Mathematics Research
Research in Mathematics
UT Tyler Department of Mathematics
The mathematics faculty at UT Tyler are very active in research, particularly in the areas of applied mathematics, complex analysis, functional analysis & operator algebras, graph theory, and number theory & combinatorics. Faculty members in each group are listed below, along with specific research interests and either selected publications or a curriculum vitae for each. There is also significant overlap and collaboration across research groups.
Applied Mathematics
Regan Beckham
Research Interests: Mathematical modeling of physical problems and statistics.
Complex Analysis
William Blair
Research Interests: Complex function theory and complex boundary value problems.
Selected Publications:
- An atomic representation for Hardy classes of solutions to nonhomogeneous Cauchy-Riemann equations, J. Geom. Anal. 33.9 (2023), Paper No. 307, 20. issn: 1050-6926,1559-002X. doi: 10.1007/s12220-023-01374-y.
- The Schwarz boundary value problem for boundary values in the sense of distributions, J. Math. Anal. Appl. 530.2 (2024), Paper No. 127690. issn: 0022-247X. doi: 10.1016/j.jmaa.2023.127690.
- Hardy spaces of meta-analytic functions and the Schwarz boundary value problem, Complex Anal. Synerg. 10.13 (2024), Paper No. 13, 9. issn: 2524-7581,2197-120X doi: 10.1007/s40627-024-00139-9.
Functional Analysis & Operator Algebras
David Milan
Research Interests: C*-algebras, groupoids, and inverse semigroups.
Selected Publications:
- On a class of inverse semigroups related to Leavitt path algebras (with John Meakin and Zhengpan Wang), Advances in Mathematics 384 (2021).
- Condition (K) for inverse semigroups and Ideal structure of their C*-algebras (with Scott LaLonde and Jamie Scott), Journal of Algebra 523 (2019), 119–153.
- On inverse semigroup C*-algebras and crossed products (with Benjamin Steinberg), Groups, Geometry, and Dynamics 8 (2014), no. 2, 485–512.
Pamela Delgado
Research Interests: Functional analysis, fixed point theory, and operator theory.
Selected Publications:
- Cesàro averaging and extension of functionals on L^infinity(0,infinity) (with Chris Lennard and Jeromy Sivek), Journal of Mathematical Analysis and Applications 529, Issue 1 (2024).
Graph Theory & Combinatorics
Christina Graves
Research Interests: Reliability polynomials, pattern avoidance in permutations, and graph automorphisms.
Stephen Graves
Research Interests: Infinite graph theory, extremal graph theory, and chemical graph theory.
Mathematical Biology
Ivan Ramirez-Zuniga
Research Interests: Mathematical biology, mathematical immunology and immunometabolism, mathematical modeling of infectious diseases and inflammatory response, epidemiology, population dynamics, parameter estimation, optimal control, uncertainty quantification, data science and machine learning.
Selected Publications:
- A.P. Smith, L.C. Lane, I. Ramirez-Zuniga, D.J. Moquin, P. Vogel, A.M. Smith (2022). Increased Virus Dissemination Leads to Enhanced Lung Injury But Not Inflammation During Influenza-Associated Secondary Bacterial Infection. FEMS Microbes, Volume 3, 2022, xtac022 (link to article).
- I. Ramirez-Zuniga, Jonathan E. Rubin, David Swigon, Gilles Clermont, and Heinz Redl. A data-driven model of the role of energy in sepsis. Journal of Theoretical Biology. Volume 533. (2022).
- I. Ramirez-Zuniga, Jonathan E. Rubin, David Swigon, and Gilles Clermont. Mathematical Modeling of Energy Consumption in the Acute Inflammatory Response. Journal of Theoretical Biology, 460. 101-114, (2019). (link to article).
Number Theory & Combinatorics
Katie Anders
Research Interests: Combinatorics and number theory, specifically digital representations and graph splines.
Madeline Dawsey
Research Interests: Combinatorics and number theory, specifically partitions, modular forms, and digital representations.
Joseph Vandehey
Research Interests: Number theory, ergodic theory, symbolic dynamics, continued fractions, normal numbers.