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Cristina Toninelli, winner of the CNRS Silver Medal for her work at the intersection of probability theory and statistical mechanics

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A CNRS Research Director at the Center for Research in Decision Mathematics (CEREMADE)1 , Cristina Toninelli is the 2026 recipient of the CNRS Silver Medal. A specialist in interacting particle systems, she has developed innovative mathematical tools to better understand slow and complex dynamics, particularly those found in kinetically constrained models designed to study the liquid-glass transition.

  • 1CNRS/UNIVERSITÉ PARIS DAUPHINE - PSL
Portrait de Cristina Toninelli
Cristina Toninelli, winner of the 2026 CNRS Silver Medal © CNRS Paris-Centre

 

Although glass is ubiquitous in our lives and its production is well understood, its fundamental nature remains partly mysterious: scientists have yet to fully grasp the glassy state and the liquid-to-glass transition. Both solid and disordered like a liquid, glass possesses a hybrid nature that is the source of its fascination.
Cristina Toninelli

After studying theoretical physics at La Sapienza University of Rome, Cristina Toninelli turned to mathematics, focusing on problems at the intersection of probability theory and statistical mechanics. This led her to join the École normale supérieure de Paris as a postdoctoral researcher, before joining the CNRS in 2006 at the Laboratory of Probability, Statistics, and Modeling2 , and then CEREMADE in 2018.

Her work focuses on interacting particle systems (IPS), which model the random evolution of a large number of particles. She is particularly interested in kinetic constraint models (KCM), introduced in physics in the 1980s to understand the liquid-glass transition. These models exhibit slow dynamics that are difficult to analyze and remained poorly understood for a long time. “One of my first results was to rigorously demonstrate that certain conjectures proposed in this context were incorrect and due to simulation artifacts,” explains the researcher. This result marks a turning point in the field and paves the way for the mathematical study of these models.

Together with her students and colleagues, she has developed mathematical tools to capture the mechanisms underlying the abnormally slow dynamics of KCMs, establish the relevant timescales, characterize their universality classes, and highlight connections with other fields, notably bootstrap percolation. “Over the years, I have thus forged connections between specialists from different fields around KCMs: probabilists, combinatorialists, physicists—both theorists and experimentalists,” explains Cristina Toninelli.

  • 2CNRS/SORBONNE UNIVERSITÉ/UNIVERSITÉ PARIS CITE
One of my main goals is to foster the development of lasting collaborations between the mathematics and physics communities. Although they work on very similar problems, they still too often operate in isolation, sometimes simply because of differences in terminology.
Cristina Toninelli

The CNRS Silver Medal recognizes her work and her strong commitment to the scientific community, an honor the researcher accepts with deep emotion. “I would like to dedicate this medal to my students: without their enthusiasm, their ideas, and their energy—and without the constant challenge of proposing thesis topics that match their talent—I could never have come this far,” she concludes.

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