Recent Developments in Number Theory:

Selmer Groups, L-functions, and Galois Deformations

March 24 - 29, 2008

UCLA, Los Angeles, CA, USA



Connections between L-functions and Galois representations are at the heart of modern research in algebraic number theory and arithmetic geometry. They are encoded, for example, in the Bloch-Kato conjectures and their p-adic analogues, the Iwasawa-Greenberg Main Conjectures. Recent years have seen explosive developments, especially in the application of automorphic methods to these problems. The aim of this research-oriented instructional workshop is to bring together students and specialists in hopes of inspiring further research and progress in the direction of the above conjectures. The conference will have two parts. Some of the lectures in the mornings will be devoted to instructional talks on the themes, while the afternoons will consist of talks on recent developments.

Announcements


  • Links to audio and photos from all the talks can be found here.
  • Please see this form for reimbursement information.
  • Note: it turns out that the Claremont didn't have quite enough space for everyone, so some funded participants have been placed at the Royal Palace Westwood. If you are receiving support for lodging, and have not yet received an email with information about where you're staying, please e-mail us right away.
  • Abstracts have been added for almost all talks. (March 11)
  • We are planning an informal trip to the Getty Center on the evening of Friday, March 28. If you are interested in attending, please e-mail us to let us know! (More details are below.) (March 9)
  • The (tentative) schedule has been posted. (March 9)
  • There will be a conference banquet on March 27. Details are below. Please let us know by February 22 if you would like to attend the banquet.


Schedule (tentative)


All talks are in MS 4000A. Tea and cookies will be in the Graduate Lounge (MS 6620). There will be a registration desk in the Lounge during the morning tea and coffee, where participants can get their nametag, pay for the banquet, ask questions, etc. If you're registered for the banquet, please stop by to pick up your ticket at the registration desk.

The desk will be closed during the lectures.


Monday, March 24

8:40am - 9:15am
Coffee, tea, and breakfast pastries

9:20am - 10:50am Frank Calegari Families of Galois representations and families of automorphic forms -- an introduction.

Notes
11:05am - 12:05pm Mladen Dimitrov Hida families for GL(2) over totally real fields

Notes
12:05pm - 1:30pm
Lunch

1:30pm - 3:00pm Michael Harris Construction of p-adic L-functions for unitary groups I

Notes
3:00pm - 3:30pm
Coffee, tea, and cookies

3:30pm - 4:30pm Adrian Iovita Crystalline comparison isomorphisms for formal schemes
4:45pm - 5:45pm Atsushi Yamagami p-adic analytic families of eigenforms of infinite slope

Tuesday, March 25

8:40am - 9:15am
Coffee, tea, and breakfast pastries

9:30am - 10:30am Florian Herzig Weights in a Serre-type conjecture for n-dimensional Galois representations

Notes
11:00am - 12:00pm Michael Schein Weights in Serre's conjecture for Hilbert modular forms

Notes
12:00pm - 1:30pm
Lunch

1:30pm - 3:00pm Chris Skinner Construction of p-adic L-functions for unitary groups II

Notes
3:00pm - 3:30pm
Coffee, tea, and cookies

3:30pm - 4:30pm Karl Rubin Growth of Selmer rank in nonabelian extensions of number fields
4:45pm - 5:45pm Kartik Prasanna Algebraic cycles and exotic Heegner points I

Wednesday, March 26

8:40am - 9:15am
Coffee, tea, and breakfast pastries

9:30am - 10:50am Jan Nekovar Parity induced growth of Selmer groups of Hilbert modular forms over ring class fields

Slides
11:15am - 12:45pm Joel Bellaiche Unitary eigenvarieties and families of Galois representations
12:45pm - 12:55pm
Conference photo


Free afternoon

Thursday, March 27

8:40am - 9:15am
Coffee, tea, and breakfast pastries

9:20am - 10:50am Hiroyuki Yoshida Periods and the multiple gamma function in the archimedean case

Notes
11:05am - 12:05pm Tomokazu Kashio Periods and the multiple gamma function in the p-adic case

Notes
12:05pm - 1:30pm
Lunch

1:30pm - 3:00pm Shou-wu Zhang Periods and heights of Heegner points

Notes
3:00pm - 3:30pm
Coffee, tea, and cookies

3:30pm - 4:30pm Ben Howard Heegner points, Iwasawa theory, and the Gross-Zagier theorem
5:00pm - 8:00pm
Conference Banquet

Friday, March 28

8:40am - 9:15am
Coffee, tea, and breakfast pastries

9:20am - 10:50am Glenn Stevens On p-adic variation for reductive groups
11:05am - 12:05pm Joel Bellaiche On the sign of the Galois representations attached to unitary automorphic forms
12:05pm - 1:30pm
Lunch

1:30pm - 2:45pm Mirela Çiperiani Tate-Shafarevich groups over anticyclotomic Z_p extensions at supersingular primes
2:45pm - 3:20pm
Coffee, tea, and cookies

3:20pm - 4:20pm Kartik Prasanna Algebraic cycles and exotic Heegner points II
4:35pm - 5:35pm Frank Calegari How many automorphic forms are there over imaginary quadratic fields?
6:00pm - 9:00pm
Informal trip to Getty Center (food available there)

Saturday, March 29

8:40am - 9:15am
Coffee, tea, and breakfast pastries

9:15am - 10:40am Eric Urban p-adic deformation of Eisenstein cohomology classes and applications

Notes
10:55am - 11:55am Hisa-aki Kawamura Ikeda's conjecture on the period of the Ikeda lifting

Notes




Speakers



Organizers: Don Blasius (UCLA), Haruzo Hida (UCLA), Chandrashekhar Khare (UCLA), Chris Skinner (Princeton), and Eric Urban (Columbia)

Support for this conference is being provided by NSF-FRG grant DMS 0456252 and UCLA Math.

Getty Center Trip



We are planning an informal trip to the Getty Center on the evening of Friday, March 28. Information about the Getty can be found on their website. The Getty is a wonderful art museum, which has a beautiful location overlooking the city. We should be there in time for sunset, which should be at about 7:10PM that day. There is also a good cafeteria at the Getty for dinner. If you are interested in attending, please e-mail us. (We hope to be able to organize carpools, but if not, we can take the bus, which is $1.25 each way per person.)


Registration and Support



Registration: If you would like to attend this conference, please register by sending your name, e-mail address, school/affiliation, and position (graduate student, postdoc, faculty, etc.). If you wish to apply for support, there are other items you must include; see below.


Conference Banquet: There will be a conference banquet on the night of March 27, from 5-8PM, at the UCLA Faculty Center. Details have been provided by e-mail to all registered participants. If you believe you are registered and have not received any information about the banquet, please e-mail us to make sure you are registered. The banquet will be $35 to attend for participants, and is free to all speakers. We must provide a head count to the Faculty Center soon, so please let us know whether or not you would like to attend the banquet by February 22.


Support: The deadline to apply for support has passed.


Travel and Lodging: The conference begins on the morning of Monday, March 24th, and the last talk will be on the morning of Saturday, March 29th. All talks will take place on the UCLA campus. We recommend that you arrive by the evening of March 23rd, and depart in the afternoon on March 29th. For those students and postdocs receiving funding for lodging, arrangements will automatically be made for you at the Claremont Hotel. Note: it turns out that the Claremont didn't have quite enough space for everyone, so some funded participants have been placed at the Royal Palace Westwood. For other participants seeking accomodations, please make arrangements at a hotel in the area. Here is a list of hotels near the UCLA campus. Of course, there is plenty to see and do near UCLA; this is a link to some information about things to see and do near UCLA, and this is a list of nearby restaurants.