Elliptic Curves

Lectures

• Tu 10:15 - 12
• We 14:15 - 16

The lectures will be given as a live stream via zoom. The link for this will be sent out to all registered participants in TUMOnline. If you have problems registering there, please contact me via email. All further details will be discussed in the first lecture on Tuesday, April 28.

Content

This course will will give an introduction to the theory of elliptic curves. We will look at both geometric and arithmetic aspects.

Topics:

• An introduction to algebraic geometry
• Algebraic curves
• Geometry of elliptic curves
• Elliptic curves over the complex numbers
• Elliptic curves over finite fields
• Mordell's Theorem
• Modular forms
• Applications to cryptography

Prerequisites

• Algebra I & II (i.e. Galois Theory and Commutative Algebra)
• Introduction to Algebraic Number Theory would be very useful, but not absolutely required

Preknowledge of algebraic geometry is not required.

References

We will follow relatively closely:

• Joseph Silverman: The arithmetic of elliptic curves

Other references on elliptic curves:

• Dale Husemöller: Elliptic Curves
• Joseph Silverman, John Tate: Rational Points on Elliptic Curves

References on commutative algebra:

• Gregor Kemper: A Course in Commutative Algebra
• Michael Atiyah, Ian Macdonald: Introduction to Commutative Algebra

 

Exercises

The exercise classes will be given by Kieu Hieu Nguyen.