Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

The moduli space of flat connections over a smooth manifold can be equipped in a very natural way with a symplectic structure. According to the theorem by Witten the symplectic volume of this space is given by a certain limit of the partition function in Yang-Mills theory. In dimension two this partition function can be calculated using a discrete approximation, which happen to give the exact value of the integral. I will present these topics and give examples when gauge group is SU(2) or SO(3)