Topology of Algebraic Varieties

Florida State University, Tallahassee FL

Investigators

Abstract

This award will support a conference on the Topology of Algebraic Varieties at the University of Zaragoza in Spain. The subject of this conference grew out of Oscar Zariski's work from the early part of the 20th century. Zariski's original questions concerning low-dimensional complex varieties, their singularities, and moduli continue to hold interest today, as more light is shed on them by continued advances in low-dimensional topology. Topics included in this conference are braid monodromy, fundamental groups, Alexander invariants, local systems, mirror symmetry, toric geometry, characteristic classes and Hodge Theory. Solutions to polynomial equations, from low degree hypersurfaces studied by the ancient Greeks to models used in string theory and quantum field theory today, form a rich class of objects. Reasons to investigate algebraic varieties from a topological point of view are 2-fold: constraints imposed by the algebraic structure lead to constraints on topology on the one hand, and on the other hand topological information can lead to algebreo-geometric information about the moduli of varieties, and about the nature of singularities. The topology of algebraic varieties intersects a wide range of research topics including singularity theory and Hodge theory.