• gpmoduli()

Joint miniworkshop on Moduli Spaces ICMAT-UCM 10-11 June 2014


This workshop will take place in two mornings under the ICMAT Research Term on the Geometry and Physics of Moduli Spaces. The first day the lectures will be in the Faculty of Mathematics of the Universidad Complutense de Madrid, and the second day they will be at the main ICMAT building in the Campus de Cantoblanco.



Download programme here. (PDF)


Tuesday 10 June

Venue: Facultad de Ciencias Matemáticas, sala 225, Universidad Complutense de Madrid.

  • 10:00 - 11:00 Peter Gothen (U Oporto, Portugal)
    Higgs bundles for the non-compact dual of the special orthogonal group.

    Abstract. We use Higgs bundles to study the character variety for representations of a surface group in the non-compact dual of the special orthogonal group. This talk is based on joint work with Steve Bradlow and Oscar Garcia-Prada.

  • 11:30 - 12:30 Richard Wentworth (U Maryland, US)
    A singular Bott-Chern formula and gauge theory

    Abstract. In this talk I will present a formula relating the second Chern character of a hermitian holomorphic vector bundle to that of the associated graded sheaf with respect to a filtration by reflexive subsheaves, where the graded sheaf is equipped with an admissible metric in the sense of Bando-Siu. This generalizes the classical Bott-Chern formula when the subsheaves are holomorphic subbundles. The proof relies on monotonicity properties for integrable connections on Kaehler manifolds with bounded Hermitian-Einstein tensors, and on the gauge fixing theorems of Uhlenbeck. The formula plays a key role in determining the bubbling locus along the Yang-Mills flow. This is joint work with Benjamin Sibley.

Wednesday 11 June

Venue: ICMAT, C/ Nicolas Cabrera, Campus de Cantoblanco, Sala Naranja.

  • 10:30 - 11:30 Leticia Brambilla Paz (CIMAT, Mexico)
    Grassmannians on the moduli space of stable vector bundles.

    Abstract. The minimal rational curves in the moduli space M(n,d) of stable bundles over an algebraic curve have been studied from different points of view. In this talk we generalize some of the results on minimal rational curves to minimal grassmannians in M(n,d). This is joint work with Osbaldo Mata.

  • 12:00 - 12:30 Steven Bradlow (U Illinois Urbana-Champain, US)
    Higgs bundles, spectral data, and isomorphisms among low dimensional Lie groups.

    Abstract. We will explore some interesting relations among Higgs bundles, from the point of view of spectral data, that result from special isomorphisms among low dimensional Lie algebras and Lie groups.


Organizing committee:

Oscar García-Prada (ICMAT)
Vicente Muñoz (UCM-ICMAT)



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