Jun 21, 2010
to
Jul 2, 2010
Organizer(s)
William Stein (University of Washington)
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
| Schedule |
|---|
| Monday, June 21, 2010 |
|
10:00AM - 10:55AM |
Tim Dokchitser
|
Elliptic curves and their L-functions
[Video available]
|
|
11:00AM - 11:55AM |
Jared Weinstein
|
Weinstein: talk 1
(
62.pdf
)
[Video available]
|
|
2:00PM - 2:50PM |
Matthew Greenberg
|
Greenberg: talk 1
[Video available]
|
|
3:00PM - 3:30PM |
Sage22 Participants
|
Sage 22 Participants
[Video available]
|
| Tuesday, June 22, 2010 |
|
9:30AM - 10:20AM |
John Cremona
|
Tables of Elliptic Curves
[Video available]
|
|
10:30AM - 11:20AM |
Matthew Greenberg
|
Arithmetic of mod p representations
[Video available]
|
|
11:30AM - 12:20PM |
Christian Wuthrich
|
Wuthrich: talk 1
[Video available]
|
| Wednesday, June 23, 2010 |
|
10:00AM - 10:50AM |
John Cremona
|
Verifying optimality and Manin's conjecture
[Video available]
|
|
10:50AM - 11:30AM |
William Stein
|
Computing Heegner points in Sage
[Video available]
|
| Thursday, June 24, 2010 |
|
10:00AM - 10:50AM |
John Cremona
|
Computing Isogenies
[Video available]
|
|
11:00AM - 11:50AM |
John Cremona
|
Finding all elliptic curves with good reduction outside a given set of primes
[Video available]
|
| Friday, June 25, 2010 |
|
9:10AM - 10:10AM |
Peter Norvig
|
What to demand from a Scientific Computing Language
[Video available]
|
|
10:10AM - 11:00AM |
Robert Bradshaw
|
Cython: the best of both worlds
[Video available]
|
|
11:00AM - 11:50AM |
Fernando Perez
|
An ecosystem for scientific computing
[Video available]
|
|
2:00PM - 2:50PM |
Prabhu Ramachandran
|
Python in science and engineering education in India
[Video available]
|
|
2:50PM - 3:40PM |
William Stein
|
Sage: creating an open source alternative to Ma*
[Video available]
|
|
3:10PM - 4:00PM |
Jarrod Millman
|
The Foundation for mathematical and scientific computing
[Video available]
|
|
5:00PM - 6:10PM |
Sage22 Participants
|
Discussion
[Video available]
|
| Monday, June 28, 2010 |
|
10:00AM - 10:50AM |
Jared Weinstein
|
Invitation to
[Video available]
|
|
11:00AM - 11:50AM |
Matthew Greenberg
|
Greenberg: talk 3
[Video available]
|
|
4:00PM - 5:00PM |
Cremona\'s Students
|
Cremona's students: presentations 1
[Video available]
|
| Tuesday, June 29, 2010 |
|
9:30AM - 10:20AM |
Tim Dokchitser
|
The Birch-Swinnerton-Dyer formula
[Video available]
|
|
10:30AM - 11:20AM |
Jared Weinstein
|
Weinstein: talk 3
[Video available]
|
|
11:30AM - 12:20PM |
Christian Wuthrich
|
Wuthrich: talk 2
[Video available]
|
| Wednesday, June 30, 2010 |
|
9:30AM - 10:20AM |
Christian Wuthrich
|
Wuthrich: talk 3
[Video available]
|
|
10:30AM - 11:20AM |
Tim Dokchitser
|
Parity predictions
[Video available]
|
|
11:30AM - 12:20PM |
Kenneth Ribet
|
Colloquium on Galois Representations
[Video available]
|
|
2:00PM - 3:00PM |
Lloyd Kilford
|
A Gentle Introduction to Overconvergent Modular Forms
[Video available]
|
| Thursday, July 01, 2010 |
|
9:30AM - 10:20AM |
Tim Dokchitser
|
L-functions and root numbers (background)
[Video available]
|
|
10:30AM - 11:20AM |
Christian Wuthrich
|
Wuthrich: talk 4
[Video available]
|
|
11:30AM - 12:20PM |
Jared Weinstein
|
Weinstein: talk 4
[Video available]
|
| Friday, July 02, 2010 |
|
9:30AM - 10:20AM |
Dokchister\'s Students
|
Dokchitser's student presentations
[Video available]
|
|
10:30AM - 11:50AM |
Greenberg\'s Students
|
Greenberg's student presentations
[Video available]
|
|
2:00PM - 2:50PM |
Stein_Weinstein\'s Students
|
Stein/Weinstein's student presentations
[Video available]
|
|
3:00PM - 3:50PM |
Wuthrich\'s Students
|
Wuthrich's student presentations
[Video available]
|
|
4:00PM - 4:30PM |
Cremona\'s Students
|
Cremona students (part 2)
[Video available]
|
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