High and low dimensional gauge theory and exceptional geometry

• Applicant: Professor Dr. Andriy Haydys
• Subject Area: Mathematics
• Term: from 2009 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 159746811

• Final Report Year: 2012

Final Report Abstract

The study of the Taubes-Pidstrygach construction for certain moduli spaces led to the discovery of a new gauge theory in dimension five. This new gauge theory was independently discovered by Witten and is related to a number of mathematical areas such as Khovanov homology, Langlands duality, and SL2(C)-Chern-Simons theory. One of the particularly interesting features of this five-dimensional gauge theory is its relation with the complex Morse theory (symplectic Lefschetz fibrations). This led in turn to a new construction of the Fukaya-Seidel category, a relatively recent invariant of symplectic Lefschetz fibrations.

Publications

• Fukaya-Seidel category and gauge theory
  A. Haydys