Hugo Duminil-Copin

Hugo Duminil-Copin
Duminil-Copin at the Mathematisches Forschungsinstitut Oberwolfach, 2014
Hugo Duminil-Copin
Born	26 8, 1985
Birthplace	Châtenay-Malabry, Île-de-France, France
Nationality	French
Occupation	Mathematician
Employer	Institut des Hautes Études Scientifiques (IHES); University of Geneva
Known for	Probability theory, statistical physics, percolation theory, Fields Medal (2022)
Education	PhD in Mathematics, University of Geneva (2011)
Awards	Fields Medal (2022), New Horizons in Mathematics Prize (2017), Loève Prize
Website	[https://www.ihes.fr/professeur/hugo-duminil-copin/ Official site]

Hugo Duminil-Copin (born 26 August 1985) is a French mathematician who works at the intersection of probability theory and statistical physics. In 2022, at the age of 36, he was awarded the Fields Medal — the highest honor in mathematics, often described as the discipline's equivalent of the Nobel Prize — for his contributions to the understanding of phase transitions, percolation theory, and the behavior of random systems at critical thresholds. His research addresses fundamental questions about how materials change state — for example, how water becomes ice, or how a substance becomes magnetized — by developing rigorous mathematical proofs for phenomena that physicists had long described through conjecture and simulation. Born in the Parisian suburb of Châtenay-Malabry, Duminil-Copin studied at the Lycée Louis-le-Grand before completing his doctorate at the University of Geneva under the supervision of Fields Medalist Stanislav Smirnov. He holds a permanent professorship at the Institut des Hautes Études Scientifiques (IHES) near Paris, one of the world's leading centers for advanced mathematical research, and also maintains a position at the University of Geneva. His work has been recognized with numerous awards, including the New Horizons in Mathematics Prize (2017) and the Loève Prize, establishing him as one of the foremost probabilists of his generation.

Early Life

Hugo Duminil-Copin was born on 26 August 1985 in Châtenay-Malabry, a commune in the Hauts-de-Seine department in the Île-de-France region, part of the greater Paris metropolitan area. He grew up in the suburbs of the French capital and displayed an early aptitude for mathematics and logical reasoning.

According to profiles published at the time of his Fields Medal award, Duminil-Copin's approach to mathematics has always been characterized by movement and physical intuition. As Quanta Magazine noted, "with Hugo Duminil-Copin, thinking rarely happens without moving," a trait that has informed both his working style and his mathematical insights into flow-related properties of complex networks. He has been described as having an "aesthetic vision" in his mathematical work — a visual and intuitive approach to problem-solving that distinguishes his contributions from those of many peers.

Duminil-Copin has spoken publicly about his relationship with mathematics as one that developed not solely from abstract fascination but from a desire to understand the physical world through rigorous logical frameworks. In interviews following the Fields Medal announcement, he discussed the creativity and sensibility involved in mathematical work, describing it as an endeavor that combines rigorous proof with intuitive and even sensory engagement with problems.

Education

Duminil-Copin attended the Lycée Louis-le-Grand in Paris, one of France's most prestigious secondary schools and classes préparatoires, known for preparing students for entrance to the grandes écoles. The school has a long history of producing leading figures in French science and mathematics.

He subsequently pursued higher education in mathematics, eventually enrolling in a doctoral program at the University of Geneva in Switzerland. There, he studied under the supervision of Stanislav Smirnov, himself a Fields Medal laureate (2010), who had been recognized for his work on critical percolation and the Ising model — areas that would also become central to Duminil-Copin's own research. Duminil-Copin completed his PhD in 2011 with a thesis titled Phase transition in random-cluster and O(n)-models. The doctoral work laid the groundwork for many of his subsequent breakthroughs, establishing new techniques for analyzing phase transitions in lattice models that would prove extraordinarily productive in the years to come.

The relationship between Duminil-Copin and Smirnov proved intellectually formative. Working with a supervisor who had already made fundamental advances in the rigorous mathematical study of statistical physics models gave Duminil-Copin access to cutting-edge tools and perspectives, and the mentorship helped shape his research program for the following decade.

Career

Early Academic Career and the University of Geneva

Following the completion of his doctorate in 2011, Duminil-Copin continued his research at the University of Geneva, where he built upon the foundations established during his thesis work. His early career was marked by rapid and prolific output in probability theory and mathematical statistical physics. He focused particularly on problems related to percolation, the Ising model, and random-cluster models — areas of mathematics that seek to describe how large-scale behavior emerges from local interactions in random systems.

