Pro-unipotent fundamental groups:
arithmetic and diophantine aspects

Bellairs Research Institute, Barbados
May 6-12, 2012



Principal Speaker: Minhyong Kim (Oxford)



Participants:

Fabrizzio Andreatta (Milano)
Jennifer Balakrishnan (Harvard)
Joel Bellaiche (*) (Brandeis)
Massimo Bertolini (Milano)
Amnon Besser (Negev)
Miljan Brakocevic (McGill)
Alina Bucur (UCSD)
Bryden Cais (Arizona)
Luca Candelori (McGill)
Francesc Castella (McGill)
Ishai Dan-Cohen (Hannover)
Michael Daub (Berkeley)
Jordan Ellenberg (Wisconsin)
Cameron Franc (UCSC)
Hidekazu Furusho (Nagoya)
Eyal Goren (McGill)
Matt Greenberg (Calgary)
Sheldon Joyner (Brandeis)
Kiran Kedlaya (San Diego)
Minhyong Kim (Oxford)
John Labute (*) (McGill)
Christopher Lazda (Imperial)
Alan Lauder (Oxford)
Chung-Pang Mok (McMaster)
Joe Rabinoff (Harvard)
Ravi Ramakrishna (Cornell)
Victor Rotger (Barcelona)
Romyar Sharifi (Tucson)
John Voight (Vermont)
Jan Vonk (Oxford)
Kirsten Wickelgren (Harvard)

Organizer: Henri Darmon (McGill University)
Co-organizer: Eyal Goren (McGill University)

                                    Photo by Jayce Getz


Scientific Program




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.


Getting to Bellairs Coming Prepared The Facilities
Topics and Background Reading The Bellairs Research Institute Recreational Activities
Bellairs Workshop 2011 Bellairs Workshop 2010
Photos contributed by Jayce Getz




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 Facilities

Recreational Activites


Coming Prepared
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