## Algebraic Geometry Seminar

Matei Toma

Nancy

Complex analytic compactifications of moduli spaces of Yang-Mills connections

**Abstract:**For a complex projective manifold (X,\omega) the Kobayashi-Hitchin correspondence gives homeomorphisms between moduli spaces of irreducible Hermitian-Yang-Mills connections and moduli spaces of stable vector bundles on X. A by now classical paper of Jun Li from 1993 shows that when X is two-dimensional this correspondence can be extended as a homeomorphism between natural compactifications of these moduli spaces existing on the gauge theoretical and on the algebraic geometric side, respectively. As a consequence one gets a complex analytic structure on the Donaldson-Uhlenbeck compactification of the moduli space of Hermitian-Yang-Mills connections on a fixed hermitian vector bundle on X. In this talk we present joint recent work together with Daniel Greb, Benjamin Sibley and Richard Wentworth extending these results to the higher dimensional situation.

Wednesday October 3, 2018 at 4:00 PM in 427 SEO