Entrance hall of the ICMS

Multiple Dirichlet Series and Applications to Automorphic Forms

Aug 04, 2008 - Aug 08, 2008

William Robertson Building, University of Edinburgh

Organisers

Name Institution
Diamantis, Nikolaos University of Nottingham
Fesenko, Ivan University of Nottingham
Goldfeld, Dorian Columbia University
Hoffstein, Jeffrey Brown University

Speakers
Ben Brubaker (MIT)
Alina Bucur (MIT)
Daniel Bump (Stanford University)
Gautam Chinta (City College of New York)
Young-Ju Choie (Postech, Korea)
Adrian Diaconu (University of Minnesota)
Sharon Frechette (College of the Holy Cross)
Solomon Friedberg (Boston College)
Paul Garrett (University of Minnesota)
Alexander Goncharov (Brown University)
Paul Gunnells (University of Massachusetts, Amherst)
Bernhard Heim (Max Planck Institut für Mathematik)
Joseph Hundley (Southern Illinois University)
Ozlem Imamoglu (ETH Zurich)
David Kazhdan (Hebrew University, Jerusalem)
Alex Kontorovich (Brown University)
Wenzhi Luo (Ohio State University)
Kohji Matsumoto (Nagoya University)
Omer Offen (Humboldt University of Berlin)
S J Patterson (University of Gottingen)
Masatoshi Suzuki (Rikkyo University, Tokyo)

 

This workshop was partially supported by the EPSRC, the NSF and the LMS.

 

Short report

Zeta and L-functions are fundamental objects in Number Theory and their deeper understanding is crucial for most major programmes in the subject. The study of multiple Dirichlet series (MDS) began more recently than that of classical Dirichlet series but is rapidly developing and, in recent years, there has been a surge of important breakthroughs. The main achievements in the theory so far include the construction of Weyl group multiple Dirichlet series, applications of MDS to the problem of non-vanishing of twists of L-functions, to convexity breaking, to moments of zeta and L-functions and the connections to multiple zeta function values. The workshop brought together the main workers in the field of MDS and other leading international experts in allied subjects, as well as younger researchers and post-graduate students working in related areas. The workshop centred around excellent talks reporting on the most recent developments in MDS and in areas that have the potential of fruitful interaction with the subject. We expect that the questions during the talks and the one-to-one discussions during the meeting will stimulate further progress in the major problems and will point to further research directions in the broader area of MDS.

Download the PDF file of the full report here

Arrangements

Venue
The workshop will be held in the Lecture Theatre, G08, on the ground floor of the William Robertson Building, University of Edinburgh, George Square. The University of Edinburgh provides this useful interactive map of the area with the building marked in a yellow circle.


Registration
There will be a combined Registration and Welcome Buffet from 19.00 to 20.30 on Sunday 3 August, in the St Trinnean's Room, St Leonard's Hall, Pollock Halls. Food will be available throughout that period and you may register at any time between 19.00 and 20.30.

Those who cannot register on Sunday evening may do so at the workshop venue before the talks start on Monday morning.

Travel
Information about travel to the UK and Edinburgh is available here.

If you have requested accommodation (see below), travel information and directions to Pollock Halls can be found on the website for Edinburgh First, who co-ordinate the accommodation bookings, http://www.edinburghfirst.com/edinburghfirst/travel.asp . We recommend that you take a taxi to the Halls. A taxi should cost between 6.00 and 7.00 GBP from the main railway station (Waverley Station) and between 17.00 and 21.00 GBP from Edinburgh airport. Alternatively there are frequent buses from the airport to Waverley Station, from where you can get a taxi to Pollock Halls. For timetable and details see http://www.flybybus.com/index.php.

The second of these two maps of Pollock Halls shows the location of both Pollock Halls and William Robertson Building where the lectures will take place. It is approximately a 15 minute walk between the two sites.

Lothian buses charge £1.10 for a single, £2.50 for a day ticket. Please note that the exact fare is required and no change is given. There are several Lothian Buses from the centre of town to Pollock Halls: Service No. 30, 14, 33 or the X48 Park and Ride Bus. If you enter the Service No on the Lothian Buses webpage, you will be able to view the timetable for each service bus. Leave the bus at The Commonwealth Pool on Dalkeith Road. Pollock Halls is situated just behind The Commonwealth Pool.

The location of Pollock Halls (18 Holyrood Park Road) can be viewed by following this link to multimap.

Accommodation
ICMS has arranged rooms in university accommodation in Pollock Halls for participants who require it. Participants are also free to make their own arrangements. A list of Edinburgh accommodation of various sorts and prices can be found on the Accommodation Page on the ICMS web site. Section 4 is particularly relevant. August is very busy in Edinburgh and early booking is recommended.

