Research

Broadly, I study a mix of algebra, topology, and category theory. More specifically, in graduate school, my focus was in homological algebra. I worked with a generalization of Hochschild (co)homology. We concerned ourselves with showing that this secondary Hochschild (co)homology has properties similar to that of the usual Hochschild (co)homology. This included topics involving bar resolutions, functoriality, Kähler differentials, and exact sequences. Finally, we investigated the simplicial structure for higher order Hochschild (co)homology over the d-sphere, for any d greater than or equal to 1. I am currently interested in a deformation theory controlled by the aforementioned higher order Hochschild cohomology.

More recently we have delved into group theory, concerning ourselves with character theory and representation theory. We are interested in graphs and determining if they can or cannot occur as the prime character degree graph of a solvable group. What started out as a project to continue the classification of prime character degree graphs with six vertices has now blossomed into other topics involving families of graphs, as well as special cases where there is no normal nonabelian Sylow subgroup associated to certain primes.

I also take great pride in working with undergraduates on suitable projects. As someone who was never afforded this opportunity during my stint as an undergraduate, I find it necessary to give them that exposure and experience of the mathematical world beyond the classroom.

If for some reason you found that interesting, you can find out more on my Articles page or from my Research Statement.

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