Geometry: Parusinski -- Weight filtration for real algebraic varieties

Title : Weight filtration for real algebraic varieties
(report on a joint work with C. McCrory) 
(Wednesday 5 August, 11-12, 707A)

Abstract :  We associate to each real algebraic variety a filtered chain
complex, the weight complex,  which induces on Borel-Moore homology
with $\Z_2$ coefficients an analog of the Deligne’s
weight filtration for complex algebraic varieties. 

The weight complex can be represented by a geometrically
defined  filtration on the complex of semialgebraic chains.  

We apply the weight complex to construct the virtual Betti numbers, 
which are new additive invariants of real algebraic varieties.