REU 2003

In Summer 2003 the Mathematics Department of the Pennsylvania State University hosted a Research Experiences for Undergraduates site. Support for the site was provided by the National Science Foundation VIGRE grant. Thirteen participants were selected from qualified applicants.

The program ran for 7 weeks from June 23 to August 8, 2003. It combined learning with research and included:

Courses 

ELLIPTIC CURVES AND ELLIPTIC FUNCTIONS

INSTRUCTOR: YURI ZARHIN

MAIN TOPICS include:

  • Plane algebraic curves
  • A rational parametrization of quadrics and singular cubics
  • Elliptic functions; Divisors and principal divisors; The Weierstrass P-function; The field of elliptic functions
  • Elliptic curves; A parametrization of elliptic curves by elliptic functions; Addition theorems for the Weierstrass P-function and its derivative
  • A characterization of the divisors of elliptic functions
  • The projective line, projective plane and infinite points; The group law on elliptic curves

INTRODUCATION TO COMPLEX DYNAMICS

INSTRUCTOR: BRYNA KRA

MAIN TOPICS include:

  • Iteration of functions, fixed points, periodic points, attracting and repelling fixed points
  • Dynamics of the quadratic family
  • Transitivity, sensitive dependence to initial conditions
  • Chaos, Julia and Fatou Sets
  • Mandelbrot Set