French mathematician Nalini Anantharaman is illuminating new frontiers in delocalization of eigenfunctions despite missing critical information on the spectrum of Schrodinger operators. E=hv is a simple equation that defines much of our understanding of particle physics and energy transfer that dates to Einstein’s realization and Planck’s discoveries. But, the equation has limitations that are still being explored. Born into a family of mathematicians, Anantharaman works to resolve contemporary problems in the areas of quantum ergodicity, partial differential equations, spectral theory through elaborating on missed opportunities in Einstein’s work.
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In her plenary lecture “Delocalization of Schrödinger eigenfunctions” at ICM 2018, Anantharaman discussed physics, classical ergodic/chaotic systems and eigenvectors. She began with a brief history of particle physics, before demonstrating the contrast and interconnectedness of classical mechanics and quantum mechanics. Frequently employing Newtonian perspectives in her approach, Anantharaman highlighted the imperative to inform modeling of modern solutions with long-standing theorems. Her main questions assess probability of position within wave functions in accordance with the Schrodinger equation.
Excited to be embracing recent developments in her field, Anantharaman aims to continue her work linking with determinations in random regular graphs, Hecke operators and Quantum ergodicity on Riemann surfaces of high genus.
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