Vector Bundles and their Interplay with Representation Theory and String Theory

University Of Missouri-Columbia, Columbia MO

Investigators

Abstract

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 by polynomial equations. It has been at the central stage of recent confluence between mathematics and physics. Many of these interactions have led to profound improvement in the 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.