Asbjørn Christian Nordentoft

Project title

Equidistribution, Number Theory and Geometry

What is your project about?

The project is about the statistical properties of arithmetic objects. A classic example is understanding how prime numbers are distributed among all positive integers. It turns out that prime numbers are distributed 'as if they were random'. This provides a bridge between number theory and probability theory, which is the focus of this project. More specifically, the goal is to determine the distribution of arithmetic objects in various geometric contexts. This is connected to hyperbolic geometry and chaotic phenomena in quantum mechanics.

How did you become interested in your particular field of research?

Since primary school, I have been fascinated by the wondrous world of prime numbers: so simple to define, yet so difficult to understand. In high school, I became interested in analytic number theory, which uses tools such as differential and integral calculus to investigate prime numbers. This highly surprising connection between continuous and discrete phenomena was like a bolt of lightning. At university, I continued to study these subjects and discovered that analytic number theory could also be used to understand geometric problems. I am continually surprised and fascinated by how different parts of mathematics (and other sciences) are connected in surprising ways.

What are the scientific challenges and perspectives in your project?

Although the project is in pure mathematics, it has an interdisciplinary profile: the goal is to combine techniques from different subfields of mathematics to understand some concrete (and challenging!) distribution questions. This is inherently a challenge, as it requires a broad perspective and a willingness to learn new theories and apply them to solve concrete (mathematical) problems. On the other hand, this approach provides an overview and an entry point into the research and ideas of many other mathematicians. Hopefully, the project can contribute to discovering new connections that future generations can benefit from.

What is your estimate of the impact, which your project may have to society in the long term?

Mathematics plays a completely central role in the world today. Much of the technology we use relies on (increasingly complicated) mathematics, and it is therefore more important than ever that we have people in Denmark who think deeply about mathematical problems. Furthermore, the project is part of a much larger intellectual undertaking, the goal of which is to understand the statistical properties of arithmetic objects (prime numbers, elliptic curves, etc.). This understanding forms the basis of all the cryptography used today. With quantum computers and artificial intelligence on the horizon, the tools that must be used are becoming increasingly sophisticated. The ideas involved in the project will undoubtedly play a role in this development.

Which impact do you expect the Sapere Aude programme will have on your career as a researcher?

The Sapere Aude program is an indispensable step in my career, as it makes it possible for me to build my first research group. This is absolutely central professionally, as it gives me the opportunity, together with my group, to make progress on the many mathematical ideas I have. The goal is to attract some of the best minds in the field who, in collaboration with me, will be able to push the boundaries of current knowledge. Additionally, it provides me with leadership experience, which I will hopefully need going forward.