Graduate Programs Showcase

Interested in one of our graduate programs?
Join us ONLINE
Saturday, October 24 from 10 am - 12:30
for a sneek peek into your next best decision.

Schedule:
10 am - Welcome Remarks
10:10 - 10:40 am - Student Panel
10:45 - 11:15 am - Research Presentations
– Math Room
– Math Ed Room
11:20 am - 12:10 pm - Meet the Advisors
12:15 - 12:20 pm - Final remarks and slide show
Students in a math class

Student Focused

We have a wide offering of general education courses designed to prepare you to major in Business and STEM (Science, Technology, Engineering, and Mathematics) fields.

Current Faculty Research

Math Happenings

students in a computer classroom

Bachelor of Science in Data Science now available!
Old Main staircase

Promotion from Associate Professor to Professor

Suho Oh

Old Main stairway

Promotion from Assistant Professor to Associate Professor & Tenure

Hamilton Hardison and Cody Patterson

Closeup of LBJ statue face

Promotion from Associate Professor of Instruction to Professor of Instruction

Bikai Nie and Amanda Walker

UAC Arch

Promotion from Assistant Professor of Instruction to Associate Professor of Instruction

Pritha Chakraborty, Jaroslaw Jaracz and Jackson Rebrovich

Students walking up the quad toward a statue of stallions

Promotion from Lecturer to Assistant Professor of Instruction

Hyun Chul Jang, Yichen Ma, Amy Lawrence-Wallquist, and Le Tran

@TXST Math

Upcoming Events

Expand Event List
– until Oct. 23
add to calendar
Location:
DERR 238; 238
Cost:
Free
Contact:
Illona Weber
ih10@txstate.edu
Campus Sponsor:
Department of Mathematics
Math CATS is here to assist in almost all MATH courses for free!  If you're intimidated by the subject, come in and let's problem solve together.  Tutors are here to help reiterate, reinforce and help you relate to the content you heard in lecture. NO APPOINTMENT NEEDED! Click here for more information
more about event
–
add to calendar
Location:
Online via Zoom
Cost:
Free
Contact:
Xiaoxi Shen
rcd67@txstate.edu
Campus Sponsor:
Department of Mathematics
Dr. Chuyan Li - University of South Carolina
Structure-Aware Scientific Machine Learning for Personalized Digital Twins: From Personalized Biomedical Inference to Reliable Neural Network Solvers for Nonlinear PDEs
Abstract: Understanding complex dynamical systems from sparse, heterogeneous data requires models that learn effectively while respecting the mathematical structures governing their evolution. In this talk, I present a structure-informed scientific machine learning research program spanning personalized health inference and reliable neural solvers for nonlinear PDEs.
First, I introduce a personalized graph-PDE framework for modeling the spatiotemporal progression of Alzheimer’s disease from longitudinal neuroimaging data such as sMRI, PET, and resting-state fMRI. The model represents 68 brain regions as nodes in a patient-specific functional-connectivity graph and uses a low-rank representation to capture individual deviations from population-level connectivity. It couples amyloid-β, tau, neurodegeneration, and cognitive decline through local interactions and network-mediated propagation. To enable identifiable parameter inference from sparse longitudinal data in this nonlinear model, I develop a hierarchical inference strategy and homotopy regularization. When applied to 1,891 participants from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), the model improves the prediction of future biomarker trajectories over homogeneous and standard clinical or neuroimaging benchmarks, with gains of up to 9.73 percentage points for individuals whose brain networks differ substantially from the population norm.
Second, scalable personalized mechanistic models require accurate forward simulation and parameter inference for nonlinear, multiscale PDEs. Using thermodynamically consistent phase-field systems as a testbed, I develop methods that improve both where neural solvers allocate computational effort and how they are optimized. Energy-dissipation-rate-guided adaptive sampling (EDRAS) targets regions with high local energy dissipation where interfacial evolution occurs, rather than refining solely where the PDE residual is large. For Allen–Cahn equations, EDRAS reduces relative mean-square error by up to a factor of six compared with residual-based refinement and is more likely to identify high-error regions. I also develop random projection neural networks (RPNNs), which fix randomly generated hidden features and determine output coefficients through deterministic nonlinear least squares, enabling second-order optimization. For the fourth-order Cahn–Hilliard system, a scaled auxiliary-variable formulation, separate random-feature spaces, adaptive sampling, and domain decomposition yield relative $L^2$ errors as low as $8.64x10^{−4}$, outperforming matched deep-PINN baselines by nearly three orders of magnitude.