His work on critical phenomena — the mathematical study of what happens at the precise point where a system undergoes a phase transition — quickly attracted international attention. Phase transitions are ubiquitous in the physical world: they describe how water freezes into ice, how metals become magnetized, and how diseases spread through populations. Understanding these transitions at a rigorous mathematical level requires tools from probability theory, combinatorics, and complex analysis, and Duminil-Copin proved adept at combining these disciplines in novel ways.

In the 2014–2015 academic year, Duminil-Copin was invited to deliver the Cours Peccot at the Collège de France, a distinction given to mathematicians under the age of 30 who have made notable contributions to their field. This honor underscored the recognition that Duminil-Copin had already achieved at a young age within the French and international mathematical communities.

Appointment at IHES

Duminil-Copin was appointed as a permanent professor at the Institut des Hautes Études Scientifiques (IHES), located in Bures-sur-Yvette near Paris. The IHES is one of the most prestigious mathematical research institutes in the world, modeled after the Institute for Advanced Study in Princeton, and employs only a small number of permanent professors at any given time. The appointment placed Duminil-Copin among a distinguished lineage of IHES mathematicians, many of whom have been Fields Medal laureates. He maintained a dual affiliation, continuing to hold a position at the University of Geneva alongside his IHES professorship.

At IHES, Duminil-Copin continued to develop his research program in statistical physics and probability. The institute's environment — designed to allow mathematicians to pursue fundamental research without teaching obligations or administrative burdens — proved conducive to his working style, which involved extended periods of deep concentration and collaboration with mathematicians around the world.

Research Contributions

Duminil-Copin's research focuses on the mathematical branch of statistical physics, using ideas from probability theory to study the critical behavior of phase transition models. His contributions span several interconnected areas:

Percolation Theory

A central theme in Duminil-Copin's work is percolation theory, which studies how connectivity arises in random networks. In a typical percolation model, one considers a lattice (such as a grid of points) and randomly opens or closes connections between neighboring points with some probability p. At a critical value of p, the system undergoes a phase transition: below the threshold, all connected clusters are finite, while above it, an infinite connected cluster appears. Duminil-Copin made multiple breakthroughs in determining the exact critical thresholds for various percolation models and in understanding the nature of the phase transition at the critical point.

His work provided rigorous proofs for behaviors that had previously been established only through physical intuition or numerical simulation. These results had implications not only for pure mathematics but also for understanding phenomena in physics, materials science, and epidemiology, where percolation models are used to describe the spread of fluids through porous media, the failure of materials under stress, and the transmission of diseases through populations.

The Ising and Potts Models

Duminil-Copin made foundational contributions to the rigorous study of the Ising model and the Potts model, two of the most important models in statistical mechanics. The Ising model, introduced in the 1920s, describes ferromagnetism by modeling a lattice of spins that can be oriented either up or down, with neighboring spins interacting through local energy terms. The Potts model is a generalization that allows for more than two spin states. Both models exhibit phase transitions at critical temperatures, and understanding the mathematical properties of these transitions has been a central problem in mathematical physics for nearly a century.

His lectures on the Ising and Potts models on the hypercubic lattice, and their connections to random graphs, phase transitions, and the Gaussian free field, have become important references in the field. Duminil-Copin developed new techniques for analyzing these models, including innovative uses of random-cluster representations — a framework that connects spin models to percolation-type problems, allowing tools from one area to be applied in the other.

Random-Cluster Models

Building on the framework established in his doctoral thesis, Duminil-Copin continued to advance the theory of random-cluster models, also known as Fortuin-Kasteleyn representations. These models provide a unified framework for studying percolation and spin models simultaneously, and Duminil-Copin's work demonstrated their power as a tool for establishing rigorous results about phase transitions. His thesis, Phase transition in random-cluster and O(n)-models, laid out many of the foundational ideas that would underpin his later breakthroughs.

Critical Phenomena and Universality

A recurring theme in Duminil-Copin's work is the study of critical phenomena — the behavior of systems precisely at the point of a phase transition. At critical points, physical systems exhibit remarkable properties, including power-law correlations and scale invariance, where the system looks statistically similar at all length scales. Physicists have long conjectured that many of these properties are universal: they depend not on the specific details of the model but only on broad features such as the dimension of the space and the symmetry of the order parameter.

Duminil-Copin's work has provided rigorous mathematical evidence for universality in several important cases. His results on the critical behavior of percolation and the Ising model in two dimensions, and his work on establishing the sharpness of phase transitions in higher dimensions, represent major advances in placing physicists' predictions on firm mathematical footing.

