Project III 2026-27


Elliptic functions, elliptic curves, elliptic integrals

Jens Funke

Description

Elliptic functions are a classical and most beautiful topic of complex analysis which in fact was crucial in development of the field. Their rich structure and applications are truly remarkable.
In this project, we still study
  • Weierstrass theory of elliptic functions.
  • Connections with elliptic curves and elliptic integrals: (and why `elliptic' even though it has little to do with ellipsis...)
  • Further Topics (term2): Jacobi theory of elliptic functions, connections to number theory, physics etc...

Resources and Outline

There are many textbooks on the subject, but in term 1 we will mainly study the lecture notes of a (discontinued) one term course and its problem sheets covering the first two topics above.

For term 2 we will then also consult other resources depending on interest.

Warning

I will be away on research leave in term 2, so the supervision will happen remotely during that period.

Prerequisites

  • Complex Analysis II
  • Algebra IIs
  • Interest in pure mathematics, demonstrated by taking pure year III modules such NT III and/or Analysis&Topology III

email: J Funke