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Department of Mathematics Faculty Research

Dr. Mohsen Aliabadi, Assistant Professor

field theory and polynomial, linear, and multilinear algebra, as well as matching theory and additive number theory

Sample publications:

  1. Odd-cycle defects in the Alon-Friedland bound , (with E. Krop), Submitted (2026).
  2. On partially matchable subspaces in a field extension, (with J. Losonczy), Submitted (2026).
  3. Higher-power inverse functional identities and Frobenius collision obstructions, Submitted (2026).
  4. A counterexample to a basis conjecture of Brualdi, Friedland and Pothen, Submitted (2026).​
  5. Diagonal parity and loop toggling for symmetric matrices over $\mathbb{F}_2$, Submitted (2026).​
  6. Paving matroids that are not sparse paving, Submitted (2026).​
  7. Structure and decomposition of deltoids in abelian groups, (with J. Losonczy), Submitted (2026).
  8. The exponential rarity of vertical digit cancellations, to appear in J. Combin. Math. Combin. Comput. (2026).
  9. Decomposition theorems for unmatchable pairs in groups and field extensions, (with J. Losonczy) To appear in Annals of Combinatorics (2026).
  10. A nonabelian twist on differences of bijections, Utilitas Mathematica, 128 (2026) 375397.
  11. Characterization of matchable sets and subspaces via Dyson transforms, (with J. Losonczy), Journal of Algebra, 706 (2026), 221-242.
  12. Matchings in matroids over abelian groups III, (with E. Krop), To appear in INTEGERS: The Electronic Journal of Combinatorial Number Theory, (2026).
  13. Matchings in matroids over abelian groups II, (with R. Y. Wu*, S. Yermolenko* ), To appear in Discrete Mathematics, Algorithms and Applications, (2026).
  14.  Classifying abelian groups through acyclic matchings, (with P. Taylor), Annals of Combinatorics. 29 (2025) 1019–1025.
  15. Conditions for matchability in groups and field extensions II,  Discussiones Mathematicae - General Algebra and Applications. 45(1) (2025) 135-157.

Mrs. Jennifer Harris, Senior Lecturer

Dr. Louisa Catalano, Assistant Professor

algebra, functional identities, linear preserver problems, radical theory

Sample publications:

  1. Catalano, L. On a certain functional identity involving inverses, Communications in Algebra, 46 (2018), 3430-3435.
  2. Catalano, L., Julius, H. On maps preserving products equal to fixed elements, Journal of Algebra, 575 (2021), 220-232.

Dr. Keith Driscoll, Professor

graph theory, k-cordiality

Sample publications:

  1. All trees are six-cordial, Keith Driscoll, Elliot Krop, and Michelle Nguyen*, Electronic Journal of Graph Theory and Applications, 5 (1): 21-35 (2017)

Mrs. Jennifer Harris, Senior Lecturer

Dr. Elliot Krop (Professor and Chair)

graph theory and combinatorics, domination, graph products, Ramsey theory, games on graphs

Sample publications:

  1. Vizing’s conjecture: a two-thirds bound for claw-free graphs, Elliot Krop, Discrete Applied Mathematics, 230: 162-165 (2017)
  2. A Vizing-type result for semi-total domination, John Asplund, Randy Davila, and Elliot Krop, Discrete Applied Mathematics, 258: 8-12 (2019)
  3. Grundy domination of forests and the strong product conjecture, Kayla Bell, Keith Driscoll, Elliot Krop, Kimber Wolff, The Electronic Journal of Combinatorics 28(2) (2021), #P2.12

Dr. Catherine Matos, Professor

Sample publications:

  1. Students’ Preferred Technology in an Ordinary Differential Equations Course, Catherine Matos, Kelli Nipper, and Hannah R. Rigdon, 2022 ASEE Southeastern Section Conference, American Society for Engineering Education, (2022)

Dr. Tomás Merchán, Assistant Professor

harmonic analysis, geometric measure theory, partial differential equations, probability theory

Sample publications:

  1. The Huovinen transform and rectifiability of measures. Benjamin Jaye, Tomás Merchán. Advances in Mathematics, Volume 400 (2022), 108-297.
  2. On the problem of existence in principal value of a Calderón-Zygmund operator on a space of non-homogeneous type. Proc. London Math. Soc. 121 (2020), 152-176.

Ms. Cassandra Parker, Lecturer

Dr. Christopher Raridan, Professor

graph theory

Sample publications:

  1. Dao, H. Hua, and M. Ngo, and C. Raridan, On the edge-balanced index sets of complete even bipartite graphs, Journal of Graph Labeling, 2(1) (2016), 79--87.
  2. Cichacz, D. Froncek, E. Krop, and C. Raridan, Distance magic Cartesian products of graphs, Discussiones Mathematicae Graph Theory, 36(2) (2016), 299--308.
  3. Hua, E. Krop, and C. Raridan, A counterexample to a conjecture of Ghosh, Bulletin of the Institute of Combinatorics and its Applications, 75 (2015), 79--82.

Dr. Jesus Sanchez Jr., Assistant Professor

Index Theory, Cyclic Cohomology, Spin Geometry, K-Theory, Spectral Geometry, Hypoelliptic Geometry, Metric Geometry, High Dimensional Gauge Theory, Infinite Dimensional Equivariant Geometry

Sample publications:

  1. Haj Saeedi Sadegh, Ahmad Reza and Liu, Shiqi and Loizides, Yiannis and Sanchez, Jesus, A fixed-point formula for Dirac operators on Lie groupoids, Journal of Functional Analysis, 287 (2024), 10.1016/j.jfa.2024.110624.
  2. Hypoellipticity of the Asymptotic Bismut Superconnection on Contact Manifolds, (2025) (with A. F. Valiente) preprint arXiv (submitted for publication)
  3. Explicit Spinor Representations (2025) preprint arXiv

Mr. Matthew Smith, Lecturer

Mrs. Jelinda Spotorno, Senior Lecturer

Dr. Everett Sullivan, Assistant Professor

combinatorics, chord diagrams, Motzkin paths

Sample publications:

  1. E. Sullivan, Linear chord diagrams with long chords, The Electronic Journal of Combinatorics 24 (4) (2017), #P4.20.
  2. N. Cameron and E. Sullivan, Peakless Motzkin Paths with Marked Level Steps at Fixed Height, Discrete Mathematics 344 (1): 112-154 (2021).

  3. Alexander R. Klotz and Everett Sullivan, “Exactly-solvable self-trapping lattice walks in ladder graphs,” Discrete Mathematics 349 (2026).

  4. Sol Addison, Sarah Blackwell, Puttipong Pongtanapaisan, Nancy Scherich, Lila Snodgrass, Everett Sullivan, “Danceability, a new definition of bridge index,” Topology and its Applications 390 (2026).

Dr. David Williams, Associate Professor

analysis, applied mathematics, numerical mathematics