Constructing stable Hilbert bundles via Diophantine approximation

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Yucheng Liu (Chonqing University)

Time：

Fri., 15:30-16:30

Feb. 28, 2025

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title:

Constructing stable Hilbert bundles via Diophantine approximation

Abstract：

In this talk, I will present a construction of stable Hilbert bundles on any compact Riemann surfaces with positive genera. The main constructive step is via investigating the arithmetic property of the upper half plane in Bridgeland's definition of stability conditions and its homological parts. We will also briefly discuss the associated monodromy representations of these stable Hilbert bundles, for example, triple ways to noncommutative tori. This is based on work joint with Heng Du, Qiangyuan Jiang and work joint with Biao Ma.