Recent Research Talks in the UTC Department of Mathematics Colloquium Series
Since 1999, the department has sponsored the Colloquium Series. This series provides both UTC math faculty as well as guest speakers the opportunity to highlight their most recent research in the field of mathematics. Below are colloquium talks that have been given recently.
Spring 2024
Fall 2023
Name: Dr. Ziwei Ma, Assistant Professor
Date: Friday, Sept. 29, 2023
Title: Estimation for Skew-Normal Based Stochastic Frontier Model
Time: 3:00pm
Location: Lupton 393
Abstract: Stochastic frontier models (SFMs) are popular econometric models for estimating the production frontier and measuring the technical efficiency of a firm. The classical SFM proposed using a normal distribution for the noise term $V_í$=Vi and a half-normal distribution for the one-sided inefficiency term $U_i$=Ui (Aigner et al. 1977; Meeusen and van Den Broeck 1977). Since the classical SFM suffers from the "wrong skewness" issue, leading to estimating full efficiencies of all firms in applications. Recently, Wei et al. (2021) proposed the skew-normal/half-normal SFM (SN-SFM) which provides a solution to the "wrong skewness" issue. In this talk, the basics of SFM and SN-SFM will be briefly introduced. Then the estimation approach for SN-SFM using the expectation conditional maximization algorithm is developed which outperforms the numerical MLE algorithm in both comprehensive simulation study and real data analysis. In the end, several potential directions of further improvement will be discussed.
Name: Dr. Xiunan Wang, Assistant Professor
Date: Friday, Oct. 6, 2023
Title: From HIV to SARS-COV2: Mathematical Modeling of Viral Dynamics
Time: 2:30PM
Location: Lupton 393
Abstract: In this presentation, we delve into the field of viral dynamics modeling within two distinct contexts: HIV and SARS-CoV-2. First, we investigate an HIV experiment that showcases the effectiveness of vectored immunoprophylaxis. Utilizing mathematical modeling, we unveil the concept of a backward bifurcation and explore its far-reaching implications. Additionally, we dissect the intricate interplay between antibodies and the virus, revealing a world of complex dynamics, including bistable behavior. Shifting our focus to SARSCoV-2, we introduce a reaction-diffusion model that characterizes viral infection within a heterogeneous environment. Our discussion encompasses the profound impact of diffusion, spatial heterogeneity, and incidence types on SARS-CoV-2 infection dynamics. This presentation provides a valuable opportunity for both students and mathematicians to explore mathematical modeling of viral dynamics.
Name: Stephanie Passmore (ASA) and JB Murphy (FSA)
Date: Friday, Oct. 20
Title: Want to be an Actuary?
Time: 2:00PM
Location: Lupton 393
Abstract: We will describe our individual jobs and typical day-to-day to experience. Then we will go over the Actuarial Department as a whole, emphasizing the three main areas: pricing, forecasting, and valuation. We will also talk more in depth on the topic of reserving. We will conclude with details of BlueCross’ Actuarial Development Program, speaking about study hours, increased pay for passing exams, and other benefits.
Name: Dr. David Walker
Date: Friday, Oct. 27
Title: Mathematical Topics in Quantum Computing
Time: 2:30PMAbstract: Quantum information science has recently emerged as an area of significant academic and commercial interest. This talk is presents a brief introduction to quantum computing and outlines areas in which mathematics is key in delineating quantum algorithms. Of particular interest are quantum algorithms for the hidden subgroup problem (HSP) for Abelian groups, which has applications in areas such as graph theory, numerical linear algebra, number theory, and cybersecurity. Shor's factoring algorithm is a well-known example that depends on solving the HSP using a quantum algorithm. Aspects of Shor's algorithm and its application to cybersecurity will be presented. Finally, the future prospects for practical and effective quantum computers will be considered.
Name: Dr. Satyan L. Devadoss
Date: Friday, Nov. 3
Title: Unfolding Regular Polytopes
Time: 3:30PM
Abstract: This talk is about a geometric mystery whose origins date back 500 years to the Renaissance master Albrecht Dürer, who first recorded examples of unfolded polyhedra. Recently, just a decade ago, it was shown that every unfolding of the Platonic solids was without self-overlap, yielding a valid net. We consider this property for all regular polytopes in higher dimensions, proving what works and puzzling over what doesn’t. This talk is heavily infused with visual imagery.
