中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Professor Mathieu Lewin（CNRS & CEREMADE, Université Paris-Dauphine, Paris）
题 目：Coulomb and Riesz gases: a review of what's known and unknown (I)
时 间：2022.10.10（星期一）16:00-17:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
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题目: Coulomb and Riesz gases: a review of what's
known and unknown (II)
时 间：2022.10.12（星期三）16:00-17:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
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题 目: Coulomb and Riesz gases: a review of what's
known and unknown (III)
时 间：2022.10.14（星期五）16:00-17:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
摘 要：Coulomb and Riesz gases play a very important role in Physics. Typical examples include galaxies or self-gravitating stars, charged systems such as plasmas, two-dimensional and geophysical flows, dipolar systems such as dielectrics and diamagnets. But long range Riesz gases also appear in many unexpected mathematical situations, including Ginzburg-Landau vortices, eigenvalues of random matrices and of random Schrödinger operators, quantum chaos, Fekete points on manifolds, zeros of the Riemann function, modular forms and sphere packing problems. Coulomb and Riesz gases appear everywhere and seem to be sort of universal.
In this course, I will review what is known and unknown for Coulomb and Riesz gases, from the point of view of statistical mechanics. I will start by recalling what has been proved in the short range case, before turning to more complicated long range systems including Coulomb. The lecture will be based on a recent review on the subject, published by the Journal of Mathematical Physics: http://dx.doi.org/10.1063/5.0086835.
Biography: Professor Mathieu Lewin is CNRS position (Directeur de Recherche) CEREMADE, Universite Paris-Dauphine. He earned His Ph.D. from Paris Dauphine University. His works concern the mathematical properties of matter at the microscopic scale, and they are mostly based on quantum mechanics. He uses tools from the calculus of variations, nonlinear functional analysis, partial differential equations, and spectral theory. For instance, he studied several nonlinear models for atoms and molecules (e.g. the Multi-configurational self-consistent field and Hartree–Fock methods), or for infinite quantum systems (e.g. in quantum field theory and condensed matter). He was a Plenary speaker at the ICMP in 2015, an Invited speaker at the ICM in 2022, and the recipient of the EMS in 2012.
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