学术报告（赵虎 2025.5.30）

Abstract: In 2000, Maxim Kontsevich and Alexander Rosenberg proposed a heuristic principle in the study of noncommutative geometry. It states that a noncommutative geometric structure on a noncommutative space, should induce its classical counterpart on its representation schemes. This principle has achieved great success in the study of noncommutative Poisson/symplectic geometry.

First, I will review noncommutative calculus and noncommutative symplectic/Poisson structures. Second, I will report my work on “quantization commutes with reduction”. At the end, I will introduce shifted double Poisson structures and and discuss applications in derived noncommutative geometry.