Home /  Sage Days 22: Computing with Elliptic Curves

Summer Graduate School

Sage Days 22: Computing with Elliptic Curves June 21, 2010 - July 02, 2010
Parent Program: --
Organizers William Stein (University of Washington)
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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
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Schedule, Notes/Handouts & Videos
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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