Talk 1. Mohamed El Alami, Pure Mathematics Department, University of Waterloo
“The Hilbert Scheme as a Classifying Space”
Given some type of geometric objects (vector bundles, elliptic curves...etc) classified up to some notion of equivalence by a set X, is it possible to put a natural scheme structure on this classifying space? In cases where it is possible, the scheme X will be called a universal scheme for our type of objects. One of the most important examples is the Hilbert scheme that will be introduced as a universal scheme for closed subschemes of the n-th projective space.
Talk 2. Ruxandra Moraru, Pure Mathematics Department, University of Waterloo
“Moduli spaces of sheaves
Continuing on Mohamed’s theme, we will consider moduli spaces of sheaves. We will see in particular that Hilbert Schemes can, in some cases, be interpreted as classifying spaces of sheaves. We will also give a description of moduli spaces of vector bundles on algebraic curves.