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.