Speaker: Dr. Robin Zhang (MIT)
Time: 16:00-17:00 January 23, 2024 (Tuesday)
Place: MCM110
Title: Harris–Venkatesh plus Stark
Abstract: The class number formula describes the behavior of the Dedekind zeta function at s = 0. The Stark conjecture extends the class number formula, describing the behavior of Artin L-functions at s = 0 in terms of units. The Harris–Venkatesh conjecture gives a mod p analogue to the Stark conjecture and sits adjacent to the conjectures of Venkatesh and Prasanna–Venkatesh on derived Hecke algebras. In this talk, I will draw an introductory picture, formulate a unified conjecture combining Harris–Venkatesh and Stark for modular forms of weight 1, and describe the proof of this in the imaginary dihedral case. Time permitting, I will also mention new questions and in-progress work on extending this to other settings.