Nalini Anantharaman: Between quantum mechanics and chaos theory

How can you hear the shape of a drum? How does the geometry of objects influence the propagation of acoustic waves emanating from them? Delving deep into the interface between mathematics and quantum physics, Nalini Anantharaman pushes back the frontiers of understanding, offering fresh insights into how the shape of an object can influence the way sound waves propagate.

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Nalini Anantharaman, born in Paris on February 26, 1976, grew up in a family of academics where the influence of the sciences was predominant. Her mother, a mathematics professor, and her father, a computer science teacher, played a central role in her academic career. From her earliest years, she distinguished herself by her excellence in mathematics, and after brilliant studies in preparatory classes at Louis-le-Grand, she entered the École normale supérieure in Paris in 1994, before obtaining a doctorate at the Pierre-et-Marie-Curie University in 2000.

After working as a lecturer at the École normale supérieure in Lyon and carrying out research at the Centre national de la recherche scientifique (CNRS), she climbed the academic ladder. In 2009, she became a professor at Paris-Sud University, marking a significant milestone in her career. Since 2014, she has held the prestigious Chair of Mathematics at the Institut de recherche mathématique avancée, consolidating her status as a leading researcher in the field of mathematics.

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Anantharaman's research delves deep into the notion of quantum chaos. She explores the intricacies of quantum mechanics, bringing to light mathematical theorems essential to understanding the chaotic nature of waves in this particular context. Her work thus offers a crucial connection between chaos theory and wave mechanics, touching on a multitude of mathematical fields such as dynamical systems theory, partial differential equations, Riemannian geometry and probability. This interdisciplinary approach testifies to the richness and diversity of his commitment to understanding complex quantum phenomena.

Her expertise in the study of Laplacian eigenfunctions has earned her many prestigious awards. In 2011, she was awarded the Salem Prize in recognition of her outstanding contributions. Her significant impact on mathematical physics, dynamical systems and the Schrödinger equation was recognized by the award of the Prix Henri-Poincaré in 2012. In 2020, his groundbreaking work on micro-local analysis and mathematical physics was rewarded with the Nemmers Prize, underlining the far-reaching impact of his research in various mathematical fields.

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In her inaugural lecture at the Collège de France, Anantharaman emphasized the importance of the right to make mistakes in the mathematical research process. She asserted with conviction that a mathematician in search of new knowledge is first and foremost a researcher who takes risks and makes mistakes. In her view, error is an indispensable element of progress, an essential catalyst for progress in all sciences. Anantharaman also emphasized the difference between the experimental approach, which encourages overcoming failure in order to move forward, and the more repetitive method often encountered in school mathematics teaching. She argued in favor of allowing time for students to experience failure, a learning process that cannot be rushed and requires a more flexible approach than the strict constraints of academic programs.

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