@MISC{Witherspoon_pastresearch, author = {Sarah Witherspoon}, title = {Past Research}, year = {} }

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Abstract

I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program has involved collaborations with many mathematicians, including work with postdocs and graduate students. Below is a summary of some of my past research projects, which fall loosely into three categories: Hochschild cohomology and deformations. A large part of my research program has involved Hochschild cohomology and deformations of algebras. Hochschild cohomology is important in deformation theory, since a deformation of an algebra is infinitesimally a Hochschild 2-cocycle, and obstructions to lifting 2-cocycles to deformations live in degree 3 cohomology. My work in deformation theory began with [9], a paper I wrote with Căldăraru and Giaquinto. We were inspired by some examples of Vafa and Witten, which are deformations of certain skew group algebras arising from orbifolds. Specifically, these are the skew group algebras S(V) ⋊ G (and twisted versions), where G is a finite group acting by graded automorphisms on the symmetric algebra S(V) of a vector space V (i.e. a polynomial