Dalimil Mazáč Awarded ERC Consolidator Grant for Research in Mathematical Physics

IHES is delighted to announce that Dalimil Mazáč, mathematical physicist and CEA Research Director at IHES, has been awarded an ERC Consolidator Grant, a prestigious recognition of his work at the interface of theoretical physics and mathematics.

Dalimil Mazáč completed his PhD at the Perimeter Institute for Theoretical Physics, followed by postdoctoral positions at Stony Brook University and the Institute for Advanced Study in Princeton. In 2023, he joined the Institut de Physique Théorique at CEA-Saclay as a permanent researcher. His research lies at the crossroads of quantum field theory and pure mathematics, particularly harmonic analysis and number theory. He aims to develop a rigorous mathematical understanding of conformal field theory (CFT) in arbitrary dimensions, inspired by the conformal bootstrap program.

Among his major contributions is the introduction of the analytic functional method, which provides precise bounds on scaling dimensions in CFTs, and the identification of a correspondence between these functionals and the solution to the sphere packing problem in dimensions 8 and 24. More recently, he has applied ideas from the conformal bootstrap to derive near-optimal bounds on spectral gaps of hyperbolic manifolds and new subconvex bounds for L-functions. His overarching goal is to leverage the interplay between physics and mathematics to deepen the foundations of quantum field theory.

To explain his project, Dalimil says:

“Quantum field theory is a cornerstone of modern physics, yet many of its foundations remain poorly understood from a rigorous mathematical perspective. My project builds on a connection I discovered between quantum field theory and classical mathematics, particularly the spectral theory of automorphic forms. This connection allows ideas to flow between the two disciplines and has already led to new mathematical results. My main goal is to use this link to provide fresh mathematical insights into conformal field theory in higher dimensions.”

Receiving the ERC Consolidator Grant is a significant recognition for him:

“I am thrilled to receive this mathematics-focused grant, even though my work is initially motivated by physics. It demonstrates that the higher-dimensional conformal bootstrap is getting inextricably linked with modern mathematics.”

This funding will allow him to recruit young researchers and organize workshops fostering exchanges between mathematicians and physicists. He also emphasizes the importance of expert feedback and the support of his team in preparing the application.