Vector Bundles and their Interplay with Representation Theory and String Theory

秦教授将研究代数几何及其与表示理论和弦理论的相互作用。主要的工具是投影曲面上点的Hilbert格式、顶点代数技术、量子上同调、曲面上Gieseker半稳定束的模空间和Calabi-Yau三折的全纯Casson不变量。这项研究将增加对Hilbert格式、顶点代数和量子上同调之间关系的认识，并阐明Calabi-Yau三折上的稳定束和Vafa和Witten提出的s对偶猜想。代数几何研究用多项式方程描述的几何对象。它一直处于近代数学与物理融合的中心阶段。许多这些相互作用导致了对数学和物理的理解的深刻改进。秦教授的研究领域为解释宇宙的物理理论提供了坚实的数学基础。

Professor Qin will work in the general area of algebraic geometry and its interplay with representation theory and string theory. The main tools are the Hilbert schemes of points on projective surfaces, techniques of vertex algebras, quantum cohomology, the moduli spaces of Gieseker semistable bundles on surfaces, and the holomorphic Casson invariants for Calabi-Yau three folds. The investigation should increase the knowledge about the relations among Hilbert schemes, vertex algebras and quantum cohomology, and shed light on stable bundles over Calabi-Yau three folds and the S-duality conjecture from physics in the form formulated by Vafa and Witten.Algebraic geometry studies geometric objects described bypolynomial equations. It has been at the central stageof recent confluence between mathematics and physics.Many of these interactions have led to profound improvement inthe understanding of both mathematics and physics.Professor Qin's research areas provide solid mathematical foundation to the physics theories which are vital to explain the universe.