= 2011 Mathematics REU at UW =

<<TableOfContents>>

June 20 - August 12, 2011 


 * Organizers: Jim Morrow (Inverse Problems) and William Stein (Elliptic Curves / Sage)

 * Mailing list: http://groups.google.com/group/uwmathreu

 * [[https://spreadsheets.google.com/viewform?hl=en&formkey=dGprbTlmSFI5c250bTk3SXdBcmlzU1E6MQ#gid=0|Application Form]]

 * [[http://www.math.washington.edu/~reu/|Inverse problems page]]

 * [[http://tinyurl.com/3m6fs8f|Participant Introductions (Video)]]


= Elliptic Curves =

 * '''Participants:''' Radoslav Kirov, William Stein, Ben LeVeque, Andrew Ohana, Paul Sharaba, Ari Klages-Mundt, Ashwath Rabindranath, Simon Spicer, Aly Deines, Jon Bober

 * Location: Sieg Hall 311; phone number: 206-543-9747

 * [[/schedule|Schedule]]

 * [[/problems|Specific Problem List]]

 * [[http://groups.google.com/group/uwntreu2011|Mailing List]]

 * [[http://code.google.com/p/uw-nt-reu2011/|Google Code]]

 * Campus dining: http://www.hfs.washington.edu/dining/hours/

 * We are mainly using [[this nt.sagenb.org server|http://nt.sagenb.org]].

The elliptic curves REU will consist of projects involving elliptic curves, modular forms, and databases, and make extensive use of [[http://sagemath.org|Sage]]. It will be organized by William Stein, and the number theory postdoc Jon Bober and grad students Alyson Deines and Simon Spicer will also likely help out.  There will be about 6 students. 

== REU Background Reading List ==

Don't worry if you can't read or understand everything here.  Just read what you can, and generally skim around.  There will be lots of talks during the REU to get you up to speed. 

   * Stein's [[http://wstein.org/books/ant/|Algebraic Number Theory, a Computational Approach]]
   * Birch's [[attachment:Birch-Conjectures_Concerning_Elliptic_Curves.pdf|article that introduces the Birch and Swinnerton-Dyer Conjecture]]
   * Wiles's article on the Birch and Swinnerton-Dyer Conjecture which can be found [[http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/|on the Clay Mathematics Institute website]]
   * Tate's [[attachment:Tate-The_Arithmetic_of_Elliptic_Curves.pdf|beautiful 1974 article on elliptic curves]] and [[http://www.math.harvard.edu/~gross/preprints/ell2.pdf|Gross's update to it]].
   * Stein's [[http://wstein.org/books/modform/|book (mainly Chapter 1)]]
   * Cremona's [[http://www.warwick.ac.uk/~masgaj/book/fulltext/|book (mainly Chapters 1 and 3)]]
   * Dembele-Voight: [[http://arxiv.org/abs/1010.5727|Explicit methods for Hilbert modular forms]]
   * Open Source Software: the [[http://www.sagemath.org/doc/tutorial/|Sage]], [[http://docs.python.org/tutorial/|Python]], and [[http://docs.cython.org/index.html|Cython]] tutorials.
   * Silverman's book [[http://books.google.co.uk/books?id=Z90CA_EUCCkC&printsec=frontcover&dq=silverman+arithmetic+of+elliptic+curves&source=bl&ots=3L0giqRd_4&sig=lDT89Z1h7q1wQy8mgtuQ59xJWfE&hl=en&ei=DjG-TeraIciv8gPH_oXYBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCEQ6AEwAA#v=onepage&q&f=false|The Arithmetic of Elliptic Curves]] is very generally relevant to much of what we will do.
   * Background on canonical minimal models [[attachment:minimal_model.pdf|Canonical Minimal Models of Elliptic Curves Over Number Fields]]

== Topics may include ==

   * '''Main topic''': Creating tables of elliptic curves over the field $\mathbf{Q}({\rm sqrt}{5})$, e.g., as described [[http://wstein.org/talks/2011-02-11-sqrt5/|in this talk]], along with extensive data related to the Birch and Swinnerton-Dyer conjecture about each curve, and investigating related conjectures.  This will involve both theoretical work and coding projects. 

   * Computing additional data about elliptic curves over $\mathbf{Q}$, thus extending the data in http://db.modform.org/

   * Computing tables of modular forms (see [[http://wstein.org/books/modform/|my book]]). 
  
== Twitter Account ==

   * We now have a Twitter account! You can log on using the email address Ben.LeVeque@gmail.com and the password sent to you. This will work for now, at least. [[http://www.twitter.com]]