematics teacher educators

Abstract: In this talk, we will examine what knowledge is required of mathematics teacher educators. I begin with some audience participation by asking members to complete two tasks: one at the elementary level and one at the secondary level. We will then have a discussion about what kinds of knowledge were required to complete these tasks. This will help us to begin to unravel what kinds of knowledge teachers need to have. Next, we will consider what kinds of knowledge we would need to enact the tasks with teachers as teacher educators. This activity will give rise to a concept that my colleagues and I call mathematical knowledge for teaching future teachers (MKTFT). I will review the existing models for mathematical knowledge for teaching in the literature and compare and contrast them with our model of MKTFT. The talk should have some significance for everyone in the math department as most of us teach preservice teachers at some stage: in addition, there will be a small flavor of dynamical systems modelling present as MKTFT is of a fractal nature as we shall see.

Lakmali Weerasena

Title: Approximation algorithm for the multiobjective set covering problem

Abstract: The multiobjective set covering problem (MOSCP), one of the challenging multiobjective combinatorial optimization problem, has received limited attention in the literature. In this study, an algorithm is presented to approximate the solution set (Pareto set) of the MOSCP. The proposed algorithm applies a local branching approach on a tree structure and is enhanced with a node exploration strategy specially developed for the MOSCP. The approach of this algorithm is to partition the search region into subregions based on the neighbors of a reference solution. Numerical experiments are conducted to check the performance of the proposed algorithm. Results on a performance comparison with benchmark algorithms from the literature show that the new algorithm is competitive.

Billy Jackson

Title: A brave new world for mathematics teacher education programs: The new AMTE standards for mathematics teacher preparation

Abstract: Have you ever wondered about what mathematics content knowledge that K-8 teacher candidates should possess? How about what the mathematics content courses for K-8 teacher candidates should look like? If you answered yes, then I have just the place for you to start looking for answers! The Association of Mathematics Teacher Educators (AMTE) has just
released a new document entitled Standards for Preparing Teachers of Mathematics. Just as the Common Core provides benchmarks for PreK-12 mathematics classrooms, so do the AMTE standards present benchmarks for programs in teacher education in producing highly qualified and effective teacher candidates. In this talk, we will examine what the AMTE Standards have to say about the mathematics content courses for K-8 teachers: i.e. what the design of such courses should look like, appropriate content for K-8 teacher candidates, appropriate models of instruction in these courses, etc. Discussions and consideration around these courses and the Standards themselves are vital for mathematics departments to have now as in the near future accreditation and licensing requirements of both future teacher candidates and teacher education programs are certainly most likely to be based upon the Standards.

Thandi Klingsbell

Title: A comparison study of statistical modeling strategies for predicting length of hospital stay in patients with and without enhanced recovery after surgery protocol

Abstract: Enhanced Recovery After Surgery (ERAS) protocols are programs incorporating multimodal interventions in the peri-operative period to expedite recovery. ERAS has been implemented in a variety of surgical specialties. Recent studies show that ERAS programs have shortened the length of hospital stay and reduced complication rates. In this prospective cohort study, 177 patients undergoing colon resection from 2011-2014 at Erlanger Hospital were compared with 68 patients who followed the implementation of ERAS from 8/2015 - 7/2016. Multiple statistical models such as Generalized LinearModels and Cox Regression models were applied and compared, to further investigate how ERAS affects the length of hospital stay with clinical covariates. This study has been conducted in collaboration with the UT College of Medicine and Erlanger Hospital.

Feng Bao

Title: High performance computing for neutron scattering problems

Abstract: We present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against omputational
models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. We use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, and refine first principles calculations to better describe the experimental data.

Leigh Halliwell

Title: Actuaries and Kronecker's delta

Abstract: If probability lays itself out in a “probability space,” what is the geometry of that space? The basics of tensor algebra and calculus (K’s δ) will be introduced, and through them idea of the probability density of a vector space will be expressed. At the least, tensor geometry should help actuaries to understand and to imagine statistical relations, especially regarding Maximum Likelihood estimation. Even better, actuaries who hook into mathematical physics may expect to reel in big fish.

Matthew Alger

Title: Dimensionality reduction and regularization regression methods with application to prostate cancer study

Abstract: In this study, we compare several statistical machine learning methods that can be used to relate prostate cancer to potential clinical predictors in prostate cancers study, where the number of variables is large (usually is far more than the number of samples). We applied Ordinary Least Squares Regression (OLS), Ridge Regression(RR), Elastic Net(EN), Principal Component Regression (PCR) and Partial Least Squares Regression (PLS) to a prostate cancer data with 97 patients. The performance of all these methods and the advantages of each method will be discussed.

Xin Dang

Title: Robust and efficient boosting method using the conditional risk

Abstract: Well-known for its simplicity and effectiveness in classification, AdaBoost, however, suffers from overfitting when class-conditional distributions have significant overlap. Moreover, it is very sensitive to noise that appears in the labels. This article tackles the above limitations simultaneously via optimizing a modified loss function (i.e., the conditional risk). The proposed
approach has the following two advantages. (1) It is able to directly take into account label uncertainty with an associated label confidence. (2) It introduces a ``trustworthiness" measure on training samples via the Bayesian risk rule, and hence the resulting classifier tends to have finite sample performance that is superior to that of the original AdaBoost when there is a large overlap between class conditional distributions. Theoretical properties of the proposed method are investigated. Extensive experimental results using synthetic data and real-world data sets from UCI machine learning repository are provided. The empirical study shows the high competitiveness of the proposed method in predication accuracy and robustness when compared with the original AdaBoost and several existing robust AdaBoost algorithms.