Name: Dr. Thien Le
Date: Friday, Nov. 10
Title: Connecting Epidemics on Networks and Mass-Action Models*
Abstract: The Black Death and COVID-19 stand as historic and contemporary reminders of the severe impact of infectious diseases, with millions of lives lost. Epidemic modeling is crucial because it helps us forecast outbreaks, manages our response, and ultimately save lives. Even though mass-action models are widely utilized in epidemic modeling, its homogeneously mixing assumption is often violated since individuals tend to interact with a small number of other people over time. This naturally leads to network models in studying epidemics, which is especially useful for studying sexually transmitted diseases. Despite extensive research on both network models and mass-action models, the relationship between them is still not well understood. We try to bridge the gap here by presenting a spreading method on networks and then mapping its spreading process to mass-action models. The proposed method is backed up by theoretical justification and simulation studies. Our discovery could pave the way for more research into network spreading processes.
*Joint work with Associate Professor Jukka-Pekka Onnela, Department of Biostatistics, Harvard T.H. Chan School of Public Health, Harvard University.
Name: Dr. Yu Jin
Date: Friday, Dec. 1
Title: Spatial Population Dynamics in Heterogeneous River Environments
Abstract: Natural rivers and streams are important habitats for aquatic species and other species that rely on them. The study of population persistence and spread in river ecosystems is key for understanding river population dynamics and invasions as well as instream flow needs. We develop process-oriented reaction-diffusion-advection equations that couple hydraulic flow to population growth and analyze the models theoretically and numerically to assess the effects of hydraulic, physical, and biological factors on population dynamics. We present a mathematical framework, based on persistence metrics such as the fundamental niche, the source and sink metric, the net reproductive rate and the principal eigenvalue of the associated eigenvalue problem to determine local and global persistence of a population in a spatially heterogeneous one-dimensional or two-dimensional river or river network. We establish asymptotic spreading speeds to understand biological invasions in the upstream and downstream directions in temporally and/or spatially heterogeneous river environments. Furthermore, we present a hybrid modeling approach to explicitly link the flow regime with ecological dynamics, which helps analyze the impact of river morphology on population persistence in a realistic river.
Spring 2023
Speaker: Mohammad Khan, Ph.D. student, Department of Mathematics
Date: Friday, February 3, 2023
Time: 2:00pm
Location: Lupton 393
Title: Numerical Evaluation of Wavenumbers of an Acoustic Wave Propagating in an Ice-Covered Ocean
Abstract: We consider acoustic wave propagation in a layered ocean waveguide covered by a thick ice cover. Standard separation of variables leads to a Sturm-Liouville problem in the cross-section of the waveguide. We are specifically interested in the two leading modes that are the separated solutions for the maximal eigenvalues. We consider the homogeneous waveguide. We prove the differentiability of the eigenvalues with respect to the frequency, the monotonicity of the eigenvalues with respect to the frequency, and the existence of the cut-off frequency. We compare these eigenvalues with the eigenvalues for the case of a waveguide with a free surface. To better understand the influence of global warming on ice covers, we study the change of these eigenvalues with respect to air temperature. Assuming that the speed of propagation varies within the given limits, we develop a numerical algorithm, based on the formalism for the layered media, that allows evaluating the minimum and maximum of the wavenumbers of the leading modes for a given continuous profile of the speed and the given values of Young's Modulus and ice thickness. After finding numerical results, we compare them with the results of the asymptotic considerations and find the simplified dispersion relations. We further consider the model of pack ice, a limiting case of thick ice. We also find the analytical, numerical, and asymptotic results for this limiting case. These results were compared with the results of the thick ice model. With the help of our results, we hope to develop the corresponding inverse problem methods for future work to further study the influence of global warming on ice covers.
Fall 2022
Speaker: Dr. Xiaoshu Sun
Post-Doctorate, University of Tennessee at Chattanooga
Date: Friday, December 2, 2022
Time: 3:30pm
Location: Lupton 393
Title: The numerical computation of Casimir energies and related spectral problems
Abstract. Computing the Casimir force and energy between objects is a classical problem of quantum theory going back to the 1940s. Since then, various approaches have been developed based on different physical principles, such as zeta function regularizations, stress tensors, and determinant of boundary layer operators. Most notably, the representation of the Casimir energy in terms of determinants of boundary layer operators makes it accessible to a numerical approach, but its mathematical derivation involves ill-defined path integrals.
