Research
I love math that draws connections between different, seemingly unrelated areas. Thus my research interests are in the branch of
Functional Analysis known as
Noncommutative Geometry, which attempts to study questions from geometry, topology, and physics by using the analytic and algebraic objects known as
C*-algebras. (As you can see, the downside of studying something interdisciplinary is that you have to know the meanings of a lot more words!)
In my research, I build C*-algebras out of topological groups, directed graphs, and their generalizations. In my PhD thesis, I studied what happens to the K-theory of the C*-algebra as I perturb the multiplication in the group(oid) C*-algebra via a 2-cocycle.
Since finishing my PhD, I have also begun to investigate the representation theory, cohomology, and vector bundles associated to these C*-algebras.
My PhD thesis was titled "K-theory and homotopies of 2-cocycles for twisted groupoid C*-algebras" and my advisor was
Erik van Erp.
To learn more about my research, please see my research statement.
Selected Publications
- K-theory and homotopies of 2-cocycles on transformation groups, J. Operator Theory 73 (2015), pp. 465 -- 490.
- (with C. Farsi, S. Kang, and J. Packer) Separable representations, KMS states, and wavelets for higher-rank graphs, J. Math. Anal. Appl. (2015).
- K-theory and homotopies of 2-cocycles on higher-rank graphs, Pacific J. Math. 278-2 (2015), pp. 407--426.
- K-theory and homotopies of 2-cocycles on group bundles,, Rocky Mountain J. Math. 46-4 (2016), 1207--1229.
- (with C. Farsi) Twists over etale groupoids and twisted vector bundles, Proc. Amer. Math Soc. 144-9 (2016), 3767--3779.
- (with C. Eckhardt) Irreducible representations of nilpotent groups generate classifiable C*-algebras, Münster J. Math. 9 (2016), 253--261.
- (with A. Kumjian) Cohomology for small categories: k-graphs and groupoids, submitted.