Number theory seminar

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Date / Time

Speaker

Title

Location

* 19 October 2017
15:15-16:15

Timothy Gendron
U.N.A.M

Event Details

Title	Hilbert's 12th Problem, Complex Multiplication and the Real Multiplication Program
Speaker, Affiliation	Timothy Gendron, U.N.A.M
Date, Time	19 October 2017, 15:15-16:15
Location	HG F 26.1

Hilbert's 12th Problem, Complex Multiplication and the Real Multiplication Program

20 October 2017
14:15-15:15

Timothy Gendron
U.N.A.M

Event Details

Title	Quantum modular invariant, quantum Drinfeld modules and a solution to the real multiplication program in positive characteristic
Speaker, Affiliation	Timothy Gendron, U.N.A.M
Date, Time	20 October 2017, 14:15-15:15
Location	HG G 43

Quantum modular invariant, quantum Drinfeld modules and a solution to the real multiplication program in positive characteristic

1 December 2017
14:15-15:15

Dr. Martin Orr
Imperial College London

Event Details

Title	Some unlikely intersections in a product of moduli spaces of abelian varieties
Speaker, Affiliation	Dr. Martin Orr, Imperial College London
Date, Time	1 December 2017, 14:15-15:15
Location	HG G 43
Abstract	I will talk about a theorem on unlikely intersections between a curve and Hecke correspondences in Ag x Ag (where Ag is the moduli space of principally polarised abelian varieties of dimension g). This is inspired by work of Habegger and Pila in the case g=1. I will outline the strategy of Pila and Zannier applied to this case, and discuss Galois bounds for isogenous abelian varieties which form one step in the proof.

Some unlikely intersections in a product of moduli spaces of abelian varietiesread_more

8 December 2017
14:15-15:15

Dr. Ian Nicholas Petrow
ETH Zurich, Switzerland

Event Details

Title	Bounds for traces of Hecke operators and points on curves over finite fields
Speaker, Affiliation	Dr. Ian Nicholas Petrow, ETH Zurich, Switzerland
Date, Time	8 December 2017, 14:15-15:15
Location	HG G 43
Abstract	Consider the space of classical holomorphic cusp forms with respect to a congruence subgroup, and the algebra of Hecke operators acting on this space. In this talk I will discuss estimates for the traces of these Hecke operators, as well as their applications to the analytic theory of elliptic curves over a finite field. For example, such bounds on traces of Hecke operators allow one to estimate the number of F_q-points on modular curves, going beyond what the Riemann hypothesis for curves over finite fields can tell us directly. I will also discuss a Petersson trace formula for newforms for general nebentype characters, which is one of the main tools used in the proof of the results in this talk.

Bounds for traces of Hecke operators and points on curves over finite fieldsread_more

15 December 2017
14:15-15:15

Dr. Daniel Barrera Salazar
UPC Barcelona

Event Details

Title	On the exceptional zeros of p-adic L-functions of Hilbert modular forms
Speaker, Affiliation	Dr. Daniel Barrera Salazar, UPC Barcelona
Date, Time	15 December 2017, 14:15-15:15
Location	HG G 43
Abstract	The use of modular symbols to attach p-adic L-functions to Hecke eigenforms goes back to the work of Manin et al in the 70s. In the 90s, Stevens developed his theory of overconvergent modular symbols, which was successfully used to construct p-adic L-functions on the eigenvariety. In this talk we will present a work in collaboration with Mladen Dimitrov and Andrei Jorza in which we generalize this approach to the Hilbert modular setting and prove new instances of the exceptional zero conjecture.

On the exceptional zeros of p-adic L-functions of Hilbert modular formsread_more

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