Originally from southern California, I received my undergraduate degree from UC Berkeley majoring in math and minoring in art practice. I did my graduate work at the University of Washington under the supervision of Eric Babson and Isabella Novik. I held postdoctoral positions at TU Berlin (Alexander von Humboldt research fellow), Stanford (NSF institutes postdoc), U Miami, and U Texas before joining the faculty at Texas State in 2016.
My research interests span a variety of topics in algebra and combinatorics. In my thesis and early postdoctoral days I worked on topological and categorical approaches to graph homomorphisms. I continue to explore these notions and these days I'm also interested in connections to statistical physics. On the algebraic side I am interested in studying homological and computational aspects of monomial and binomial ideals with an emphasis on combinatorial aspects. This includes free resolutions, betti numbers, betti tables, Groebner bases, etc. The algebraic objects arise in a variety of settings including graphs and hypergraphs, simplicial complexes, lattice points of polytopes, chip-firing on graphs, hyperplane arrangements, matroids, and tropical geometry. I am also interested in algebraic and categorical aspects of persistent homology.
I enjoy teaching mathematics at a variety of undergraduate and graduate levels, as well as working with students on research and directed reading. I also seek to widen the scope, impact, and understanding of mathematics in terms of outreach, public events, and connections to other disciplines.
- Face rings of cycles, associahedra, and standard Young tableaux, Electron. J. Combin., Volume 23, Issue 3, 2016.
- Cellular resolutions via mapping cones, with Fatemeh Mohammadi, J. Combin. Theory Ser. A 128: 180–206, 2014.
- Laplacian ideals, arrangements, and resolutions, with Raman Sanyal, J. Algebraic Combin. 40(3):805 – 822, 2014.
- Coarse tropical type decompositions and associated cellular resolutions, with Michael Joswig and Raman Sanyal, J. Algebra, 356: 304–324, 2012.
- Cellular resolutions of cointerval ideals, with Alexander Engstrom, Math. Z. 270(1): 145–163, 2012.
- Topology of Hom complexes and test graphs for bounding chromatic number, with Carsten Schultz, Israel J. Math 187(1): 371–417, 2012.
- Algebraic properties of edge ideals via combinatorial topology, with Alexander Engstrom, Electron. J. Combin., 6(2) (Bjorner Festschrift Volume), 23 pages, 2009.
- The universality of Hom complexes of graphs, Combinatorica, 29 (4): 433–448, 2009.
- Hom complexes and homotopy in the category of graphs, European J. Combin., 30(2): 490–509, 2009.