Pollock Halls of Residence
18 Holyrood Park Road
Edinburgh, EH16 5AY
Reception Contact Numbers
+44 (0)131 667 1971 (Tel)
+44 (0)131 668 3217 (Fax)

On arrival at Pollock Halls, please go to the Reception Building on your left, where you will pick up your key and some further information. You can get into your room after 14.00. If you arrive earlier you can leave your luggage at Reception. Pollock Halls has 24 hour reception.

Meals and Refreshments
There will be a Registration buffet in the St Trinneans Room in St Leonards, Pollock Halls on Sunday evening 3 August and a Workshop dinner on the evening of Thursday 7 August at the Playfair Library, Old College. Morning and afternoon refreshments will be provided at the workshop venue as well as lunch on Monday 4 August.

Computer access
At Registration you will be issued with a username, password and further information which will enable you to access either the wireless network or a public PC nearby. William Robertson Building is within a wireless zone as are parts of Pollock Halls.

Financial support available
The buffet supper on Sunday, a light lunch Monday, and the workshop dinner on Thursday evening will be provided free of charge to participants.

We hope that some participants may be able to cover their own travel expenses so we can offer some degree of financial assistance to more junior participants. Further information will be provided in individual invitation letters.

If ICMS has agreed to reimburse some of your travel costs, this will be stated in the 'Financial Arrangements' section of the 'Final Information' email. All reimbursement occurs after the workshop. You will be given a claim form at Registration and asked for your bank details to enable payment directly into your account. Please note that receipts are required for all expenses claimed. It would be useful if you can bring your bank details to the workshop.

US delegates can claim directly through an NSF grant in the USA. You will be issued with an NSF claim form at the workshop Registration. To claim through NSF you MUST use a US carrier. Please note that original receipts and boarding passes are required for all expenses claimed. All receipts and completed forms should be submitted within 10 business days after completion of travel. If ICMS has agreed to reimburse some of your travel costs through the NSF grant, this will be stated in the 'Financial Arrangements' section of the 'Final Information' email.


Programme

Monday 04 August

09.00 - 09.45

Registration

09.45 - 10.00

Introduction and welcome

10.00 - 11.00

Solomon Friedberg Boston College
WMDs and Crystals I

11.00 - 11.30

Coffee/tea break

11.30 - 12.30

Özlem Imamoglu ETH Zürich
On the cycle integrals of the j function

12.30 - 14.00

Lunch

14.00 - 15.00

Paul Garrett University of Minnesota
Integral Moments I

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Alexander Goncharov Brown University
Arithmetic analysis of the multiple zeta values

 

Tuesday 05 August

09.00 - 10.00

Ben Brubaker Massachusetts Institute of Technology
WMDs and Crystals II

10.00 - 10.15

Coffee/tea break

10.15 - 11.15

David Kazhdan Hebrew University of Jerusalem
The 2-dimensional Langlands correspondence

11.30 - 12.30

YoungJu Choie POSTECH
Quasi modular forms

12.30 - 14.00

Lunch

14.00 - 15.00

Adrian Diaconu University of Minnesota
Integral Moments II

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Sharon Frechette College of the Holy Cross
Multiple Dirichlet series for B_n

 

Wednesday 06 August

09.00 - 10.00

Gautam Chinta City College of New York
WMDs and Crystals III

10.00 - 10.15

Coffee/tea break

10.15 - 11.15

Alex Kontorovich Brown University
First nonvanishing theorems

11.30 - 12.30

Kohji Matsumoto Nagoya University
Multiple zeta-functions of root systems

 

Free Afternoon

 

Thursday 07 August

09.00 - 10.00

Paul Gunnells University of Massachusetts Amherst
WMDs and Crystals IV

10.00 - 10.15

Coffee/tea break

10.15 - 11.15

S J Patterson Georg-August-Universität Göttingen
Metaplectic multiple Dirichlet series - arithmetic aspects

11.30 - 12.30

Paul Garrett University of Minnesota
Automorphic spectral identities involving second moments of L-functions

12.30 - 14.00

Lunch

14.00 - 15.00

Alina Bucur Massachusetts Institute of Technology
Integral Moments III

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Wenzhi Luo Ohio State University
The closed geodesics on the modular surface and the Maass-Shintani lift

 

Friday 08 August

09.00 - 10.00

Daniel Bump Stanford University
WMDs and Crystals V

10.00 - 10.15

Coffee/tea break

10.15 - 11.15

Omer Offen Humbold University Berlin
Unitary periods

11.30 - 12.30

Masatoshi Suzuki Rikkyo University
Mean-periodicity and zeta functions

12.30 - 14.00

Lunch

14.00 - 15.00

Bernhard Heim Max Planck Institut für Mathematik
A trace formula of special values of automorphic L-functions

15.00 - 15.30

Coffee/tea break

15.30 - 16.30

Joseph Hundley Southern Illinois University
The adjoint L function of SU(2,1)


Presentations:

