No class on 4/6

**Broadcasting at Rm. 509 Chee-Chun Leung Cosmology Hall, National Taiwan University

1. Background

Recent developments in mathematical physics saw not only the traditional applications of mathematics in physics problems but also a remarkable effectiveness of physics in providing motivations and ideas in the discovery and understanding of mathematical structures. The goals of this course are to treat certain topics in geometry, topology and gauge theory in a unified approach and to help students appreciate some of the spectacular progresses and open problems with both points of view.
 

2. Outline

There are two aspects. In mathematics, after a review in algebraic topology and differential geometry, the course covers the geometry and topology of fibre bundles, spin and spin-c structures, fourmanifolds and their invariants. In physics, after a review in classical electromagnetism, the course covers non-Abelian gauge theory in various spacetime dimensions, with or without supersymmetries, their quantisation, anomalies, dualities and relations to the geometry of four-manifolds. The lectures are given by Prof. Siye Wu of NTHU.

3. Credit: 3