Research in Mathematics
UT Tyler Department of Mathematics
The mathematics faculty at UT Tyler are very active in research, particularly in the areas of combinatorics/graph theory, functional analysis/operator algebras, and number theory. Faculty members in each group are listed below, along with specific research interests and selected publications for each. There is also significant overlap and collaboration across research groups.
Combinatorics & Graph Theory
Research Interests: Enumerative combinatorics.
- Enumeration of cyclic permutations in vector grid classes (joint with L.-K. Lauderdale), J. Comb., 11 (2020), no. 1, 203–230.
- Rooted forests that avoid sets of permutations (joint with Katie Anders), European J. Combin., 77 (2019), 1–16.
- Allowed patterns of symmetric tent maps via commuter functions (joint with Scott LaLonde), SIAM J. Discrete Math., 31 (2017), no. 1, 317–334.
Research Interests: Reliability polynomials.
Research Interests: Infinite graph theory, extremal graph theory, chemical graph theory.
Functional Analysis & Operator Algebras
Research Interests: C*-algebras, dynamical systems, non-selfadjoint operator algebras.
Research Interests: C*-algebras, groupoids, inverse semigroups, dynamical systems and crossed products, Morita equivalence.
- On some permanence properties of exact groupoids, Houston J. Math, 46 (2020), no. 1, 151–187.
- Some consequences of the stabilization theorem for Fell bundles over exact groupoids, J. Operator Theory, 81 (2019), no. 2, 335–369.
- Amenability and uniqueness for groupoids associated with inverse semigroups (with David Milan), Semigroup Forum, 95 (2017), no. 2, 321–344.
- Nuclearity and exactness for groupoid crossed products, J. Operator Theory, 74 (2015), no. 1, 213–245.
Research Interests: C*-algebras, groupoids, and inverse semigroups.
- 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.
Research Interests: Combinatorics and number theory, specifically digital representations and graph splines.
Research Interests: Combinatorics and number theory, specifically partitions and modular forms.
Research Interests: Number theory, ergodic theory, symbolic dynamics, continued fractions, normal numbers.