T&G: Elisheva Adina Gamse (Toronto), The moduli space of parabolic vector bundles over a Riemann surface

Tue, 22/05/201812:00-13:30
Room 110, Manchester Buildling, Jerusalem, Israel
Let $\Sigma$ be a Riemann surface of genus $g \geq 2$, and p be a point on $\Sigma$. We define a space $S_g(t)$ consisting of certain irreducible representations of the fundamental group of $\Sigma \setminus p$, modulo conjugation by SU(n). This space has interpretations in algebraic geometry, gauge theory and topological quantum field theory; in particular if Σ has a Kahler structure then $S_g(t)$ is the moduli space of parabolic vector bundles of rank n over Σ. For n=2, Weitsman considered a tautological line bundle on $S_g(t)$, and proved that the (2g)^th power of its first Chern class vanishes, as conjectured by Newstead. In this talk I will outline my extension of his work to SU(n) and to SO(2n+1).