Together, these works advance interpretable, personalized mechanistic digital twins underpinned by reliable scientific machine learning. Click here for more information
more about event
–
add to calendar
Location:
DERR 328; 328
Cost:
Free
Contact:
Geonhee Cho
gunheecho@txstate.edu
Taeik Kim - TXST PhD Student
Brownian Motion on a Riemannian Manifold: From Quadratic Variation to the Laplace–Beltrami Operator
Abstract: Brownian motion in Euclidean space can be described by continuous paths with independent Gaussian increments, but this familiar definition does not transfer directly to a curved space: points on a manifold cannot be added to random vectors, tangent spaces change from point to point, and zero Itô drift is not preserved by nonlinear coordinates. In this talk, I will begin with the quadratic variation of Euclidean Brownian motion and use the example (\int B_t,dB_t) to motivate the Itô integral, Itô’s formula, and the distinction between Itô and Stratonovich representations. This leads to the infinitesimal-generator characterization of Euclidean Brownian motion by (\frac12\Delta), which suggests the intrinsic definition of Brownian motion on a Riemannian manifold through (\frac12\Delta_g). I will then construct this process using horizontal stochastic development on the orthonormal frame bundle. The main calculation shows that the horizontal sum-of-squares operator projects to the Laplace–Beltrami operator. I will conclude by briefly describing how coupled Brownian motions and their distance processes can be used to probe curvature and other geometric information. The necessary ideas will be introduced briefly as they arise. No prior background in stochastic calculus is required.
–
add to calendar
Location:
Zoom
Cost:
Free
Contact:
Vera Ioudina
vi11@txstate.edu
Campus Sponsor:
Department of Mathematics
Grouped Spatio-Temporal Autoregressive Modeling: A Case Study of Human Immunodeficiency Virus and Substance Use Disorder in South Carolina 
Ting Fung Ma
University of South Carolina
Abstract: Spatiotemporal data often exhibit dependence across connected spatial units together with heterogeneity in covariate-response relationships. Motivated by county-level HIV and substance use disorder (SUD) rates in South Carolina, we develop a grouped spatiotemporal autoregressive (GSTAR) model whose spatial coefficients and regression coefficients vary across latent groups while retaining cross-county dependence. Parameters are estimated by a three-step procedure that combines node-level least squares, clustering, and group-level least squares. A group-adjusted Bayesian information criterion (GBIC) selects the common covariate set and the number of latent groups. Under explicit regularity conditions, we derive uniform node-level consistency, group-level asymptotic normality, model-selection results, and conditional generalized-bootstrap validity for smooth functionals of group-specific parameters. Theoretical results and computational guarantees are presented under some regularity conditions. Simulation studies examine estimation, selection, coverage, and group recovery. The South Carolina analysis illustrates how latent groups can reveal heterogeneous associations between HIV-SUD rates and social, healthcare, transportation, and segregation measures.  Click here for more information
more about event
– until Oct. 23
add to calendar
Location:
DERR 329; 329
Cost:
Free
Contact:
Ellen Couvillion
ebr21@txstate.edu
Campus Sponsor:
Department of Mathematics
TalkMath2Me is a seminar for students and by students organized by Pi Mu Epsilon. Talk Math 2 Me provides students, both graduate and undergraduate, an opportunity to present anything related to mathematics to an audience of their peers. The talks can be 15-90 minutes long. Past topics have included talks on impressive student research, famous mathematicians, sports, puzzles and games, and time travel! Click here for more information
more about event
–
add to calendar
Location:
DERR 331; 331
Cost:
Free
Contact:
Jian Shen
js48@txstate.edu
Campus Sponsor:
Department of Mathematics
Title:  AI-Assisted Proof of the Δ-Conjecture for CIS d-Graphs
Speaker:        Dr. Jian Shen (Your AI Translator)
Location:       Derrick Hall 331


