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Arithmetic and Quantum Chaos (ARITHQUANTUMCHAOS)
Date du début: 1 févr. 2013, Date de fin: 31 janv. 2018 PROJET  TERMINÉ 

Quantum Chaos is an emerging discipline which is crossing over from Physics into Pure Mathematics. The recent crossover is driven in part by a connection with Number Theory. This project explores several aspects of this interrelationship and is composed of a number of sub-projects. The sub-projects deal with: statistics of energy levels and wave functions of pseudo-integrable systems, a hitherto unexplored subject in the mathematical community which is not well understood in the physics community; with statistics of zeros of zeta functions over function fields, a purely number theoretic topic which is linked to the subproject on Quantum Chaos through the mysterious connections to Random Matrix Theory and an analogy between energy levels and zeta zeros; and with spatial statistics in arithmetic.