Mathematical Sciences Research Institute - Sage Days 22: Computing with Elliptic Curves

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

Currently Available Videos

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

You can find videos of other workshops and events on our VMath - Streaming Video page.

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