Speaker: Hu Zhao (Zhejiang University)
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, if it exists, should induce its classical counterpart on its representation schemes. This principle has achieved great success in the study of noncommutative Poisson/symplectic geometry.
In this talk, I will focus on Nakajima quiver varieties. Firstly, I will review double Poisson structures and bisymplectic structures on a noncommutative space. Secondly, I will show how to obtain Nakajima quiver varieties via “noncommutative Hamiltonian reduction”. Thirdly, I will explain why the conjecture “quantization commutes with reduction” holds on quiver algebras and how it fits into the Kontsevich-Rosenberg principle. Finally, I will discuss some applications, such as Calogero-Moser systems.
Time: 13:00-16:00, Friday, Jan. 17, 2025
Location: Room 1410 at SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai