Collaborative Research: Cohomology and Deformations of Algebras

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The mathematical community shows expanding interest in the deformations Shepler and Witherspoon study, for example, in graded Hecke algebras and symplectic reflection algebras. These algebras pervade mathematics, appearing in algebra, geometry, number theory, combinatorics, topology, statistics, harmonic analysis, mathematical physics, and the theory of special functions (for example, they appear in the Langlands program, the theory of quantum groups, knot theory, and conformal field theory). Shepler and Witherspoon work towards a theory of skew group algebras and Hochschild cohomology that connects work by various prominent mathematicians working in different mathematical fields. Their research leads to international talks and collaborations and results in publications in selective international journals. Shepler and Witherspoon dynamically engage the wider community by collaborating with international experts,organizing conferences and workshops, delivering invited talks in various countries, and working with outreach programs. They actively prepare junior colleagues and students (at all stages) for engaging careers which use mathematics. Their work supports research of several graduate students and summer research experiences for undergraduates.