Geometry of coupled equations and moduli spaces

Principal Investigator: Oscar García Prada

Research Members:

Dan Jeremy Forrest

Luis Álvarez Cónsul

Mario García Fernández

Carl Tipler

Nigel James Hitchin

Simon Kirwan Donaldson



Moduli spaces are central objects that appear in the most natural classification problems in geometry. Their importance has been accentuated over the years due to the occurrence of these spaces in such diverse areas of mathematics as algebraic geometry, differential geometry, topology, algebra, and, perhaps more surprisingly, theoretical physics. This project is devoted to the study of moduli spaces arising from coupled equations in gauge theory and complex geometry, involving geometric structures of diverse types.

The proposed objectives of the project are organized around the following central themes: Higgs bundles, mirror symmetry, and Langlands duality; topology of moduli spaces of Higgs bundles and character varieties; generalizations of quivers and moduli spaces of coupled systems; the Kähler-Yang-Mills equations; the Strominger system and special holonomy; and critical symplectic connections and flat real projective structures.

The research topics proposed in this project proposal are novel, original, and of great current interest. With a rennovated team, we plan to pursue some of the most challenging problems in the field. These are themes of great interest, in the study of which there is much activity internationally, and to which the members of the project have made important contributions, leading many of their developments. For all these reasons, new and important results are to be expected.