Working Style and Approach

Multiple profiles have noted Duminil-Copin's distinctive approach to mathematics. Phys.org described him as having an "aesthetic vision" — a visual and intuitive approach that allows him to see connections between seemingly disparate mathematical structures. Quanta Magazine emphasized the physical, kinetic quality of his thinking, noting that movement and physical intuition play essential roles in his problem-solving process. In interviews, Duminil-Copin has described mathematics as a creative and sensory endeavor, pushing back against the stereotype of the discipline as purely abstract and detached from human experience.

A profile published in 2024 in Tagebücher der Wissenschaft noted that Duminil-Copin's reputation within the mathematical community rests not only on the depth and significance of his individual results but also on the breadth of his contributions across multiple related areas, and on his ability to develop new techniques that other researchers have subsequently adopted and extended.

Personal Life

Duminil-Copin has maintained a relatively private personal life. He splits his professional time between the IHES in Bures-sur-Yvette, near Paris, and the University of Geneva in Switzerland. He has spoken in interviews about the importance of physical activity and movement in his daily life and in his intellectual process, describing how walking and other forms of physical engagement help him work through difficult mathematical problems.

In his public appearances following the Fields Medal, Duminil-Copin has emphasized the collaborative nature of modern mathematics, crediting his many co-authors and collaborators for their roles in the research recognized by the award. He has also spoken about the importance of making mathematics accessible to broader audiences and has participated in public outreach activities, including media appearances on French-language and international broadcasts.

Recognition

Hugo Duminil-Copin has received a number of prestigious awards and honors for his mathematical contributions.

Fields Medal (2022)

In July 2022, the International Mathematical Union awarded Duminil-Copin the Fields Medal at the International Congress of Mathematicians. The Fields Medal, awarded every four years to mathematicians under the age of 40, is considered the most prestigious recognition in mathematics. The citation recognized his work on phase transitions in statistical physics, and particularly his contributions to percolation theory, the Ising model, and related topics. Le Monde reported on the award, describing Duminil-Copin as a "percolateur universel" (universal percolator).

Duminil-Copin became the latest in a line of IHES mathematicians to receive the Fields Medal, continuing the institute's association with the highest levels of mathematical achievement. The award was viewed as part of a broader period of success for French science; RFI noted that Duminil-Copin's Fields Medal "crowns [a] great year for French science."

New Horizons in Mathematics Prize (2017)

In 2017, Duminil-Copin was awarded the New Horizons in Mathematics Prize, given by the Breakthrough Prize Foundation. The prize recognized his "brilliant solutions to multiple landmark problems in probability, particularly regarding critical phenomena." The New Horizons prize is awarded to early-career researchers who have already made significant contributions to the field.

Loève Prize and Grand Prix Jacques Herbrand

Duminil-Copin received the Loève Prize, awarded biennially to a young probability theorist, and the Grand Prix Jacques Herbrand from the French Academy of Sciences in 2017. The IHES announced both awards, noting their recognition of his contributions to the rigorous mathematical study of phase transitions.

Cours Peccot

In the 2014–2015 academic year, Duminil-Copin delivered the Cours Peccot at the Collège de France, an invitation extended to mathematicians under 30 who have made notable early contributions to their field.

Legacy

Hugo Duminil-Copin's contributions have reshaped the landscape of mathematical probability theory and the rigorous study of statistical physics. His work has provided definitive mathematical proofs for conjectures and predictions that had guided physicists for decades, bridging a gap between physical intuition and mathematical rigor that had persisted since the early development of statistical mechanics in the twentieth century.

His techniques — particularly his innovative uses of random-cluster representations and his methods for establishing the sharpness of phase transitions — have become standard tools in the field, adopted and extended by researchers worldwide. The CNRS, France's national center for scientific research, has highlighted his work as exemplifying the productive interplay between pure mathematics and theoretical physics, noting that his results have implications not only for mathematics but for the broader understanding of critical phenomena in nature.

The Fields Medal in 2022 cemented Duminil-Copin's place among the leading mathematicians of the early twenty-first century. His award also reinforced France's prominent position in the mathematical world; France has produced more Fields Medalists than any country except the United States, and the IHES has been home to numerous recipients of the prize. At the time of the award, he was one of the youngest Fields Medalists in recent years, reflecting the rapidity and impact of his contributions.

Beyond his technical achievements, Duminil-Copin has contributed to the public understanding of mathematics through media appearances and interviews in which he has articulated the creative dimensions of mathematical research. His description of mathematics as involving aesthetics, intuition, and sensibility has offered an accessible portrayal of the discipline to non-specialist audiences. As profiled by multiple international outlets, his career illustrates how the abstract structures of probability theory connect to concrete questions about the physical world — from the magnetization of metals to the percolation of fluids through rock — and how rigorous mathematical proof can illuminate phenomena that touch upon everyday experience.