应兰州大学数学与统计学院邀请，浙江大学数学高等研究院赵虎博士将于2025年10月24日做线上学术报告。

报告题目: Double Poisson Structures and Noncommutative Poisson Extensions

报告时间：2025年10月24日晚19：00-20：00

腾讯会议：999-710-221

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摘要：Due to the central role of quiver varieties in mathematical physics and geometric representation theory, preprojective algebras have emerged as one of the most prominent noncommutative spaces. A direct consequence of noncommutative Hamiltonian reduction is that the quotient space ΠQ/[ΠQ, ΠQ] carries a Lie bracket, and the image of the trace map endows the coordinate ring of the quiver variety with a Poisson algebra structure.

In this talk, we introduce noncommutative Poisson extension theory and demonstrate that the Lie bracket extends to the entire reduced cyclic homology. We further show that shifted double Poisson structures are well-behaved in the derived setting. Under the Kontsevich-Rosenberg principle, we discuss the relationship between shifted double Poisson structures and shifted Poisson structures on the derived moduli stack of representations.

报告人简介

赵虎，浙江大学数学高等研究院博士后，合作导师阮勇斌院士；2023年在四川大学获得博士学位，指导老师李安民院士和陈小俊教授。研究领域为非交换泊松/辛几何与相关应用、3d N =4 镜像对称理论、Calogero-Moser 可积系统与应用。

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