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Workshop

Introductory Workshop: Arithmetic Statistics January 31, 2011 - February 04, 2011
Registration Deadline: January 31, 2011 over 3 years ago
To apply for Funding you must register by: October 31, 2010 almost 4 years ago
Parent Program: Arithmetic Statistics
Organizers Barry Mazur (Harvard University), Carl Pomerance (Dartmouth College), and Michael Rubinstein* (University of Waterloo)
Speaker(s)

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Description

Our Introductory Workshop will focus largely on the background, recent work, and current problems regarding:


  • Selmer groups and Mordell-Weil groups, and the distribution of their ranks (and "sizes") over families of elliptic curves, including recent work of Manjul Bhargava and Arul Shankar where they have shown that the average size of the (2)-Selmer group of an elliptic curve over (mathbb{Q}) is (3), and thereby obtains information about the average rank of Mordell-Weil groups.

  • Related work on the asymptotics of number fields.

  • Certain natural families of (L)-functions, and the statistical distribution of their zeros and values.

  • Complementary algorithmic methods and experimental results regarding (L)-functions, automorphic forms, elliptic curves and number fields.

  • The statistical behavior of eigenvalues of Frobenius elements in Galois representations, and of related trigonometric sums.


  •  

Bibliography (PDF)
 

Accommodations

A block of rooms has been reserved at the Hotel Durant. Please mention MSRI and the workshop name when making reservations via phone, fax or e-mail. If you are making your reservations on line, please go to Hotel Durant website, choose your dates of stay and enter the "1101MSRIIN" promo code in the box. The cut-off date for reservations is December 30, 2010. The rate is $110 per night plus tax.

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

The cut-off date for reservations is January 13, 2011.

New, completely renovated Hotel Shattuck Plaza has rooms available for you!

MSRI’s preferred rate is $131. Guests can either call the hotel’s main line, 510-845-7300, and ask for the MSRI rate or go to http://www.hotelshattuckplaza.com, click on "Corporate Rates" in the reservation screen and type the code msri10.

 

 

 

Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability.

MSRI has preferred rates of $149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri.

MSRI has preferred rates of $110 - $140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
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Jan 31, 2011
Monday
08:55 AM - 09:10 AM
  Welcome
09:10 AM - 10:10 AM
  Introduction to asymptotics of number fields, conjectures, computation, experiments
Henri Cohen
10:10 AM - 10:40 AM
  Tea
10:40 AM - 11:40 AM
  Selmer groups and ranks I
Karl Rubin (University of California, Irvine)
11:40 AM - 12:40 PM
  Asymptotics of number fields
Manjul Bhargava
12:40 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Overview of NT and RMT
Michael Rubinstein (University of Waterloo)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  The ratios conjecture and applications
Nina Snaith (University of Bristol)
Feb 01, 2011
Tuesday
09:00 AM - 10:00 AM
  Selmer groups and ranks II
Karl Rubin (University of California, Irvine)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Asymptotics of number fields, II
Manjul Bhargava
11:30 AM - 12:30 PM
  Counting Galois Sextic Fields by Varying Invariants
Melanie Wood
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  Orthogonal Ensembles and Central Values of L-functions
Brian Conrey (AIM - American Institute of Mathematics)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Hyperelliptic curves, L-polynomials, and random matrices
Andrew Sutherland
05:00 PM - 06:00 PM
  Reception
Feb 02, 2011
Wednesday
08:30 AM - 09:30 AM
  Statistics of number and function fields I
Jordan Ellenberg (University of Wisconsin)
09:30 AM - 10:30 AM
  Asymptotics of elliptic curves I
Manjul Bhargava
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Finding L-Functions out of Nothing
David Farmer
12:00 PM - 01:00 PM
  Computations with Hilbert modular forms
John Voight (Dartmouth College)
Feb 03, 2011
Thursday
09:00 AM - 10:00 AM
  Asymptotics of elliptic curves II
Manjul Bhargava
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Bilinear Forms over Elliptic Curves with a Fixed Frobenius Field
Henryk Iwaniec
11:30 AM - 12:30 PM
  Statistics of number and function fields
Akshay Venkatesh (Stanford University)
12:30 PM - 02:15 PM
  Lunch
02:15 PM - 03:15 PM
  Computing Elliptic Curves using Modular Symbols
John Cremona (University of Warwick)
03:15 PM - 03:45 PM
  Tea
04:10 PM - 05:00 PM
  \(x^2 + y^3 = z^7\)
Bjorn Poonen (Massachusetts Institute of Technology)
Feb 04, 2011
Friday
09:00 AM - 10:00 AM
  Towards an analogue over Q(sqrt(5)) of Cremona\'s Tables
William Stein (University of Washington)
10:00 AM - 10:30 AM
  Tea
10:30 AM - 11:30 AM
  Random Maximal Isotropic Subspaces and Selmer Groups
Bjorn Poonen (Massachusetts Institute of Technology)
11:30 AM - 12:30 PM
  Moments of L-functions
Kannan Soundararajan
12:30 PM - 02:30 PM
  Lunch
02:30 PM - 03:30 PM
  The distribution of the zeros of L-functions in families over function fields
Chantal David (Concordia University)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Thorne: Lower terms in counting cubic fields