Research
Research Interests

Broadly speaking, I am interested in functional analysis and operator algebras. I primarily study C*-algebras built from locally compact groups and groupoids, including crossed products and other related constructions. Some of my more recent work also involves C*-algebras associated to directed graphs and inverse semigroups. These sorts of constructions provide operator algebraists with interesting examples of C*-algebras, whose properties are often determined by the underlying algebraic object and/or dynamics. Most of my work revolves around crossed products of C*-algebras by locally compact groupoids and more general objects known as Fell bundles.

I also occasionally engage in research projects outside the realm of functional analysis. In particular, I have recently worked on some problems in pattern avoidance and dynamical systems.

More information can be found in the current version of my research statement.



Publications

The following is a current list of publications, including some from my days as an undergraduate/applied mathematician.

  1. On the likelihood of certain allowed patterns for shift maps (with Kassie Archer), in preparation.
  2. On some permanence properties of exact groupoids, Houston J. Math 46 (2020), no. 1, 151–187. arXiv:1703.05190 [math.OA]
  3. Some consequences of the stabilization theorem for Fell bundles over exact groupoids, J. Operator Theory 81 (2019), no. 2, 335–369. arXiv:1710.03808 [math.OA]
  4. Condition (K) for inverse semigroups and the ideal structure of their C*-algebras (with David Milan and Jamie Scott), J. Algebra, 523 (2019), 119–153. arXiv:1710.04696 [math.OA]
  5. Amenability and uniqueness for groupoids associated with inverse semigroups (with David Milan), to appear in Semigroup Forum, 2016. arXiv:1511.01517 [math.OA]
  6. Allowed patterns of symmetric tent maps via commuter functions (with Kassie Archer), SIAM J. Discrete Math., 31 (2017), no. 1, 317–334. arXiv:1606.01317 [math.DS]
  7. Equivalence and exact groupoids, Houston J. Math, 42 (2016), no. 4, 1267–1290. arXiv:1411.1027 [math.OA]
  8. Nuclearity and exactness for groupoid crossed products, J. Operator Theory, 74 (2015), no. 1, 213–245. arXiv:1406.1749 [math.OA]
  9. Understanding the effects of polymer extrusion filter layering configurations using derivative-free optimization (with K.R. Fowler and E.W. Jenkins), Optimization and Engineering, 11(2), 339-354, June 2010.
  10. A simulation-based optimization approach to polymer extrusion filter design (with K.R. Fowler, E.W. Jenkins, and C.L. Cox), Filtration, 9(3), 224--230, July 2009.
  11. A simulation-based optimization approach to polymer extrusion filter design (with K.R. Fowler, E.W. Jenkins, and C.L. Cox), Proceedings of the American Filtration and Separations Society Annual Conference, (May 19-22) Valley Forge, PA 2008.