- Elliptic curves.
- The group of points on an elliptic curve. See this Maple document for an introduction.
- Lenstra's algorithm for factoring integers with elliptic curves.
- Numerical computations.

- Topics in Riemann Surfaces.
- Uniformization

- Topics in computer algebra.
- Lattice reduction algorithm.
- Factoring polynomials.

- August 30: Organizational meeting, plus a introduction, intended for those who are new to this, to the following topic: The additive group of points of an elliptic curve over the complex numbers.
- September 6: Properties of the additive group of points of an elliptic curve over the real numbers, the rational numbers, and finite fields.
- September 13: Factoring integers with elliptic curves, Tyler Sutton.
- September 20: The Mordell-Weil Theorem.
- September 27: The lattice reduction algorithm.
- October 4: No seminar.
- October 11: Applications of lattice reduction.
- October 18: More on factoring polynomials.
- October 25: Resultant of Composed Polynomials, Manfred Minimair from NCSU.
- November 1: No seminar.
- November 8: Solving polynomial equations with resultants.
- November 15: No seminar.
- November 22: Factoring multivariate polynomials over the complex numbers.
- November 29: Finding subfields of an algebraic number field.

Time: Wednesday 3:35 - 4:50

The Complex-Symbolic Seminar will concentrate on the following topics.