Complex-symbolic seminar, MAA 6939, Fall 2000
Click here for Spring 2001.
Time: Wednesday 3:35 - 4:50
The Complex-Symbolic Seminar will concentrate on the following
topics.
- 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.
- Topics in computer algebra.
- Lattice reduction algorithm.
- Factoring polynomials.
These topics of the seminar include material that is very well
suited for graduate studies. Graduate students are welcome to
follow the seminar (even if not enrolled to the class).
The program above is tentative, as always, the participants
are welcome to propose other topics.
Topics by date:
- 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.