Mehran Kardar

Mehran Kardar is an Iranian-American theoretical physicist who has become one of the world's leading authorities in statistical physics, the branch of science that explains how the collective behavior of vast numbers of interacting particles gives rise to the rich phenomena we observe in nature. Born in 1957 in Tehran, Iran, Kardar grew up in a culture with a profound respect for learning and mathematics, and from an early age he was drawn to the elegant ways in which simple underlying rules can produce complex emergent patterns. His career has been devoted to understanding precisely this kind of emergence, from the growth of surfaces and interfaces to the behavior of fluctuating membranes and the statistical mechanics of disordered systems.

Kardar received his early education in Iran before traveling abroad to pursue advanced study. He went to the University of Cambridge in England, where he completed his undergraduate education, immersing himself in the rigorous British tradition of mathematical physics. He then crossed the Atlantic to undertake doctoral research at the Massachusetts Institute of Technology, one of the premier centers for physics in the world. At MIT he was trained in the methods of modern statistical mechanics and the renormalization group, the powerful set of techniques developed in the 1970s for understanding phase transitions and critical phenomena. He completed his PhD and then held a position at Harvard University before returning to MIT, where he joined the faculty and has remained as a professor of physics, building a distinguished career in both research and teaching.

The work for which Kardar is most widely celebrated emerged in 1986, when together with Giorgio Parisi and Yi-Cheng Zhang he formulated what is now universally known as the Kardar-Parisi-Zhang equation, almost always abbreviated as the KPZ equation. The question they addressed was deceptively simple: how does a surface grow over time when material is deposited on it randomly? Such growth occurs in countless natural and technological settings, from the burning front of a piece of paper to the advance of a bacterial colony, from the deposition of atoms in thin-film manufacturing to the spreading of a coffee stain. The KPZ equation provided a remarkably general nonlinear mathematical description of how the roughness of such growing interfaces evolves. The crucial insight was the inclusion of a particular nonlinear term that captured the lateral growth of the surface, a term that fundamentally changed the statistical behavior of the interface compared to simpler linear models.

What makes the KPZ equation so important is the concept of universality. Kardar and his collaborators showed that an enormous range of physically distinct growth processes, despite differing greatly in their microscopic details, all share the same large-scale statistical behavior, characterized by the same scaling exponents. This means that the rough surface of a growing crystal, the wandering edge of a flame, and the interface in a randomly driven fluid all belong to the same universality class. This idea of universality is one of the deepest in all of physics, and the discovery that surface growth obeyed its own universal law was a landmark achievement. The KPZ equation became one of the most studied equations in nonequilibrium statistical physics, generating thousands of research papers and inspiring developments across physics, mathematics, and even probability theory.

In the decades since its formulation, the KPZ equation has proven to be far richer than even its discoverers initially anticipated. In the realm of pure mathematics, the study of the KPZ universality class has connected to deep results in probability, including random matrix theory and the celebrated Tracy-Widom distribution, which describes the statistics of the largest eigenvalues of random matrices. These connections revealed that the fluctuations of growing interfaces in one dimension are governed by exactly the same probability distributions that appear in seemingly unrelated areas of mathematics, a discovery that has driven a major program of rigorous mathematical research and earned recognition for several mathematicians working in the field. That a physics equation about growing surfaces would illuminate such deep mathematical structures is a testament to the unity of the mathematical sciences and to the profundity of Kardar's original insight.

Beyond the KPZ equation, Kardar has made wide-ranging contributions across statistical and condensed matter physics. He has studied the statistical mechanics of polymers and membranes, including the way that thermal fluctuations affect the shapes and interactions of flexible sheets, work with relevance to the physics of biological membranes and materials such as graphene. He has investigated fluctuation-induced forces, including the Casimir effect and its thermal and geometric generalizations, exploring how the constraints imposed by boundaries on a fluctuating field can give rise to measurable forces between objects. He has also worked on problems in evolutionary biology and immunology, applying the tools of statistical physics to understand how populations of organisms and immune systems adapt and respond to challenges. This breadth reflects a conviction that the methods of statistical physics are universal tools applicable far beyond their original domain.

Kardar is also renowned as a teacher and expositor of physics. His graduate-level courses on statistical mechanics at MIT became famous for their clarity and rigor, and they formed the basis of two widely used textbooks, one on the statistical physics of particles and another on the statistical physics of fields. These books are studied by physics students around the world and have helped train a generation of researchers in the subject. His lecture notes and course materials, made freely available, have extended his influence far beyond the walls of any single university. In this way Kardar has shaped the field not only through his original research but also through his role in defining how statistical physics is taught and understood by newcomers to the discipline.

Over his career Kardar has received numerous honors recognizing his contributions. He is a fellow of the American Physical Society and has been recognized for both his research achievements and his excellence in teaching. His name, permanently attached to the KPZ equation, ensures that his work will be cited and studied as long as physicists and mathematicians investigate the behavior of growing interfaces and nonequilibrium systems.

The legacy of Mehran Kardar lies in his demonstration that order and universal law can emerge from randomness and disorder. The KPZ equation revealed that even something as seemingly mundane as a growing rough surface obeys deep and universal mathematical principles, principles that connect physics to the frontiers of pure mathematics. Through his research, his textbooks, and his teaching, Kardar has enriched our understanding of the collective behavior of complex systems and has inspired countless students and colleagues. His career, like that of so many scientists of Iranian heritage, exemplifies how a mind nurtured in one of the world's oldest centers of learning can contribute to the universal and ever-advancing enterprise of science.