学术报告报告题目：Cohomology theory of meromorphic open-string vertex algebras
报 告 人：齐飞 博士（耶鲁大学）
报告时间：2019年6月6日（星期四）下午16:00-17:00
报告地点：4号楼4131会议室
邀 请 人：曾德炉 教授
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数学学院
2019年5月28日
报告摘要：
In the study of associative algebras and modules, cohomology theory plays an important role. In particular, the first Hochschild cohomology is a vector space isomorphic to the space of outer derivations; if the first cohomology vanishes for every bimodule, then every left module for the algebra is completely reducible; and the second Hochschild cohomology is in one-to-one correspondence with the set of first-order deformations of the algebra. We would like to develop cohomology methods for vertex algebras. A vertex algebra is the algebraic structure formed by vertex operators, which are suitable infinite series of endomorphisms on a vector space. These vertex operators satisfy conditions that are analogous to those in a commutative associative algebra. YiZhi Huang discovered in 2012 that the cohomology theory can also be defined for grading-restricted vertex algebras and obtained analogues of some of the previously mentioned results. Joint with Huang, the speaker generalized the theory for meromorphic open-string vertex algebras (where commutativity does not hold and can be viewed as analogues of noncommutative associative algebras) that are not necessarily grading-restricted and obtained analogues of all the previously mentioned results.
报告人简介：
齐飞博士为耶鲁大学博士后助理教授( Gibbs Assistant Professor), 于2008年获得华南理工大学学士，2012年获得南开大学陈省身数学研究所硕士，2018年获Rutgers University数学博士。其研究方向为顶点代数与数学物理。目前的研究成果包括顶点代数的非交换推广及其上同调理论。