Presentation Details
Brubaker, Ben
WMDs and Crystals (mini-course)
View Abstract Down
Bucur, Alina
Integral Moments III
View Abstract Down
Bump, Daniel
WMDs and Crystals (mini-course)
View Abstract Down
Chinta, Gautam
WMDs and Crystals (mini-course)
View Abstract Down
Choie, YoungJu
Quasi modular forms
View Abstract Down
Diaconu, Adrian
Intergral Moments II
View Abstract Down
Frechette, Sharon
Multiple Dirichlet series for Bn
View Abstract Down
Friedberg, Solomon
WMDs and Crystals (mini-course)
View Abstract Down
Garrett, Paul
Automorphic spectral identities involving second moments of L-functions (also Intergral Moments I)
View Abstract Down
Goncharov, Alexander
Arithmetic analysis of the multiple zeta values
View Abstract Down
Gunnells, Paul
WMDs and Crystals (mini-course)
View Abstract Down
Heim, Bernhard
A trace formula of special values of automorphic L-functions
View Abstract Down
Hundley, Joseph
The Adjoint L function of SU(2,1)
View Abstract Down
Imamoglu, Özlem
On the cycle integrals of the j function
View Abstract Down
Kazhdan, David
The 2-dimensional Langlands correspondence
View Abstract Down
Kontorovich, Alex
First nonvanishing theorems
View Abstract Down
Luo, Wenzhi
The closed geodesics on the modular surface and the Maass-Shintani lift
View Abstract Down
Matsumoto, Kohji
Multiple zeta-functions of root systems
View Abstract Down
Offen, Omer
Unitary Periods
View Abstract Down
Patterson, S J
Metaplectic multiple Dirichlet series - arithmetic aspects
View Abstract Down
Suzuki, Masatoshi
Mean-periodicity and zeta functions
View Abstract Down

Participants

Name Institution
Aizenbud, Avraham Weizmann Institute of Science
Alkauskas, Giedrius University of Nottingham
Baruch, Ehud Israel Institute of Technology
Beineke, Jennifer Western New England College
Bian, Ce University of Bristol
Boecherer, Siegfried University of Mannheim
Booker, Andrew University of Bristol
Brubaker, Ben Massachusetts Institute of Technology
Bucur, Alina Massachusetts Institute of Technology
Bump, Daniel Stanford University
Chida, Masataka Kyoto University
Chinta, Gautam City College of New York
Choie, YoungJu POSTECH
Cornelissen, Gunther Universiteit Utrecht
Diaconu, Adrian University of Minnesota
Diamantis, Nikolaos University of Nottingham
Feigon, Brooke University of Toronto
Ferapontov, Jenya Loughborough University
Fesenko, Ivan University of Nottingham
Frechette, Sharon College of the Holy Cross
Friedberg, Solomon Boston College
Fujii, Akio Rikkyo University
Funke, Jens Durham University
Garbin, Daniel City University of New York
Garrett, Paul University of Minnesota
Giovannopoulos, Fotios Georg-August-Universität Göttingen
Goldfeld, Dorian Columbia University
Goncharov, Alexander Brown University
Gourevitch, Dimitry Weizmann Institute of Science
Gunnells, Paul University of Massachusetts Amherst
Heim, Bernhard Max Planck Institut für Mathematik
Hoffstein, Jeffrey Brown University
Howell, Gareth Cardiff University
Hughes, Christopher University of York
Hundley, Joseph Southern Illinois University
Huxley, Martin Cardiff University
Imamoglu, Özlem ETH Zürich
Kazhdan, David Hebrew University of Jerusalem
Kontorovich, Alex Brown University
Lagarias, Jeffrey C. University of Michigan
Lapid, Erez Hebrew University of Jerusalem
Lee, Min Columbia University
Li, Wen-Ching Penn State University
Louvel, Benoit Georg-August-Universität Göttingen
Luo, Wenzhi Ohio State University
Matsumoto, Kohji Nagoya University
Mohler, Joel Lehigh University
Moreno, Carlos City University of New York
Morrow, Matthew University of Nottingham
O'Sullivan, Cormac Bronx Community College
Offen, Omer Humboldt University of Berlin
Pál, Ambrus Imperial College London
Patterson, S J Georg-August-Universität Göttingen
Perelli, Alberto Universita' di Genova
Petridis, Ioannis University College London
Plunkett-Levin, Shaunna Cardiff University
Pollington, Andrew National Science Foundation
Raulf, Nicole Université des Sciences et Technologies de Lille
Ricotta, Guillaume Université de Bordeaux 1
Risager, Morten University of Aarhus
Sahi, Siddhartha Rutgers University
Sczech, Robert Rutgers University
Sengupta, Jyoti Tata Institute of Fundamental Research
Stark, Harold University of California, San Diego
Suzuki, Masatoshi Rikkyo University
van Order, Jeanine University of Cambridge
Whitehouse, David Massachusetts Institute of Technology
Yamasaki, Yoshinori Kyushu University
Zhang, Qiao Texas Christian University