Welcome!

The singular cohomology of an algebraic variety over C carries a number of additional structures which are collectively known as a Hodge structure.  Hodge theory seeks to classify these structures and understand how they move in families of varieties.  It is therefore an indispensable tool in algebraic geometry.  

This research group will start by introducing Hodge theory using hands-on examples and computations and will thereafter focus on applications to moduli theory and arithmetic geometry.  This is a rich area with many applications, so the exact trajectory of the course will depend on the interests of the students, but some possible more advanced topics could include:  Hermitian symmetric domains, Torelli theorems, K3 surfaces and abelian varieties, Higgs bundles, applications to fundamental groups and Galois representations, and hyperbolicity phenomena.