Wenhan Dai

Seminar on Relative Langlands Duality (II)

This seminar focuses on the recent work of Ben-Zvi-Sakellaridis-Venkatesh [BZSV] on relative Langlands duality. The aim of this seminar is to understand the work Relative Langlands Duality by Ben-Zvi, Sakellaridis and Venkatesh, abbreviated as [BZSV] in what follows. We have completed the Parts 1 (structure theory of hyperspherical Hamiltonian varieties) and 2 (local theory) via Seminar on Relative Langlands Duality (I) in Fall 2023. In this semester, we plan to continue with the Parts 3 (global theory) and 4 (local-to-global aspects), by following the linear order in [BZSV].

• Time: Every Monday, 1:00-3:00pm.
• Location: BICMR 82J12.
• Organizer: Wen-wei Li and Liang Xiao.

Syllabus

• (3/4) Wenhan Dai: Period functions and period sheaves I. (notes)
• (3/11) Wenhan Dai: Period functions and period sheaves II. (notes)
• (3/18) Wen-wei Li: L-functions and L-sheaves I. (notes)
• (3/25) Xingzhu Fang: L-functions and L-sheaves II. (notes)
• (4/1) Liang Xiao: Global geometric conjecture I. (notes)
• (4/8) Chenglong Ma: Global geometric conjecture II.
• (4/15) Daming Zhou: The case over projective line P^1.
• (4/22) Wen-wei Li: Numerical conjecture I. (notes)
• (No seminar due to International Workers’ Day.)
• (5/6) Wen-wei Li: Numerical conjecture II. (notes)
• (5/13) Qijun Yan: Θ-series and local-global compatibility. (notes)
• (5/20) Marc Besson: Local spectral quantization. (notes)
• (5/27) TBA: Global spectral quantization. (notes)

References

1. [BZSV] David Ben-Zvi, Yiannis Sakellaridis, and Akshay Venkatesh, Relative Langlands duality, preprint, available here.