Mathematical Sciences: Aspects of Integrability

首席研究员将研究发生混沌和孤子行为的非线性现象。研究的主题包括非交换环上的哈密顿理论、d -棒方法的代数和解析方面、代数几何方法的代数方程解、Painleve方程及其在量子引力矩阵模型中的表现、以及超几何函数的推广。可积系统和逆散射问题在基础物理和数学模型之间建立联系方面起着重要作用。

The principal investigator will study nonlinear phenomena in which chaotic and solitonic behavior occur. Topics to be studied include Hamiltonian theory over non-commutative rings, algebraic and analytical aspects of the D-bar method, solutions of algebraic equations using algebraic geometric methods, Painleve equations and their appearance in the matrix models of quantum gravity, and generalizations of the hypergeometric functions. Integrable systems and inverse scattering problems play a fundamental role in establishing links between fundamental physics and the way in which mathematical models are used to describe it.