The Geometry and Physics of Hitchin Systems

Steven Rayan Associate Professor, Department of Mathematics & Statistics at the University of Saskatchewan
Director, Centre for Quantum Topology and Its Applications

Abstract: The moduli space of stable Higgs bundles on a Riemann surface, known as the Hitchin system, arises as a space of gauge-equivalent, dimensionally-reduced solutions to the self-dual Yang-Mills equations. This moduli space turns out to be a completely integrable Hamiltonian system; a noncompact Calabi-Yau manifold; and the natural setting for a mirror symmetry that is intertwined with Langlands duality. In this talk, I will introduce the Hitchin system from multiple points of view and sketch the interesting algebraic and geometric features that have been discovered over the past 30 years. I will conclude by speculating on connections between Higgs bundles and condensed-matter physics.