Speaker: JB Murphy, Stephen Adams, Stephanie Passmore, and Jeremiah Ludwinski
Actuaries, Blue Cross Blue Shield
Date: Friday, November 11, 2022
Time: 2:45pm
Location: Lupton 393
Title: Want to be an Actuary?
Abstract. We will describe our individual jobs and typical day-to-day experience. Then we will go over the Actuarial Department as a whole, emphasizing the three main areas: pricing, forecasting and valuation. We will also talk about risk adjustment with some examples and outline its increasing impact due to the medical insurance industry no longer being allowed to rate on health status. We will follow up with the impacts of COVID and how it has affected pricing and forecasting. We will conclude with details of BlueCross' Actuarial Development Program, speaking about study hours, increased pay for passing exams and other benefits.
Speaker: Dr. Lan Gao, UTC Math Department
Date: Friday, November 4, 2022
Time: 3:30pm
Location: Lupton 393
Title: Predicting COVID-19 Outcomes During Pandemic via Analysis of Google Trends Data: A Statistical Deep Learning Study
Abstract: The still ongoing global outbreak of COVID-19 is affecting many countries throughout the entire world. The US is one of the most affected countries. Search engines like Google provide a useful near real-time indicator of public interest during a pandemic. The Google Trends data allows users to measure interest in particular search keywords across the United States, down to the city-level. We proposed a workflow with pre-processing procedure to test stationarity of time series data and then feed the inputs to two predictive models: a classical statistical method vector autoregressive model (VAR) and a deep learning neural network Long Short-Term Memory (LSTM). Performance of these two models is evaluated using four performance metrics. We will also discuss the reliability issues of Google Trend data and necessity of pre-processing procedure to remove seasonality.
Name: Dr. Ziwei Ma, Assistant Professor
UTC Math Department
Date: Friday, October 21, 2022
Time: 2:15pm
Location: Lupton 393
Title: Estimate parameters of COVID-19 Dynamics models by deep neural network approach
Abstract: In the talk, a deep neural networks (DNNs) approach to fit COVID-19 dynamics model is introduced based on recently developed computational packages. Consider the model involving the long COVID component or the concentration of the coronavirus in the environment, it is a challenge task to estimate the key parameters of those models in traditional numerical methods. We employed the feed-forward neural network structure and optimization algorithms to estimate the key parameters. The results indicate that the proposed methods provides better estimation of the parameters than the classical method.
Name: Dr. Xiunan Wang
Assistant Professor, UTC Math Department
Date: Friday, October 7, 2022
Time: 3:30pm
Location: Lupton 393
Title: Modeling Rabies Transmission in Spatially Heterogeneous Environments
Abstract: Spatial heterogeneity plays an important role in determining spatial patterns of rabies and the cost-effectiveness of vaccinations. In this talk, I will introduce a spatially heterogeneous dog rabies transmission model by using the $\theta$-diffusion equation, where $\theta$ reflects the way individual dogs make movement decisions in the underlying random walk. I will show the dynamics of the model in two cases: homogeneous and city-wild diffusion, discuss the impact of initial conditions on the steady-state solutions and the progressing speed of traveling waves, and present some interesting phenomena including an “active” interface between city and wild regions. At last, I will compare the efficiencies of different vaccination strategies.
Name: Tanner Smith
Ph.D. Student, University of Tennessee at Chattanooga
Date: Thursday, October 6, 2022
Time: 1:00pm
Location: Grote 317
Title: Optimization for a Sturm--Liouville Problem with the Spectral Parameter in the Boundary Condition
Abstract: We find an optimal mass of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. While previous work on the subject focused on a somewhat simplified model, we consider a more general S-L problem. We use the calculus of variations approach to determine a set of critical points of the corresponding functional - yet these “predesigns” themselves do not represent meaningful solutions. We additionally introduce a set of solvability conditions on the data of the S-L problem which confirm that these critical points do represent meaningful solutions we refer to as designs.