Mathematics

Research

  • The Chabauty Coleman Bound at a Prime of Bad Reduction (preprint, slightly revised from the arXiv version)


  • Expository

  • Serre Spectral Sequences and Applications (Term Paper for Peter Teichner's Math 215b, Algebraic Topology; May 2, 2006)
  • Hilbert's Tenth Problem over Rings of Integers of Number Fields (Term Paper for Thomas Scanlon's Math 229, Model Theory; December 18, 2006)

    Lecture Notes

       
    My notes
    Course title (link to course page)
    Lecturer(s)
    Semester
    Additional Resources
    (pdf)
    Moduli of Surfaces BAGS: the joint Harvard/MIT Baby Algebraic geometry seminar Fall 2007
    (pdf)
    Finite Groups in Number Theory Lectures by Serre Fall 2007

    I (will soon) provide the source for most of my notes for a couple of reasons.
    1. Somebody might download all my notes, correct the errors and unclear presentation, and then send them back to me. It's not likely, but it could happen.
    2. If a bomb drops on my house and I lose all my stuff, maybe somebody can give me a copy of my notes.
    3. The source is much faster to download and compile if you're on a slow connection.
    4. Personally I appreciate being able to view the tex files of other people, and if I do use someone's notes for a course or seminar I like to have a local copy that I can modify, search quickly, format as I wish, etc.

    This part of this page (and in fact most of my TeXing abilities and conventions, and reasons 1-3 above) have been shamelessly copied from Anton Gerashenko, who has a whole bunch of goodies on his page.

    Also (again paraphrased from Anton), if you see a typo it is trivial to correct it so please let me know! And if you see a genuine mathematical error it would be immoral to not correct it, so please let me know.

    NSF

    In the interest of repeating myself less, I made an NSF GRF advice page.

    Check these out too.

    Why Everyone Should Know Number Theory

    The Rising Sea