Abstract: 

Let the edges of a complete graph K_n  be colored with d colors from {1,2,…,d}, and for each i let G_i be the graph on the same vertex set formed by the edges of color i. In 1978, Gurvich proposed the following conjecture:

Gurvich’s Δ-Conjecture (1978). If every choice of a maximal independent set S_i of G_i, one for each  i∈{1,2,…,d}, has nonempty intersection, then the coloring contains no rainbow triangle. Here a rainbow triangle is a triangle whose edges have three different colors.

In a recent arXiv preprint (August 27, 2026), Liu and Tang presented an AI-assisted proof of this conjecture. 

In this talk, I will explain the main ideas of their proof, emphasizing the intuition behind the argument. I will aim to make the presentation self-contained and accessible to faculty and graduate students from different areas of mathematics.

Questions for discussion
        What does it mean to understand a proof beyond verifying its correctness?
        How should we validate AI-assisted proofs and acknowledge human and AI contributions?
        Where can AI contribute most effectively to mathematical research?
        How should graduate training respond to AI-assisted discovery and proof formalization?
– until Oct. 23
add to calendar
Location:
DERR 336; 336
Cost:
Free
Contact:
Logan Greenland
logan.greenland@txstate.edu
Campus Sponsor:
Department of Mathematics
This is a learning seminar intended for discussion and questions throughout, and no prior knowledge is assumed!
–
add to calendar
Location:
Online
Cost:
Free
Contact:
Piyush Shroff
pshroff@txstate.edu
Campus Sponsor:
Department of Mathematics
Join us virtually via Zoom for the Math Graduate Programs Showcase on Saturday, October 24, from 10 am to 12:30 pm. You will have the opportunity to meet faculty and students and learn about their research. Additionally, you will get a chance to meet the Graduate program advisors and ask questions to current grad students during the student panel session. Please register https://txstate.co1.qualtrics.com/jfe/form/SV_eJwcMqtmaOPxB2K and see the schedule below. Event information, including the registration link, is also available on the Math Department webpage https://www.math.txst.edu/. For any questions, please contact us at mathgrad@txstate.edu. 

Schedule:
  1. Welcome Remarks: 10 am
  2. Student Panel: 10:10 - 10:40 am
  3. Research Presentations: 10:45 - 11:15 am
    1. Math Room
    2. Math Ed Room
  5. Advisor Meet: 11:20 am - 12:10 pm
  6. End remarks/slide show: 12:15 - 12:20 pm
– until Oct. 25
add to calendar
Location:
DERR 238; 238
Cost:
Free
Contact:
Illona Weber
ih10@txstate.edu
Campus Sponsor:
Department of Mathematics
Math CATS is here to assist in almost all MATH courses for free!  If you're intimidated by the subject, come in and let's problem solve together.  Tutors are here to help reiterate, reinforce and help you relate to the content you heard in lecture. NO APPOINTMENT NEEDED! Click here for more information
more about event
– until Oct. 28
add to calendar
Location:
DERR 238; 238
Cost:
Free
Contact:
Illona Weber
ih10@txstate.edu
Campus Sponsor:
Department of Mathematics
Math CATS is here to assist in almost all MATH courses for free!  If you're intimidated by the subject, come in and let's problem solve together.  Tutors are here to help reiterate, reinforce and help you relate to the content you heard in lecture. NO APPOINTMENT NEEDED! Click here for more information
more about event
– until Oct. 27
add to calendar
Location:
DERR 336; 336
Cost:
Free
Contact:
Cameron Farnsworth
clf129@txstate.edu
Campus Sponsor:
Department of Mathematics
Love a good problem?  Like to solve difficult puzzles?
Join professors, graduate students and undergraduates as we tackle problems presented from several mathematical journals.  An interest in higher level mathematics is all that is required to join our round table. Offer what you know, learn what you don't in a relaxed environment with some of our department's finest!