Title of the course: Spin Geometry and Seiberg-Witten Equations
Instructor: Dr. Eyüp Yalçınkaya
Institution: –
Dates: 6-12 January 2020
Prerequisites: Linear Algebra, Riemannian Geometry
Level : Graduate
Abstract: The Spin Geometry has its roots in physics and the study of spinors. We will cover spin geometry around algebra, geometry and analysis. When combined with the Atiyah-Singer index theorem – one of the most remarkable results in twentieth century mathematics – it has far-reaching applications to geometry and topology. This course has some goals. The first goal is to understand the concept of Dirac operators. The second is to state, and prove, the Atiyah-Singer index theorem for Dirac operators. The last goal is to apply these concepts to topology: A remarkable number of topological results – including the Chern-Gauss-Bonnet theorem, the signature theorem and the Hirzebruch-Riemann-Roch theorem – can be understood just by computing the index of a Dirac operator. Finally, we focus on Seiberg-Witten invariants of four-manifolds.
Textbook or/and References:
Lawson, H. B. and M. Michelsohn – Spin Geometry , Princeton University Press, Princeton, New Jersey, 1989.
Lounesto P.- Clifford Algebras and Spinors , Cambridge University Press, London Mathematical Society Lecture Note Series 239, 2001
Language: EN/TR