On the Harris-Venkatesh conjecture for weight one forms.
Title: On the Harris-Venkatesh conjecture for weight one forms.
Speaker: Emmanuel Lecouturier (YMSC & BIMSA)
Time: 10:00-11:00 Beijing time, Mar. 20, 2023
Zoom ID: 4552601552 Passcode: YMSC
Location: Jin Chun Yuan West Building, 3rd Floor Lecture Hall (近春园西楼三楼报告厅）
Venkatesh recently made very general conjectures regarding the relation between derived Hecke operators and a ``hidden'' action of a motivic cohomology group for an adjoint motive. These conjectures are in the setting of the cohomology of arithmetic groups. Venkatesh and Harris made an analogous conjecture in the setting of coherent cohomology in the first non-trivial case: weight one cuspidal eigenforms. This conjecture has been proved in some dihedral cases by Darmon-Harris-Rotger-Venkatesh recently. I found another approach using triple product L-functions. After some introduction on the conjecture, I will try to explain some ideas behind my method.