Mathematical Sciences: Dynamical Methods in Variational Problems

洛斯和卡伦将继续调查 非线性分析中的问题，其起源于 物理学 主要的努力之一将是获得延期 最小化非线性泛函的新方法，称为 竞争对称性 这些方法将应用于谐波 分析物理和几何 沿着类似的路线，他们将 研究玻尔兹曼方程的平衡方法， 熵产生的不平等。 现代物理学，量子力学和相对论，是一个 二十世纪的产物。 它牢固地建立在 上世纪人们试图研究物质的微观结构 并掌握远距离行动的概念， 电磁和热辐射。 数学 这些发展的基础，统称为 数学物理，范围从详细分析 薛定谔算子，控制着粒子的动力学， 统一场论，试图统一四个已知的 形成一个单一的理论。

Loss and Carlen will continue their investigations into problems in nonlinear analysis which have their origins in physics. One of the main efforts will be to obtain an extension of a new approach for minimizing nonlinear functionals, called competing symmetries. These methods will be applied to harmonic analysis, physics and geometry. Along similar lines, they will study the approach to equilibrium in the Boltzmann equations by means of entropy production inequalities. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.