= Sage Days 18: Computations related to the Birch-Swinnerton-Dyer Conjecture =

There is an [[http://www.claymath.org/workshops/sage/|Official Clay Mathematics Institute Page]] for this workshop among their [[http://claymath.org/programs/cmiworkshops/|list of workshops]].

Read the [[attachment:report.pdf|final report (pdf)]]

== Coordinates ==
  
 Date: December 1-5, 2009

 Location: Clay Mathematics Institute (Cambridge, MA) ([[http://www.claymath.org/visitors/|directions]])

== Mailing List ==

 http://groups.google.com/group/sageday18

== Projects ==

 * [[/sprints|Coding sprint projects]]
 * [[/edu|Education projects]]

== Video ==

 * The raw super-high-res HD video is here, and can be played with VLC: http://wstein.org/sagedays18/

== Schedule ==

 [[http://wstein.org/misc/sagedays18_papers.zip|sagedays18_papers.zip -- a zip archive of 23 research papers that are highly relevant to these talks]]

 [[http://wstein.org/misc/sagedays18_papers/|Browse the above zip archive of papers]]

=== Tuesday Dec 1:   Research Day ===
||9:00am -  9:30am||Registration||
||9:30am - 12:30pm||Morning working sessions||
||12:30pm -  2:00pm||Lunch||
||2:00pm -  3:00pm||William Stein:  The Kolyvagin-Gross-Zagier Approach to the Birch and Swinnerton-Dyer Conjecture  [[attachment:stein-talk-the_bsd_conjecture.pdf]]||
||3:10pm -  4:10pm||Robert Miller:  Computationally verifying BSD for individual curves||
||4:20pm -  5:20pm||Andrew Sutherland:  Images of Galois representations associated to elliptic curves[[http://math.mit.edu/~drew/ImageOfGalois.pdf]]||
||5:30pm -  6:00pm||Project organization||


=== Wednesday Dec 2: Research Day ===
|| 9:00am - 12:30pm||Morning working sessions||
||11:00am - 12:00am||Intro to Sage (linear algebra) http://sagenb.org/home/pub/1196/ [[attachment:Days 18 Linalg Demo.sws]]||
||12:30pm -  2:00pm||Lunch||
|| 2:00pm -  3:00pm||William Stein:  Computing Kolyvagin classes [[attachment:stein-talk-computing_kolyvagin_classes.pdf]] and [[attachment:389a-demo.pdf]]||
|| 3:10pm -  4:10pm||Robert Bradshaw:  Computing motivic L-functions||
|| 4:20pm -  5:20pm||Salman Baig:  Elliptic curves over function fields||
|| 5:30pm -  6:00pm||Project status reports||

=== Thursday Dec 3:  Research Day ===
|| 9:00am - 12:30pm||  Morning working sessions||
||10:00am || David Roe: Tate's algorithm over number fields (informal tutorial)||
||11:00am || Robert Miller: 2-descent in Sage (informal tutorial) ||
||12:30pm -  2:00pm||Lunch||
|| 2:00pm -  3:00pm|| Karl Rubin:  Kolyvagin systems and refined class number formulas.  Reading list: [[http://arxiv.org/abs/0909.3916|this new paper]].||
|| 3:10pm -  4:10pm||Jared Weinstein:  Distribution of Kolyvagin classes||
|| 4:20pm -  5:20pm|| Robert Pollack:  Computing p-adic L-functions||
|| 5:30pm -  6:00pm|| Project status reports||

=== Friday Dec 4:    Research Day ===
|| 9:00am - 12:30pm|| Morning working sessions||
|| 11am || Computing images of Galois representations (informal tutorial, Drew Sutherland and William Stein); See http://sagenb.org/home/pub/1205/||
||12:30pm -  2:00pm|| Lunch||
|| 2:00pm -  3:00pm|| Dimitar Jetchev:  Equidistribution of Heegner points and ternary quadratic forms||
|| 3:10pm -  4:10pm|| Mirela Ciperiani:  Solvable points and Kolyvagin's Euler system. Reading list: [[http://www.ma.utexas.edu/users/mirela/solvable.pdf|research apper]]||
|| 4:20pm -  5:20pm|| Matthew Greenberg:  Fundamental domains for Shimura curves and computation of Stark-Heegner points [[attachment::slides -- greenberg.pdf]]||
|| 5:30pm -  6:00pm|| Project status reports (final wrap up)||
 
=== Saturday Dec 5:  Sage Education Day ===
(See [[education1|Education Day]] wiki page for more stuff.)
|| 9:00am -  9:30am|| Registration||
|| 9:30am -  9:45am|| Introduction and announcements||
|| 9:45am - 10:30am|| Karl Crisman: Using Sage in the classroom    http://sagenb.org/home/pub/1212  ||
||10:30am - 11:00am|| Math software capabilities: what is and isn't in Sage||
||11:00am - 11:10am|| Break||
||11:10am - 11:30am|| Introduction to Lurch (Lite)||
||11:30am - 11:50am|| Math and word processing: what works, what doesn't, and the state of Lurch and Sage||
||11:50am - 12:20am|| Sage for newbies: logistics, browsers, portability, where documentation really is, etc.||
||12:20pm -  1:30pm|| Lunch||
|| 1:30pm -  2:30pm|| Session on undergraduate teaching with Sage [[attachment:beezer-2009-sageedu1-group-theory.pdf|Beezer, Group Theory]]||


== Organizing Committee ==
 * Craig Citro
 * Kiran Kedlaya
 * Barry Mazur
 * William Stein (chair)

All sessions are open to the public. Funding is mostly limited to invited participants; however, if you just found out about this meeting and want to participate, contact [[KiranSKedlaya|Kiran Kedlaya]] and we'll see what we can do.

On December 5, we also plan to hold the first [[education1|Sage Education Day]], coordinated by Karl-Dieter Crisman and Nathan Carter.
 
== Registered Participants ==

 * Avner Ash 
 * Salman Baig 
 * Jen Balakrishnan 
 * Thomas Barnet-Lamb 
 * Joël Bellaïche 
 * Robert Bradshaw 
 * Mirela Ciperiani 
 * Victoria Dequehen 
 * Noam Elkies (unable to come)
 * Cameron Franc 
 * Matt Greenberg 
 * Dick Gross 
 * David Harvey 
 * Dimitar Jetchev 
 * Kiran Kedlaya 
 * Robert Miller 
 * Victor Miller 
 * Robert Pollack 
 * Bjorn Poonen 
 * Jonathan Pottharst 
 * Ken Ribet 
 * David Roe 
 * Karl Rubin 
 * William Stein 
 * Glenn Stevens 
 * Andrew Sutherland 
 * John Tate 
 * Richard Taylor 
 * Jared Weinstein