Last updated: May 11,2009.
The Bellairs Workshop in Number Theory

Borcherds products and their applications to arithmetic geometry
May 3-10, 2009

Speaker: Jan Bruinier (Technische Universitat Darmstadt)

Organizer: Eyal Goren (McGill University)

The workshop is dedicated to Borcherds' theory concerning a singular theta lift from weakly holomorphic elliptic modular forms to automorphic forms on orthogonal groups which are forms of SO(2, n), and its applications and generalizations. A series of lectures will be given by Jan Bruinier on this topic, supplemented by lectures from attending experts, for a total of 20 hours and many more hours of stimulating exchanges. The intention of the workshop is to provide an access point to the field, assuming at least a background comparable to advanced graduate students. Participation is by invitation only.


The Bellairs Research Institute

Recreational Activities


Getting to Bellairs

Coming prepared


The facilities



The general schedule is morning lectures (2 hrs) by Bruinier and after dinner lectures by participating experts (2hrs per day). The program is designed to encourage discussion and new research initiatives by allowing enough free time and having all the participants in the same residence. Click here for a tentaive program.



Morning  9:00 - 11:00

Evening  7:30 - 9:30


------ (arrival)

Welcome meeting at 21:00 in the shed in the main yard (near the kitchen)


Jan Bruinier: Orthogonal groups and modular forms

Steve Kudla: The Weil representation and the Siegel Weil formula


Jan Bruinier: Theta liftings of holomorphic and weakly holomorphic modular forms

Udi DeShalit: Half-integral weight modular forms and the Shimura lift


Jan Bruinier: Borcherds products and automorphic Green functions

Gerard Freixas: Local and global heights on curves


Jan Bruinier: CM values and Faltings heights

Henri Darmon: Modular curves and Heegner points


Jan Bruinier: Harmonic weak Maass forms and the Gross-Zagier formula

Shouwu Zhang: The Gross-Zagier formula and some applications


discussion time

discussion time


----- (departure)









email and webpage

Airport Arrival and Departure time


Fabrizio Andreatta

University of Milano

Sun VS 29 13:45, Sun VS 30 16:45


Massimo Bertolini

University of Milano

Sun VS 29 13:45, Sun VS 30 16:45


 Jan Bruinier

Technische Universitat Darmstadt

 Sun VS 77 18:05, Sun 20:40


Ivan Blanco

U. Barcelona (graduate student)



Jose Burgos Gil

U. Barcelona

Sun BA 2155 14:50, Sun  BA 2154 16:40


Bryden Cais

CICMA post doctoral fellow

Sun AC974 13:55, Sun AC975 14:55


 Candelori, Luca

 McGill University (graduate student)

SUN AA 651 9:50 PM,
SUN AA 602 6:45 AM


Henri Darmon

McGill University

Sun AC966 14:00, Sun AC967 15:00


Chantal David

Concordia University

Sun AC966 14:00, Sun AC967 15:00


Ehud DeShalit

Hebrew U

Sun AA 1385 13:, Sat AA 1384 14:35



Stephan Ehlen

Technische Universitat Darmstadt (graduate student)

Sun VS 77 18:05, Sun 20:40


Andrew Fiori

McGill University (graduate student)

Sun AC974 13:55, Sun AC975 14:55


Cameron Franc

McGill University (graduate student)

Sun AC974 13:55, Sun AC975 14:55


Gerard Freixas i Montplet

CICMA (postdoctoral fellow)



 Luis Garcia

 Columbia U (graduate student)

Sun AA1385 13:25, Sun AA1384 14:35



 Jayce Getz


Sun AA 651 21:50, Sun AA 602 06:45


 Eyal Goren

McGill University

Sun AC966 14:00, Sun AC967 15:00


Matthew Greenberg

U. Calgary



Eric Hofmann

Technische Universitat Darmstadt (graduate student)

Sun VS 77 18:05, Sun 20:40


Kimberly Hopkins

U. Texas, Austin (graduate student)

Sun AA   651 21:50, Sun AA 602 6:45


Steve Kudla

Toronto University

Sunday 14:00,  Sunday 15:00


 Ulf Kuehn

 Hamburg University

Sun VS 038 18:05, Sun VS038 20:00


 Kristin Lauter

 Microsoft Research



 Yifeng Liu

 Columbia U (graduate student)

Sun AA1385 13:25, Sun AA1384 14:35


 Marc Masdeu-Sabate

 McGill University (graduate student)

Sun AC974 13:55, Sun AC975 14:55


Dong Quan Ngoc Nguyen


McGill University (graduate student)

Sun AC 966 14:00, Sun AC 967 15:00


Jeehoon Park

CICMA post doctoral fellow

Sun AC966 14:00, Sun AC967 15:00



 Kartik Prasanna

University of Maryland

 Sun 13:01 AmAir 1089, Sun 14:20, AmAir 1078


Siddarth Sankaran

U Toronto (graduate student)

Sun 14.00 AC966, Sun AC 967 15:00


John Voight

U. Vermont in Burlington

Sun Liat 563 18:20, Sun 14:25.


