What is your field of research - briefly described?

Mathematics. Inside of Mathematics: Algebraic-Arithmetic Geometry. Algebraic geometry uses algebraic methods (in the very broad sense) to study geometry. Arithmetic Geometry uses Algebraic Geometry to solve problems stemming from Number Theory (it might also work in the other way, problems in Algebraic Geometry approached with ideas stemming from Number Theory).

What are the research challenges in your field?

They are manifold. Close to me, to understand the arithmetic properties of local systems to come closer to the understanding of conjectures relating the geometry and the arithmetic of varieties.

Why is this research area particularly interesting?

It touches various aspects of foundational objects in Algebraic-Arithmetic Geometry, a discipline which is itself at the core of pure mathematics, touching Number Theory, Topology, Differential Geometry, Analysis, Differential Equations.

What do you expect from your membership in the Royal Academy?

To communicate with scientists of other fields.

Tell us a bit about the person behind the researcher.

Oh, this is too difficult for me to do. Perhaps a good description is contained in a recent ZEIT interview by Stefan Klein

https://www.zeit.de/zeit-magazin/2021/47/mathematik-anziehungskraft-zahlen-helene-esnault