Elliptic curves are holomorphic tori, usually considered as subsets of C². They have many amazing properties, including a group law, and form a bridge between number theory (theta functions) and analysis (Weierstrass P-function). They also find important application in cryptography. A good introduction to the subject is the lecture notes of a mini-workshop on elliptic curves that was held in Mary Immaculate College, Limerick in November 2006.

My own interest is rather more modest, as I'm working with Dr. Madeeha Khalid (St. Patricks College, Drumcondra) on elliptic curves and, more generally, holomorphic curves, in TS², with applications in line space. We have applied some of our ideas to spectral curves of monopoles in this preprint.