Tonghai Yang

U. Wisconsin - Madison

Sun AA 651 21:10, Sun AA 602 07:05


Shouwu Zhang

Columbia University

Thu AA 1385 13:25, Sun AA 1384 14:35


 Yu Zhao

 McGill University (graduate student)

 Sun AC974 13:55, Sun AC975 14:55



The Bellairs Research Institute
Here is a link to the Institute's website. It is located in St. James, which is just to the north of Holetown. The exact location is
13.192104, -59.640130 (I think... you can plug these coordinates in


Getting to Bellairs
Here you can find maps of Barabados, as well as much information about tourism. The local airport is in Bridgetown, Barbados (code BGI), while the Bellairs institue is more towards the north of the island, on its west coast. The easiest is to share a taxi from the airport to the institute. Most taxi drivers will know where is the Bellairs reserach institue; if not, tell them is in St. James, north to Holetown. When you pass the St. James Parish and the Folkstone marine park look for the Bellairs research institute on the left (sea side) of the road. Hook up at the airport with other participants based on arrival information to reduce the cost.

View Larger Map


The facilities

  • The institute is well equipped for marine research. One can rent air tanks there very cheaply. Regardless, it is an excellent place for scuba diving and swimming, but you should bring your own gear (good quality mask and snorkel can be purchased for a reasonable price at a local sport store).
  • Most people take their breakfast at the institute, but this is optional. Dinner at the institute is mandatory and is charged separately at $25US. This is not the cheapest, but the food is great and local and in generous portions and it is a nice way for us to get together. For lunch everyone is on his/her own. Usually people get together and go to one of the restaurants in Holetown. There is a kitchen there where, if needed, you can store food and cook for yourself if you cannot eat the food served.
  • There is a flat rate of $15US for use of internet for the whole week. There is wireless in the Institute and also a few terminals and a printer (not for heavy jobs!). Laptop is the easiest way to be connected and to call home (using Skype, say). There is a public phone at the institute. 
  • Though Barbados in the large is a safe place, there have been cases of thefts from rooms in the institute. Some prudence is recommended: do not leave valuables unattended. Lock your room at night and do not leave valuables near the window (allowing someone from the outside to get to them). The institute has a safe where you can deposit your valuables.
  • There is a modest size blackboard, and there is a data projector (to use with a laptop).
  • Please wash your body from sand very carefully using the taps outside (in the main yard, for example). Sand can cause very difficult problems of blockage at the showers.
  • The institute accepts Visa, Mastercard, cash and checques, which gives flexibility in settling your bill.
  • The prices of room are as per the posted rate on the Institute website. Postdocs and “up” are considered research faculty and students, well… as students. The price depends on the specific room. Students, as a rule, will be staying at the more affordable rooms.
  • Breakfast at a cost of $7 will be served on Monday morning (it includes toast, cereal, fruit, tea, coffee, juice and something hot like pancakes, eggs or bacon). After that we’ll ask people to choose either to have breakfast at the institute for the rest of the week, or not (at the same cost). One has the option of buying groceries and preparing breakfast independently, however what they offer seem to me a rather fair deal and the only option people may wish to take is to have their breakfast outside the institute altogether (there are no obvious choices, though).


Recreational Activities

  • Here is a link to a tourist information site.
  • The institute is located 1 minute walk (literally) from the beach. It is a beautiful beach with a coral reef. The Folkstone marine park is next door.
  • Some world-class cricket (an acquired taste...).
  • Bridgetown is a fun city to visit.
  • Crane beach on the east-coast is great fun (waves and white sands).


Coming prepared

  • The local currency is Bajan dollars. US dollars are accepted everywhere, at a fair rate, and it is easy to withdraw money from any ATM. You can change some money at the airport before exiting, though the taxi will accept US dollars.
  • Barbados is hot and sunny. Some information about the weather can be found here and claims almost constant temperature during night and day at the range of 25-30 Celsius. In particular, sunscreen is a must and one should plan on summer-like weather with the possibility of showers and occasional chilly evenings. A musquito repellent is also highly recommended.
  • The institute is in St. James, which is a short walking distance to Holetown, where there is an excellent supermarket, banks, pharmacies and souvenir shops and so on, as well as cheap to expensive (and excellent) restaurants, cafes and bars. If you have a special diet (kosher, halal, vegan, ...) it is worth doing some research before hand and making sure you have what you need. Dinners in the institute will not have special dishes prepared for people with special diet. Life, in general, gravitates between the institute and Holetown. For an occasional trip to Bridgetown the public buses are a fun experience and cheap, and shared taxis are a reasonable expense. Normally, one would not rent a car for the stay.
  • Stationary is not provided.
  • Coffee lovers should be mindful that the local coffee is instant coffee and bring with them ground coffee and filters.