Beyond Shimura: cycles, Riemann surfaces and non-reductive linear algebra
Prof. Zhiyu Zhang
2025-06-23 15:30-17:00
MCM110
Speaker: Prof. Zhiyu Zhang (Stanford University)
Time: 15:30-17:00 June 23, 2025 (Monday)
Venue: MCM110
Title: Beyond Shimura: cycles, Riemann surfaces and non-reductive linear algebra
Abstract: It is hard-if not impossible-to study general geometric Galois representations (e.g. Artin motives) using Shimura varieties, even via R=T congruences. Could we find more geometric spaces (resp. Riemann surfaces) beyond Shimura varieties (resp. Shimura curves)? I will discuss very partial answers, via studying new objects arising as cycles with symmetry on known objects, e.g. some non-reductive cycles, starting with toy models. Non-reductive features are essential in linear algebra and Langlands, see e.g. stabilizer subgroups and Fourier coefficients. Also, there are so many L-functions compared to reductive groups. I will present their basic geometry, some“exotic” conjectures and evidences from other areas.
