Vector Bundles and their Interplay with Representation Theory and String Theory

秦教授将致力于代数几何及其与表示论和弦理论的相互作用的一般领域。主要工具有射影曲面上点的Hilbert格式、顶点代数技巧、量子上同调、曲面上Gieseker半稳丛的模空间以及Calabi-Yau三重的全纯Casson不变量。这项研究将增加对希尔伯特方案、顶点代数和量子上同调之间关系的认识，并揭示Calabi-Yau三重上的稳定丛和由Vafa和Witten提出的物理上的S对偶猜想。代数几何研究用多项式方程描述的几何对象。它一直处于最近数学和物理融合的中心阶段。这些相互作用中的许多都导致了对数学和物理的理解的深刻提高。秦教授的研究领域为解释宇宙至关重要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.