12th Westlake Online Math Forum | Emmanuel Lecouturier: On the Harris--Venkatesh conjecture for weight one modular forms

2023-08-31 14:54:29
报告人 时间 14:00-15:00
地点 E4-233 & ZOOM 2023
月日 09-06

Time14:00-15:00, Wednesday, September 6 2023

ZOOM ID: 921 6725 8223

PASSCODE: 064984


Speaker:Emmanuel LecouturierYMSC

Biography: Emmanuel Lecouturier joined Tsinghua University in 2018, he is an associate Professor at Yau Mathematical Science Center (YMSC). He is working on number theory (modular forms, elliptic curves, L-functions).

Title:On the Harris--Venkatesh conjecture for weight one modular forms

Abstract:

In the spirit of general conjectures of Venkatesh on the action of derived Hecke operators on the cohomology of arithmetic groups, Harris and Venkatesh formulated a conjecture relating the action of certain derived Hecke operators on weight one eigenforms to a certain group of units in a number field. Much work has been done, by several authors, in the case of a dihedral weight one form. We will survey these results. Following the recent ideas of Robin Zhang, we will also motivate the conjecture from the perspective of special values of L-functions. This is based on the work of the author [IMRN 2023, DOI 10.1093/imrn/rnad119] and work in progress with Loïc Merel.


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