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

Kassie Archer

Research Interests: Enumerative combinatorics.

Selected Publications:

  • 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.

 

Christina Graves

Research Interests: Reliability polynomials.

Curriculum Vitae

 

Stephen Graves

Research Interests: Infinite graph theory, extremal graph theory, chemical graph theory.

Curriculum Vitae

 

Functional Analysis & Operator Algebras

Alex Bearden

Research Interests: C*-algebras, dynamical systems, non-selfadjoint operator algebras.

Curriculum Vitae

 

Scott LaLonde

Research Interests: C*-algebras, groupoids, inverse semigroups, dynamical systems and crossed products, Morita equivalence.

Selected Publications:

  • 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.
     

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.
     

Number Theory

Katie Anders

Research Interests: Combinatorics and number theory, specifically digital representations and graph splines.

Curriculum Vitae

 

Madeline Dawsey

Research Interests: Combinatorics and number theory, specifically partitions and modular forms.

Curriculum Vitae

 

Joseph Vandehey

Research Interests: Number theory, ergodic theory, symbolic dynamics, continued fractions, normal numbers.

Curriculum Vitae