Curriculum vitae
Jason Andrew Colwell
Updated 2006.02.07
EDUCATION
  • Ph.D. in Mathematics (2004)
    Thesis successfully defended November 2003
    California Institute of Technology
    Field: Algebraic Number Theory
    Thesis: The Conjecture of Birch and Swinnerton-Dyer for elliptic curves with complex multiplication by a nonmaximal order
    Let E be an elliptic curve with complex multiplication (by a possibly nonmaximal order), and defined over an abelian extension F of the complex multiplication field K. Suppose that F contains the Hilbert class field of K, and that p is a prime not dividing the class number of K. Suppose further that the Mordell–Weil group of E has rank 0. Then we prove for E a strengthening, in the language of derived categories, of the p-part of Gross' refinement of the Birch–Swinnerton-Dyer Conjecture.
  • M.Sc. in Mathematics (1997)
    University of Alberta, Canada
    Field: Algebraic Geometry
    Thesis: Normal functions and their application to the Hodge Conjecture
    We explain part of the Griffiths Program for proving the Hodge Conjecture. The class map on rational algebraic cycles is split into the composition of the Abel–Jacobi map and another map which we prove is surjective. The conjecture is thus reduced to the surjectivity of the Abel–Jacobi map. A class of projective algebraic manifolds is given for which this holds.
  • B.Sc. (Honors) in Mathematics (1995)
    University of Alberta, Canada
    with First Class Honors
    the university's youngest graduate
    • ACADEMIC AWARDS AND ACHIEVEMENTS
    POSITIONS HELD

    University of California, San Diego     July 2004 to June 2006
    I hold the position of S. E. Warschawski Assistant Professor in the Department of Mathematics. It is a postdoctoral research position, and includes teaching 9 courses over 2 years.

    University of Southern California     September 2003 to May 2004
    I held a year-long appointment at the rank of Assistant Professor. In the Fall term, I taught two sections of statistics for Business students. In the Spring Term, I taught two sections of calculus. My teaching duties allowed time for research.

    Pepperdine University     June 2003
    As an Adjunct Instructor, I taught a course in Calculus, Probability, and Linear Algebra to business majors from June 2 to June 27.

    California Institute of Technology      September 1998 to June 2003
    During my five years at the California Institute of Technology, I was a teaching assistant in twenty different course sections of freshman mathematics, which included Calculus and Linear Algebra. In the last two years, I was the Lead Teaching Assistant for freshman mathematics, responsible for coordinating the work of all teaching assistants for the same course.

    My duties included giving weekly recitations, grading assignments and exams, writing homework solutions and the corresponding grading schemes, and holding office hours, both scheduled and by appointment.

    University of Alberta      September 1997 to May 1998
    At the University of Alberta, I was a lecturer in four courses in the Department of Mathematical Sciences. In the fall term, I taught Combinatorial Geometry, a course which I was asked to design. In the winter term, I taught two Calculus courses, one to Engineering students and the other to Science students. Finally, I offered a course in Axiomatic Geometry in the spring term.

    University of Alberta September     1995 to May 1997
    During two years as a graduate teaching assistant, I conducted labs in three sections of Calculus III.

    PUBLICATIONS
    SUBMITTED WORK
    CONFERENCE PRESENTATIONS
    CONFERENCES ATTENDED
    PLANS FOR FUTURE RESEARCH

    I plan to continue my study of L-functions and elliptic curves. I hope to extend results like the Burns-Flach Conjecture to the case where the Mordell–Weil group has positive rank. As well, I would like to prove similar results for powers of the Grössencharacter.

    For the case where the Mordell–Weil group has positive rank, I would make the assumption that the order of vanishing of each factor of the L-function (the factors being indexed over the characters of Gal(F/K) is at most 1. The Gross–Zagier formula would be used to find the derivative of the L-function. This would then involve the study of the heights of Heegner points and of the Rankin L-series associated to the product of two modular forms.

    NON-MATHEMATICAL ACTIVITIES
    Invention
    Crank assembly for a full-suspension bicycle
    U.S. Patent #6,474,669
    November 5, 2002

    Publications

    Conference presentation
    Annual Conference of the American Scientific Affiliation
    Pepperdine University     August 2002
    Presented "Chaos and Providence."

    LEISURE ACTIVITIES

    Reading, Mountain biking, Hiking, Snowboarding, Dancing, Horseback riding, Roller-skating

    REFERENCES