Wednesday, May.20, 2026

Time: 16:10-17:00

venue: Mathematics Building Room 527

Speaker: Prof. Shih-Yu Chen (Department of Mathematics, National Tsing Hua University )

Title: Deligne's conjecture and the cross-ratio formula

Abstract:

At the 1977 Corvallis conference, P. Deligne proposed a remarkable conjecture describing the algebraicity of critical $L$-values in terms of motivic periods. The conjecture has recently been settled for pure motives of rank one. In all other known cases in the literature, proofs typically depend on integral representations of the relevant $L$-functions.

In the framework of the Langlands--Clozel correspondence, we introduce, on the automorphic side, a cross-ratio formula for the critical values of Rankin--Selberg $L$-functions. This formula provides a new method for addressing Deligne's conjecture.

In this talk, we will introduce Deligne's conjecture on the symmetric power $L$-functions of modular forms, and present the cross-ratio formula.