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Pro-unipotent fundamental groups: arithmetic and diophantine aspects Bellairs Research Institute, Barbados May 6-12, 2012 Principal Speaker: Minhyong Kim (Oxford) Participants: Organizer: Henri Darmon (McGill University) Co-organizer: Eyal Goren (McGill University) |
 Photo by Jayce Getz |
The purpose of the workshop will be to present aspects of the algebraic theory of the pro-unipotent fundamental group and its arithmetic applications to diophantine questions, following Minhyong Kim's progam to study rational points on varieties through anabelian descent and Chabauty-type techniques. The lectures aim to be accessible to non-experts and new-comers to the subject, including graduate students, although some background in number theory and algebraic geometry will be assumed.
A series of five two-hour lectures will be delivered in the mornings by Minhyong Kim, supplemented by lectures from attending experts in the evenings.
The Bellairs Institute provides a unique environment for scientific interaction, and the afternoons are set aside for informal discussions.
The lectures are to be held from Monday to Friday, with Sunday, May 6 as the arrival day and Saturday, May 12, as the departure day. Early arrivals (on Saturday May 5) and late departures (Sunday May 13) can be accomodated on an individual basis but please let the organisers know in advance if you wish to avail yourself of either option.
Participants' arrival and departure dates
Fabrizio Andreatta. Arr: May 6, 14:50, BA2155. Dep: May 12, 16:40, BA2154.
Jennifer Balakrishnan. Arr: May 5, 14:00, US1131. Dep: May 12, 15:15, US1132.
Massimo Bertolini. Arr: May 6, 14:50, BA2155. Dep: May 12, 16:40, BA2154.
Amnon Besser. Arr: May 7, 13:30, AA1089. Dep: May 11, 7:25, AA602.
Miljan Brakocevic. Arr: May 6, 21:55, AA651. Dep: May 12, 14:30, AA1384.
Alina Bucur. Arr: May 6, 21:55, AA651. Dep: May 11, 14:55, AA1078.
Bryden Cais. Arr: May 5, 20:10, AA514. Dep: May 13, 9:55, AA615.
Luca Candelori. Arr: May 6, 21:55, AA651. Dep: May 12, 14:30, AA1384.
Francesc Castella. Arr: May 6, 21:55, AA651. Dep: May 12, 14:30, AA1384.
Ishai Dan-Cohen. Arr: May 4, 2:50PM, BA2155. Dep: May 12, 4:40PM BA2154.
Henri Darmon. Arr: May 6, 13:55, AC966. Dep: May 12, 14:55, AC967.
Mike Daub. Arr: May 6, 12:55, AA1385. Dep: May 12, 7:25, AA602.
Jordan Ellenberg. Arr: May 6, 21:55, AA651. Dep: May 11, 7:25, AA602.
Cameron Franc. Arr: May 5, 20:10, AA514. Dep: May 11, 7:05, AA602.
Hidekazu Furusho. Arr: May 6, 13:55, AC966. Dep: May 11, 14:55, AC967.
Eyal Goren. Arr: May 6, 13:55, AC966. Dep: May 12, 14:55, AC967.
Matthew Greenberg. Arr: May 6, 13:55, AC966. Dep: May 12, 14:55, AC967.
Sheldon Joyner. Arr: May 6, 21:55, AA651. Dep: May 12, 14:55, AA1078.
Kiran Kedlaya. Arr: May 6, 21:55, AA651. Dep: May 11, 14:55, AA1078.
Minhyong Kim. Arr: May 5, 14:50, BA2155. Dep: May 12, 16:40, BA2154.
Alan Lauder. Arr: May 5, 14:50, BA2155. Dep: May 11, 16:45, BA2154.
Christopher Lazda. Arr: May 5, 13:45, VS29. Dep: May 12, 16:45, VS30.
Chung-Pang Mok. Arr: May 5, 14:44, WS2152. Dep: May 14, 15:45, WS2513.
Ravi Ramakrishna. Arr: May 6, 13:20, JetBlue 871. Dep: May 12, 14:20, JetBlue 872.
Joe Rabinoff. Arr: May 6, 21:55, AA651. Dep: May 12, 14:55, AA1078.
Victor Rotger. Arr: May 6, 13:55, AC966. Dep: May 12, 14:55, AC967.
Romyar Sharifi. Arr: May 5, 20:10, AA514. Dep: May 12, 7:25, AA602.
John Voight. Arr: May 6, 13:29, JetBlue 871. Dep: May 12, 14:25, JetBlue 872.
Jan Vonk. Arr: May 5, 14:50, BA2155. Dep: May 11, 16:45, BA2154.
Kirsten Wickelgren. Arr: May 6, 21:55, AA651. Dep: May 12, 14:55, AA1078.
Reading List
Here is a link to the Graduate Student seminar in Montreal, one of whose goals has been to cover the background necessary to understand Kim's program. Some lecture notes are posted there, aimed at the non-experts.
