Dynamics and Variational Problems

点击翻译按钮获取中文摘要

Dynamics and Variational ProblemsAbstract of Proposed ResearchMichael Loss and Eric A. Carlen This project will support research on some mathematical problems that are motivated by questions arising from issues about the behavior of complex physical systems. We shall develop analytic and probabilistic tools to study a number of problems in statistical mechanics. These include proving results about Cercignani's conjecture, deriving optimal geometric correlation inequalities, studying certain variational principles that arise in the study of phase transitions and also some topics in Quantum electrodynamics. Many of these results center on the proof of physically motivated inequalities. The investigators have had considerable success in recent years in discovering some sharp geometrical and analytic inequalities using techniques from the calculus of variations.