The course this year concern "gauge theory on a Riemann surface". Mathematically, gauge theory is a method for studying topology of manifolds via spaces of solutions to geometrically defined partial differential equations which are invariant under certain large symmetry groups. Gauge theory is also fundamental in physics as it describes all the fundamental particles and forces. We will study one of the first applications of Gauge theory in mathematics: a proof by Donaldson of the Nahriman-Seshadri Theorem equation the space of stable holomorphic vector bundles on a Riemann surface with the projective unitary representations of its fundamental group.
- Teacher: Yoel Groman