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