Courant Institute of Mathematical Sciences, NYU

*Systems of points with Coulomb interactions. I*Monday October 30, 2023 at 16:00, Tuttleman Learning Center, room 103Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, partial differential equations and probability. In the first lecture, we will review these motivations and describe the main results. In the subsequent lectures, we will present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale, and then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, as well as describing the effect of temperature.

*Systems of points with Coulomb interactions. II*Wednesday November 1, 2023 at 11:00, Wachman 617Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, partial differential equations and probability. In the first lecture, we will review these motivations and describe the main results. In the subsequent lectures, we will present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale, and then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, as well as describing the effect of temperature.

*Systems of points with Coulomb interactions. III*Wednesday November 1, 2023 at 14:00, Wachman 617Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, partial differential equations and probability. In the first lecture, we will review these motivations and describe the main results. In the subsequent lectures, we will present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale, and then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, as well as describing the effect of temperature.

April 1991 | March 1992 | March 1993 | April 1994 | November 1994 | April 1996 | October 1996 | January 1997 | April 1998 | April 1999 | March 2000 | March 2001 | March 2002 | October 2003 | April 2004 | March 2005 | November 2006 | November 2007 | November 2008 | April 2009 | April 2010 | February 2012 | April 2012 | September 2013 | September 2014 | October 2015 | September 2016 | February 2018 | October 2018 | September 2019