Mathematical Sciences: Topology and Geometry of Moduli Spaces of Vectro Bundles

9504297达斯卡洛普洛斯拟议的研究涉及数学物理的一般领域，更具体地说，是规范理论。研究人员试图更好地理解向量丛的模空间，这些向量丛是理论物理和代数几何中某些问题的解空间。分析方法，如CR流形技术，将被用来研究这些模空间及其不变量。这项拟议的研究可能会阐明唐纳森和塞贝格-维腾理论之间的关系。近年来，在理论物理(量子场论)和数学的各个部分(微分拓扑学、代数和微分几何)之间发现了一些意想不到的联系。规范理论最初是试图为描述自然的四种基本力量提供一个统一的理论框架，并在纯数学中发现了许多令人惊讶的应用。

9504297 Daskalopoulos The proposed research lies in the general area of mathematical physics; more specifically, gauge theory. The investigator seeks to gain a better understanding of moduli spaces of vector bundles arising as spaces of solutions to certain problems in theoretical physics and algebraic geometry. Analytic methods such as CR-manifold techniques are to be used to investigate these moduli spaces and their invariants. It is possible that the proposed research will shed light on the relationship between Donaldson and Seiberg-Witten theories. In recent years several unexpected connections between theoretical physics (quantum field theories) and various parts of mathematics (differential topology, and algebraic and differential geometry) have been discovered. Gauge theory began as an attempt to give a unified theoretical framework for describing the four basic forces of nature, and has found many surprising applications in pure mathematics.