In addition, here is a brief reading list recommended by Minhyong. Having a look at these before the workshop will help you to arrive prepared for the lectures in Bellairs.
Minhyong Kim. The unipotent Albanese map and Selmer varieties for curves. Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 89--133.
Minhyong Kim. The motivic fundamental group of P^1-{0,1,infty} and the theorem of Siegel. Invent. Math. 161 (2005), no. 3, 629--656.
Minhyong Kim. p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication. Annals of Math. 172 (2010), no. 1, 751--759.
Minhyong Kim. Galois Theory and Diophantine geometry (expository)
These are all downloadable from Minhyong's web page. Other useful references include:
A. Besser, Coleman integration using the Tannakian formalism, Math. Ann. 322 (1) (2002) 19-48.
H. Furusho, p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation, Inventiones Mathematicae, Volume 155, Number 2, 253-286, (2004).
K. Kato. Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. I, Arithmetic algebraic geometry (Trento, 1991), Lecture Notes in Math., vol. 1553, Springer, Berlin, 1993, pp. 50-163.
S Bloch, K Kato L-functions and Tamagawa numbers of motives Grothendieck Festschrift, 1 (1990), pp. 333-400
The Bellairs Research Institute
The workshop will take place at the Bellairs Research Institute located in Holetown, St. James, Barbados. It is on the west coast of Barbados, roughly centered on the island.
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Getting to Bellairs
- The local airport is in Bridgetown, Barbados (code BGI).
- The easiest strategy to get from the airport to the institute is to take a taxi. We'll post the arrival information of other participants once we get closer to time. As there are relatively few flights into Barbados each day, you can meet up at the airport and share taxis to reduce the cost. Most taxi drivers will know how to find the Bellairs Research Institute; if not, tell them it is in St. James, north of 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. Be sure to settle the price before you start off and agree on whether it's quoted in U.S. or Barbados dollars. A 10% tip is standard.
The Facilities
- The prices of rooms vary according to the posted rate on the Institute's web site. Note that we get the "Research Staff" rate. The Institute is quite small, so we will in all likelihood have double occupancy in some rooms. Single rooms will be given in order of seniority.
- 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.
- There is a modest sized blackboard, and there is a data projector (to use with a laptop).
- Breakfast will be served at the Institute for a cost of $7 per day. In the past, it has included toast, cereal, fruit, tea, coffee, juice and something hot like pancakes, eggs or bacon. If you prefer not to have breakfast at the Institute, please let the organizers know as soon as possible.
- Dinner at the Institute is mandatory and is charged separately at $25US per night. This is not the cheapest, but the local food is great, in generous portions, and it provides a nice social opportunity. For lunch everyone is on his/her own. Usually people get together and go to one of the restaurants in Holetown. At the Institute there is a kitchen where, if needed, you can store food and cook for yourself.
- The Institute accepts Visa, Mastercard, and cash.
- The institute is a very short walk away from Holetown, where one can find a supermarket, banks, a pharmacy, restaurants, cafes, etc. Life, in general, gravitates between the institute and Holetown.
Recreational Activites
- Below We have given some suggestions for recreational activities, but this is by no means a complete list. The travel web sites Fodor's and Frommer's and Lonely Planet all have useful travel information, including maps and restaurant suggestions. There is also the tourism site barbados.org, but we have found it to be a little less user friendly.
- Bridgetown is a fun city to visit.
- The institute is well-equipped for marine research. One can rent air tanks there very cheaply. It is an excellent place for scuba diving and swimming, but you should bring your own gear.
- The institute is a 1-minute walk (literally) from the beach. It is a beautiful beach with a coral reef. The Folkstone marine park is next door.
- Crane beach on the east coast of the island was rated ``one of the ten best beaches in the world'' by Lifestyles of the Rich and Famous.
- Mount Gay Rum is one of the best rums in the world. You can take a tour and eat lunch there. Click here for details.
- Harrison's Cave looks interesting as well.
- Don't forget about math! The scientific program promises to be the highlight as well as the raison d'etre for this excursion to Barbados.
Coming Prepared
- The current exchange rate (as of March 25) is approximately 1 USD = 2 BBD (Barbados dollars). US currency and credit cards are accepted across the island (but be sure you know which currency prices are quoted in).
- Barbados uses the same electricity and outlet conventions as the United State and Canada, so most participants won't need to worry about converters or adapters.
- Pack sunscreen and mosquito repellant. A rain coat would also be advisable. Here is a link to some weather information to help you pack.
- Stationery will not be provided. It can be purchased a short walk away in Holetown, but it would be advisable to bring enough pens and paper for the trip.
- Though Barbados is largely 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).
- Sheets and towels will be provided, but this isn't a hotel. Please be sure to bring all necessary toiletries such as soap, shampoo, etc. These items can also be purchased up the road in Holetown if you forget something.