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BIMSA-YMSC Tsinghua Number Theory Seminar
On the Harris-Venkatesh conjecture for weight one forms
On the Harris-Venkatesh conjecture for weight one forms
Organizers
Hansheng Diao
, Yueke Hu
, Emmanuel Lecouturier
,
Cezar Lupu
Speaker
Emmanuel Lecouturier
Time
Monday, March 20, 2023 10:00 AM - 11:00 AM
Venue
JCY-3
Abstract
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.