Mathematical Sciences: Analytical and Computer Methods in the Study of Dynamics

De La Llave教授将研究控制许多问题的几个极大算子。在动力系统中，他将研究余循环方程及其在刚性问题中的应用，以及计算科尔莫戈洛夫。阿诺德。莫泽理论。他还将开发方法来获得薛定谔算子的数值精确下界。这个研究项目集中在数学分析中的几个问题上，这些问题与动力学系统和量子力学中的N.Body问题有关。将使用各种各样的方法。一方面，正则性问题将通过传统的硬分析方法来解决，定义适当的空间，并证明作用于它们的算子的精确估计。另一方面，这项研究将系统地使用计算机，不仅作为启发式的辅助工具，而且还将在德拉拉夫等人开发的框架中用于自动化分析估计证明的常规部分。这将使得使用人类数学家无法使用的证明策略成为可能，因为涉及到大量的基础工作。

Professor de la Llave will study several maximal operators that control many problems. In dynamical systems, he will investigate cocycle equations and their applications to rigidity problems, and computational Kolmogorov . Arnold . Moser theory. He will also develop methods to obtain numerically accurate lower bounds for Schrodinger operators. This research project concetrates on several questions in mathematical analysis that are relevant to dynamical systems and to the N.body problem in quantum mechanics. A wide variety of methods will be used. On the one hand, regularity problems will be approached by the traditional methods of hard analysis, defining appropriate spaces and proving sharp estimates for operators acting on them. On the other hand, the research will systematically use computers, not only as a heuristic aid but also in a framework being developed by de la Llave and others for automating the routine parts of proofs of analytic estimates. This will make it possible to employ proof strategies inaccessible to a human mathematician just because of the large amount of elementary work involved.