Critical points and spectral curves


Hitchin, N. (2017). Critical points and spectral curves. Perimeter Institute. https://pirsa.org/17020017


Hitchin, Nigel. Critical points and spectral curves. Perimeter Institute, Feb. 13, 2017, https://pirsa.org/17020017


          @misc{ pirsa_PIRSA:17020017,
            doi = {10.48660/17020017},
            url = {https://pirsa.org/17020017},
            author = {Hitchin, Nigel},
            keywords = {Mathematical physics},
            language = {en},
            title = {Critical points and spectral curves},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020017 see, \url{https://pirsa.org}}

Nigel Hitchin University of Oxford


Critical values of the integrable system correspond to singular spectral curves. In this talk we shall discuss critical points, points in the moduli space where one of the Hamiltonian vector fields vanishes. These involve torsion-free sheaves on the spectral curve instead of line bundles and a lifting to a 3-manifold which fibres over the cotangent bundle. The case of rank 2 will be described in more detail.