Biography

Bartosz Trojan is currently a scholar at the Institute of Mathematics of the Sciences Academy of Poland

Collaboration with IHRIM Laboratory

Professor Trojan is an analyst, specializing in harmonic analysis, a field that deeply explores the Fourier transform in all its aspects, often at the crossroads with probability theory. His work frequently deals with harmonic analysis on geometrical structures linked to group theory, such as Riemannian symmetric spaces, affine buildings, and solvable groups. His research aligns with several areas of interest within the mathematics department, particularly the “Geometry, Groups and Dynamics” team, but also the “Probability” and “Analysis and Modeling” teams. 

Two main research directions could shape professor Trojan's collaboration with ENS de Lyon, especially in joint work with Bertrand Remy:

1. Littlewood-Paley Theory on Affine Buildings

This project aims to extend classical real-analysis results into the setting of non-Archimedean algebraic groups, particularly by developing harmonic analysis on the boundaries of affine buildings. This would allow for a more systematic use of functional transforms analogous to those well-known in the setting of Riemannian symmetric spaces (associated with real Lie groups). The broader goal is to contribute to a growing trend in group theory, which increasingly uses analytic tools.

2. Quantum Unique Ergodicity in a Non-Archimedean Setting

This area connects mathematical physics and dynamical systems, and asks whether certain quantum systems exhibit equidistribution of eigenfunctions at high energies. The goal is to study this problem not on classical symmetric spaces, but on their non-Archimedean counterparts: affine buildings.