Workshop: Bianchi and Siegel modular forms

About the workshop

Following great progress in automorphic forms over totally real fields, there has recently been renewed interest in the case of automorphic forms over imaginary quadratic fields (aka Bianchi modular forms). One way to study their arithmetic properties is to lift them to Siegel modular forms via the theta correspondence between O(3,1) and Sp(4).

This workshop brought together experts on automorphic forms, Galois representations and computational number theory to present their work on different aspects of Bianchi and Siegel modular forms. The workshop's aim was to inform participants of the latest developments as well as stimulate further work in this exciting area of research.

The event took place in the Hicks Building at the University of Sheffield, opening on Monday morning and closing on Wednesday at 1pm. There was also a conference dinner on Tuesday.

Topics

• Computations of Bianchi modular forms

• Paramodular conjecture of Brumer-Kramer

• Böcherer's conjecture

• Images of Galois representations

• Modularity of Galois representations/ Serre's conjecture

• Arithmetic of L-values of Siegel modular forms

• Bloch-Kato conjecture for L-values

Speakers

• Siegfried Böcherer (Mannheim)

• Thanasis Bouganis (Durham)

• Jim Brown (Clemson)

• Lassina Dembele (Warwick)

• Neil Dummigan (Sheffield)

• Kris Klosin (CUNY)

• Jolanta Marzec (Bristol)

• Ameya Pitale (Oklahoma)

• Alexander Rahm (Galway)

• Abhishek Saha (Bristol)

• Haluk Sengun (Warwick)

• Jacques Tilouine (Paris)

• Lynne Walling (Bristol)

Other participants

• Samuele Anni (Warwick)

• Tobias Berger (Sheffield)

• Andrew Corbett (Bristol)

• Jonathan Crawford (Durham)

• Martin Dickson (Bristol)

• Dan Fretwell (Sheffield)

• Frazer Jarvis (Sheffield)

• Andrew Jones (Sheffield)

• Jayanta Manoharmayum (Sheffield)

• Michalis Neururer (Nottingham)

• George Schaeffer (UCLA)

• Konstantinos Tsaltas (Sheffield)

• Chris Williams (Warwick)

Sponsors

This event was supported by the London Mathematical Society and EPSRC.

Organiser and contact

Tobias Berger (t.t.berger@sheffield.ac.uk)

Programme

Abstracts

View the abstracts of the talks (PDF, 151KB)

Version 17 June 2014

Monday 14 July 2014

10.30am
Haluk Şengün (Sheffield)
Cohomology of Bianchi groups and arithmetic

11.20am Q&A

11.35am
Jolanta Marzec (Bristol)
Non-vanishing of fundamental Fourier coefficients of Siegel modular forms

12.20pm Q&A

2.00pm
PhD students introductions

2.20pm
Abhishek Saha (Bristol)
Siegel modular forms of degree 2: Fourier coefficients, L-functions, and functoriality

3.10pm Q&A

3.25pm
Thanasis Bouganis (Durham)
On special values of L-functions attached to half-integral weight Siegel modular forms

4.15pm Q&A

4.55pm
Ameya Pitale (Oklahoma)
Local and global Maass relations

5.45pm Q&A

7.00pm
Optional: Pub dinner at University Arms

Tuesday 15 July 2014

10.00am
Neil Dummigan (Sheffield)
Langlands functoriality and Harder's conjecture

10.50am Q&A

11.30am
Lynne Walling (Bristol)
Diagonalising spaces of Siegel Eisenstein series

12.20pm Q&A

2.10pm
Siegfried Böcherer (Mannheim)
Congruence primes via higher L-functions

3.00pm Q&A

3.15pm
Alexander Rahm (Galway)
Bianchi modular forms of varying discriminant, level and weight

4.05pm Q&A

4.45pm
Lassina Dembélé (Warwick)
Theta lifts of torsion classes of Bianchi groups

5.35pm Q&A

5.45pm
Discussion session

7.30pm
Conference dinner at Aagrah, Leopold Square

Wednesday 16 July 2014

9.30am
Jim Brown (Clemson)
The Ikeda ideal and a conjecture of Katsurada

10.20am Q&A

11.00am
Kris Klosin (CUNY)
Congruences and R=T theorems

11.50am Q&A

12.05pm
Jacques Tilouine (Paris)
Big image of Galois representations and congruence ideals

12.55pm Q&A