主    講 人：陳昰宇助理教授(國立清華大學數學系)

演講題目：DELIGNE’S CONJECTURE AND THE CROSS-RATIO FORMULA

演講時間：2026年04月23日(星期四) 15:30~17:00

演講地點：中央大學鴻經館 M107

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 and present the cross-ratio formula. If time permits, we will also outline a proof of Deligne’s conjecture for the symmetric power L-functions of modular forms.