Collaborative Research: Cohomology and Deformations of Algebras

合作研究：代数的上同调和变形

• 批准号: 1101177
• 负责人: Anne Shepler
• 金额: $ 13.22万
• 依托单位: University of North Texas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101177&HistoricalAwards=false
• 关键词: Collaborative; Research; Cohomology; Deformations; Algebras

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.

数学界对Shepler和Witherspoon的变形研究表现出了越来越大的兴趣，例如，在分次Hecke代数和辛反射代数中。这些代数遍布数学，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，它们出现在朗兰兹纲领、量子群理论、纽结理论和共形场论中）。 谢普勒和威瑟斯彭的工作对理论的斜群代数和Hochschild上同调，连接工作的各种杰出的数学家在不同的数学领域。他们的研究导致国际会谈和合作，并在选定的国际期刊上发表成果。 Shepler和Witherspoon通过与国际专家合作，组织会议和研讨会，在各个国家提供邀请演讲以及与外展计划合作，积极参与更广泛的社区。他们积极准备初级同事和学生（在各个阶段）从事职业生涯使用数学。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。