报告题目：Differential graded vertex algebras
报告人：林宗柱教授（Kansas State University）
时间：2025.5.23 8:00
地点：1C207
摘要：Vertex algebras are models to formulate conformal field theories, which algebraically can be thought as theories of punctured additive group Ga, which algebra of distributions reflects the tangential preservation. Thus a vertex operator (a field) is an operator valued distribution of the group punctured group G_a^* and a vertex algebra is a state-field correspondence. In this talk, I will discuss its algebraic analog over arbitrary commutative ring with a goal to formulate vertex algebras for derived algebraic geometry. In this setting the duality should be corresponding to Poincar´e duality (Serre duality). Therefore, vertex algebras and conformal field theories have to be formulated in the derived category of an algebraic variety. In this talk I will outline some of the ideas. In the differential graded case, the state spaces are differential complexes, while operators are actually not chain maps. This will bring interesting derived algebraic geometry objects such as associated schemes of vertex algebra becomes a dg scheme.
报告人简介：美国Kansas州立大学终身教授，在美国麻省大学师从代数名师Humphrey教授。曾任美国科学基金会NSF小组评审专家。主要从事代数群、量子群、李代数以及它们的表示等领域的研究工作，是该领域内国际知名学者。主要成果发表在Trans. Amer. Math. Soc, Contemp. Math，Invent. Math, Commun. Math. Phys.等国际顶尖学术期刊上，标志性成果包括著名的Lin-Nakano定理。出版学术著作5部，并组织过多次国际会议，产生很大影响。现为《中国科学》等重要国际期刊的编委。