Mathematics Algebra Seminar - Luca Candelori
This event is in the past.
Detroit, MI 48202
Speaker: Luca Candelori
Title: Elliptic curves, Hodge theory and transcendence (Part 1)
Abstract: In this series of two talks, I will give a proof of the following conjecture of Nick Katz from 1976: an elliptic curve defined over a number field has complex multiplication if and only if its Hodge decomposition is defined over the algebraic closure of Q. This geometric conjecture is equivalent to a conjecture of Nesterenko in transcendence theory regarding the transcendence properties at CM points of the real analytic Eisenstein series of weight 2. The first talk in the series will be aimed at graduate students and non-experts: I will introduce basic notions from elliptic curves and Hodge Theory, as well as the main tools that I will need from transcendence theory. The second talk will be more technical: I will discuss the key elements of the proof, its applications, p-adic analogs and the relation with Grothendieck’s Period Conjecture.