Academic Year 2016/2017 - Number Theory Seminars

The Algebra and Number Theory group of the University of Luxembourg hosts three seminars.

Unless announced otherwise, the seminars take place in the "work place" in the 6th floor of the Maison du Nombre in Esch-Belval.

Everyone is invited to attend! For more information, please contact Gabor Wiese.


Luxembourg Number Theory Seminar

Date Speaker Title
16/11/2016, 16:00 Anna Medvedovsky (Brown/MPIM Bonn) An explicit universal Galois representation on the mod-3 Hecke algebra
07/12/2016, 16:00 Sebastian Schönnenbeck (Aachen) Computing in unit groups of orders with Voronoi's algorithm
24/04/2017, 15:45 Chun Yin Hui (Amsterdam) On the semisimplicity of geometric monodromy action in F_\ell coefficients


Work in Progress Seminar

Date Speaker Title
28/09/2016, 16:00 Shaunak Deo Mod-p Hecke algebras
26/10/2016, 14:15 Laia Amorós Images of Galois representations in mod p Hecke algebras
02/11/2016, 14:15 Shaunak Deo The geometry of eigenvarieties at classical points of weight one: Part 1
09/11/2016, 16:00 Shaunak Deo The geometry of eigenvarieties at classical points of weight one: Part 2
14/12/2016, 16:00 Alexander D. Rahm Serre's solution to the congruence subgroup problem


Summer Term 2017: Research Seminar: Deformation theory of Galois representations and pseudo-characters

Our main reference for the beginning are Gouvea's Park City Lectures on Deformations of Galois Representations.

WeekDate Speaker Title
106/03/2017, 14:00 Shaunak Deo Lectures 1-2
227/03/2017, 14:00 Alexander D. Rahm Lecture 3
303/04/2017, 14:00 Mariagiulia De Maria Lecture 4
410/04/2017, 10:00 Gabor Wiese Lecture 5
524/04/2017, 14:00 Emiliano Torti Lecture 6
608/05/2017, 14:00 Jasper Van Hirtum Lecture 7
715/05/2017, 14:00 Shaunak Deo Lecture 8


Winter Term 2016: Research Seminar: Bruhat-Tits trees and buildings

Reference for Weeks 1 to 9 is Jean-Pierre Serre : "Trees"/"Arbres, amalgames et SL_2".
Reference for Week 10 is a paper by Bellaiche and Chenevier
Reference for Week 11 is Laia's and Piermarco's joint preprint

WeekDate Speaker Title
128/09/2016, 14:00 Alexander D. Rahm Introduction, Amalgams, Trees
205/10/2016, 14:00 Laia Amorós Chapter 3 of J.-P. Serre's book | Trees and free groups
312/10/2016, 14:15 Shaunak Deo Chapter 4 of J.-P. Serre's book | Trees and amalgams
419/10/2016, 14:00 Mariagiulia De Maria Chapter 5 of J.-P. Serre's book | Structure of a group acting on a tree
509/11/2016, 14:00 Gabor Wiese Chapter 6 of J.-P. Serre's book | Amalgams and fixed points
616/11/2016, 14:00 Shaunak Deo Chapter II.1.1 - II.1.4 of J.-P. Serre's book | The tree of SL_2 over a local field
723/11/2016, 14:00 Gergely Kiss Chapter II.1.5 - II.1.7 of J.-P. Serre's book | Ihara's and Nagao's theorems, connections with Tits systems
830/11/2016, 14:00 Mariagiulia De Maria Chapter II.2.1 - II.2.5 of J.-P. Serre's book | Arithmetic subgroups of the groups GL_2 and SL_2 over a function field of one variable
907/12/2016, 14:00 Alexander D. Rahm Trees, Amalgams and the Quillen conjecture
1014/12/2016, 14:15 Shaunak Deo Bellaiche's generalization of Ribet's Lemma using Bruhat-Tits trees
1121/12/2016, 14:15 Laia Amorós Applications of Bruhat-Tits trees to Shimura curves


Collection of abstracts

Anna Medvedovsky (Brown/MPIM Bonn) An explicit universal Galois representation on the mod-3 Hecke algebra

We will construct a Galois representation attached to modular forms of level and all weights modulo 3 whose trace is universal. We will analyze its properties in detail and write down the representation explicitly in terms of matrices. Depending on time and interest we will discuss applications to distribution of Fourier coefficients of forms mod 3 and/or generalizations to p > 3, especially in the reducible level-one case. This work owes a great deal to published and unpublished work of Bellaiche and Serre on the case p = 2.

Sebastian Schönnenbeck (Aachen) Computing in unit groups of orders with Voronoi's algorithm

Unit groups of maximal orders in simple rational algebras (e.g. GL_n(Z) as the unit group of Mat_n(Z)) form an interesting class of (finitely presented) infinite groups. In general there are only few algorithms known for dealing with infinite groups; however, in this case we will see how one can employ a generalization of Voronoi's perfect form theory (which originally classified densest sphere packings) to answer of couple of basic questions about these groups. In particular we will compute a presentation, study how one can perform constructive membership and, if time permits, will construct a free resolution and classify the finite subgroups of such a unit group.


Last modification: 21 April 2017.