Hodge Theory Working Seminar-Spring 2005


In the  1930’s  a British mathematician  by the name of William Hodge showed    that the  homology   of a compact  smooth algebraic  manifold    has a very rich structure which  impacts its topology.                 



A few decades later, a Belgian mathematician by the name of Pierre Deligne




showed  that this type of structure  exists on any  algebraic variety, be it smooth or singular, compact or non compact.



The goal of this working seminar is to understand  Deligne’s influential paper Theorie de Hodge,II, starting from scratch.  


The seminar will take place Fridays from 4:00 pm to 5:30 pm in 258 Hurley.


This is a joint effort   and we need  volunteers to cover the material.




January 28, Liviu I. Nicolaescu: Sheaves


February 4, John Harper: Derived functors and hypercohomology


February 11, Daniel Cibotaru: The cohomology of sheaves



February 25, Allegra Berliner: Spectral Sequences and All That



March 18, Mario Maican: The Hodge and Lefschetz decompositions of compact Kahler manifolds



April 1, Liviu I. Nicolaescu: Hodge numbers of projective hypersurfaces.  Mixed Hodge structure fundamentals


April 8, Ben Jones,  Deligne’s mixed Hodge structures for complete projective varieties with only normal crossings singularities


April 15-22, Liviu I. Nicolaescu: Mixed Hodge structures on smooth quasiprojective varieties