Luxembourg Number Theory Day 2022



Luxembourg Number Theory Day 2022



The Luxembourg Number Theory Day will take place on December 16, 2022, on the Esch-Belval Campus of the University of Luxembourg.

A Webex link to attend the talks remotely will be sent upon request. Please let us also know if you plan to attend in person.


Speakers

Lassina Dembelé (King's College London)

Harald Helfgott (CNRS, University of Göttingen)

Igor Shparlinski (University of New South Wales)

Lola Thompson (Utrecht University)


Contacts

Antonella Perucca, Pietro Sgobba, Gabor Wiese. Email addresses: name.surname at uni.lu


Location

All of the talks will take place in room MNO 1.050 on the 1st floor of the Maison du Nombre at 6, Avenue de la Fonte, Esch-sur Alzette. You can see this on Google Maps or OpenStreetMap.


Schedule

Time Speaker Title
9:30-10:10Igor ShparlinskiIntegers of prescribed arithmethic structure in residue classes
10:10-10:30Coffee break
10:30-11:10Lassina DembeléHilbert-Siegel modular forms, congruences and applications to abelian surfaces
11:20-12:00Lola Thompson
12:00-13:00Lunch break
13:00-13:40Harald Helfgott



Abstracts

Igor Shparlinski (University of New South Wales) Integers of prescribed arithmethic structure in residue classes

We give an overview of recent results about the distribution of some special integers in residues classes modulo a large integer $q$. Questions of this type were introduced by Erdos, Odlyzko and Sarkozy (1987), who considered products of two primes as a relaxation of the classical question about the distribution of primes in residue classes. Since that time, numerous variations have appeared for different sequences of integers. The types of numbers we discuss include smooth, square-free, square-full and almost primes integers.

We also expose, without going into technical details, the wealth of different techniques behind these results: sieve methods, bounds of short Kloosterman sums, bounds of short character sums and many others.

Lassina Dembelé (King's College London) Hilbert-Siegel modular forms, congruences and applications to abelian surfaces

In this talk, we will explain how to compute congruences of Hilbert-Siegel modular forms. We will then discuss how to use these congruences to find abelian surfaces with everywhere good reduction and trivial endomorphism rings.