Collaborative Research: Cohomology and Deformations of Algebras

数学界对变形谢普勒和威瑟斯彭的研究表现出越来越大的兴趣，例如，对分次Hecke代数和辛反射代数的研究。这些代数渗透在数学中，出现在代数、几何、数论、组合学、拓扑学、统计学、调和分析、数学物理和特殊函数理论中(例如，它们出现在朗兰兹程序、量子群论、纽结理论和共形场论中)。Shepler和Witherspoon致力于建立一个关于斜群代数和Hochschild上同调的理论，该理论将不同数学领域的杰出数学家的工作联系起来。他们的研究导致了国际讨论和合作，并在精选的国际期刊上发表了成果。谢普勒和威瑟斯彭通过与国际专家合作、组织会议和研讨会、在不同国家进行受邀演讲以及与外展项目合作，动态地与更广泛的社区接触。他们积极为初级同事和学生(在所有阶段)从事使用数学的职业做好准备。他们的工作支持几个研究生的研究和本科生的暑期研究经验。

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.