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Summer Graduate School

Sage Days 22: Computing with Elliptic Curves June 21, 2010 - July 02, 2010
Organizers William Stein (University of Washington)
Lecturer(s) No Lecturers Assigned Yet.
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Description This workshop will introduce graduate students to several central ideas in the arithmetic of elliptic curves. Participants will join a project group that will focus mainly on one topic, possibly involving elliptic curves over number fields, complex or p-adic L-functions, Heegner points and Kolyvagin classes, Iwasawa theory, and the Birch and Swinnerton-Dyer conjecture. The workshop will emphasize the essential interplay of abstract mathematics with explicit computation, which has played a central role in number theory ever since Birch and Swinnerton-Dyer made their famous conjecture in the 1960s. Participants will use, and improve, the free open-source Python-based mathematical software system Sage (http://www.sagemath.org) for computational projects. Project Groups
  • John Cremona (Warwick University): ''Tables of elliptic curves''
  • Tim Dokchitser (Cambridge University): ''Complex L-functions and the Birch and Swinnerton-Dyer conjecture''
  • Matthew Greenberg (University of Calgary): ''Mod p representations associated to elliptic curves''
  • Jared Weinstein (UCLA) and William Stein (Univ. of Washington): ''Heegner Points and Kolyvagin's Euler system''
  • Christian Wuthrich (Nottingham): ''p-adic L-series and Iwasawa theory''
Additional information regarding the workshop can be found at http://wiki.sagemath.org/days22

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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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Jun 21, 2010
Monday
10:00 AM - 10:55 AM
  Elliptic curves and their L-functions
Tim Dokchitser
11:00 AM - 11:55 AM
  Weinstein: talk 1
Jared Weinstein (Boston University)
02:00 PM - 02:50 PM
  Greenberg: talk 1
Matthew Greenberg
03:00 PM - 03:30 PM
  Sage 22 Participants
Sage22 Participants
Jun 22, 2010
Tuesday
09:30 AM - 10:20 AM
  Tables of Elliptic Curves
John Cremona (University of Warwick)
10:30 AM - 11:20 AM
  Arithmetic of mod p representations
Matthew Greenberg
11:30 AM - 12:20 PM
  Wuthrich: talk 1
Christian Wuthrich
Jun 23, 2010
Wednesday
10:00 AM - 10:50 AM
  Verifying optimality and Manin's conjecture
John Cremona (University of Warwick)
10:50 AM - 11:30 AM
  Computing Heegner points in Sage
William Stein (University of Washington)
Jun 24, 2010
Thursday
10:00 AM - 10:50 AM
  Computing Isogenies
John Cremona (University of Warwick)
11:00 AM - 11:50 AM
  Finding all elliptic curves with good reduction outside a given set of primes
John Cremona (University of Warwick)
Jun 25, 2010
Friday
09:10 AM - 10:10 AM
  What to demand from a Scientific Computing Language
Peter Norvig
10:10 AM - 11:00 AM
  Cython: the best of both worlds
Robert Bradshaw
11:00 AM - 11:50 AM
  An ecosystem for scientific computing
Fernando Perez
02:00 PM - 02:50 PM
  Python in science and engineering education in India
Prabhu Ramachandran
02:50 PM - 03:40 PM
  Sage: creating an open source alternative to Ma*
William Stein (University of Washington)
03:10 PM - 04:00 PM
  The Foundation for mathematical and scientific computing
Jarrod Millman
05:00 PM - 06:10 PM
  Discussion
Sage22 Participants
Jun 28, 2010
Monday
10:00 AM - 10:50 AM
  Invitation to
Jared Weinstein (Boston University)
11:00 AM - 11:50 AM
  Greenberg: talk 3
Matthew Greenberg
04:00 PM - 05:00 PM
  Cremona's students: presentations 1
Cremona's Students
Jun 29, 2010
Tuesday
09:30 AM - 10:20 AM
  The Birch-Swinnerton-Dyer formula
Tim Dokchitser
10:30 AM - 11:20 AM
  Weinstein: talk 3
Jared Weinstein (Boston University)
11:30 AM - 12:20 PM
  Wuthrich: talk 2
Christian Wuthrich
Jun 30, 2010
Wednesday
09:30 AM - 10:20 AM
  Wuthrich: talk 3
Christian Wuthrich
10:30 AM - 11:20 AM
  Parity predictions
Tim Dokchitser
11:30 AM - 12:20 PM
  Colloquium on Galois Representations
Kenneth Ribet (University of California, Berkeley)
02:00 PM - 03:00 PM
  A Gentle Introduction to Overconvergent Modular Forms
Lloyd Kilford
Jul 01, 2010
Thursday
09:30 AM - 10:20 AM
  L-functions and root numbers (background)
Tim Dokchitser
10:30 AM - 11:20 AM
  Wuthrich: talk 4
Christian Wuthrich
11:30 AM - 12:20 PM
  Weinstein: talk 4
Jared Weinstein (Boston University)
Jul 02, 2010
Friday
09:30 AM - 10:20 AM
  Dokchitser's student presentations
Dokchister's Students
10:30 AM - 11:50 AM
  Greenberg's student presentations
Greenberg's Students
02:00 PM - 02:50 PM
  Stein/Weinstein's student presentations
Stein_Weinstein's Students
03:00 PM - 03:50 PM
  Wuthrich's student presentations
Wuthrich's Students
04:00 PM - 04:30 PM
  Cremona students (part 2)
Cremona's Students