Riccardo Pengo

Riccardo Pengo

PhD Student

I am a PhD student, working under the supervision of Ian Kiming and Fabien Pazuki in the Department of Mathematics of the University of Copenhagen.

Current research

Publications and preprints

  1. "Mahler's measure and elliptic curves with potential complex multiplication" - arXiv:2005.04159
  2. "A motivic interpretation of Maillot's trick" (joint with François Brunault) - In preparation

Research interests

My primary research interests lie in arithmetic geometry, which is to say that I like to study number theoretical problems related to geometric objects, such as curves defined over the rational numbers. I am interested in the arithmetic of L-functions, which are meromorphic functions that can be associated to arithmetic objects such as Galois representations.

In particular, I like to study the relations between the "special" values of these L-functions and many kinds of height, such as the Mahler measures of polynomials. I also like thinking about various Diophantine questions related to special values of L-functions and higher regulators, such as Northcott, Bogomolov and Lehmer properties in families.

To learn more, you can read my research statement here (updated in December 2019).

Teaching

Academic year 2019/2020

During the current academic year I do not have any formal teaching duties.

I participated from time to time in this year's edition of Fabien Pazuki's course "Topics in Algebra and Number Theory" (Block 2) at the University of Copenhagen. You can find here some (handwritten) notes for my lecture on Pell's equation, and here some (handwritten) notes for my lectures (one week in January) on the local version of the Kronecker-Weber theorem

Academic year 2018/2019

During this academic year I was a teaching assistant in Fabien Pazuki's course "Topics in Algebra and Number theory" (Block 2) at the University of Copenhagen. I covered two weeks of lectures, trying to convey some ideas around the geometric notion of height and in particular around the link between Faltings height and the formula of Chowla and Selberg, as proved by Colmez. You can find the lecture notes for the course here.

I was also a teaching assistant Ian Kiming's course "Algebraic number theory" (Block 4) which took place at the University of Copenhagen.

Academic year 2017/18

During this academic year I was one of the main instructors in Fabien Pazuki's course "Topics in Algebra and Number Theory", which took place during Block 4 at the University of Copenhagen. Here you can find a program of the course. You can find the notes for this course on my blog.

Academic year 2016/17

During this academic year I was the teaching assistant of Sanne Willems for the course "Mathematics for Statisticians", which is part of the Master in Statistical Science for the Life and Behavioural Sciences of Leiden University.

ID: 182567925