PhD defence by Francesco Campagna

Arithmetic and diophantine properties of elliptic curves with complex multiplication

In the last three years, elliptic curves with complex multiplication have been the test subject of my mathematical research. During this period I have tried to dissect them using several different blades, ranging from the knife of diophantine geometry to the scissors of arithmetic statistics.

But what are these "elliptic curves with complex multiplication" that are mentioned in the title of my thesis, and how are they relevant to number theory? I will try to answer this question by adopting an historical point of view and by retracing the process that led mathematicians like Euler, Abel, Jacobi and many others to the discovery of elliptic functions and complex multiplication. Once the main characters of my thesis have been introduced, I will outline some of the problems that I have been studying during my PhD.

The first part of the talk is meant to be accessible to non-specialists.



ID: 666 7462 3649
Kode: 1728

Fabien Mehdi Pazuki
Institut for Matematiske Fag (IMF) - Københavns Universitet (KU)

Assessment committee
Jasmin Matz (Chair)
Institut for Matematiske Fag (IMF) - Københavns Universitet (KU)

Yuri Bilu
Institut de Mathématiques de Bordeaux (IMB) - Université de Bordeaux

René Schoof
Università di Roma “Tor Vergata” Dipartimento di Matematica