## UNIVERSITY OF PENNSYLVANIA

## Department of Mathematics

Fall 2011 -Hans Rademacher Lectures in Mathematics

Claire Voisin

## Institute of Mathematics de Jussieu

University of Paris VI: Pierre and Marie Curie

will speak on

## Chow rings, decomposition of the diagonal and the topology of families

Summary: These lectures are devoted to the interplay between cohomology and Chow groups of a complex algebraic variety, and also to the consequences, on the topology of a family of smooth projective varieties, of statements concerning Chow groups of the general fiber. A crucial notion is that of coniveau of the cohomology and its conjectural relation with the shape of Chow groups of small dimension. A common theme will be that of decomposition of the diagonal, which will appear in various contexts.

Introduction to Chow groups and coniveau

Monday....October 3, 2011....4:30pm....A6 DRL

On the generalized Bloch and Hodge conjectures for complete intersections

Tuesday....October 4, 2011....4:30pm....A6 DRL

Decomposition of the small diagonal and the topology of families

Wednesday....October 5, 2011....4:30pm....A6 DRL

Integral coefficients; application to birational invariants

Thursday....October 6, 2011....4:30pm....4C8 DRL

Lectures will be held in the David Rittenhouse Laboratory (DRL),

S.E. corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: 4E17 DRL at 4:00pm.

For further information, please call the Department of Mathematics at the University of Pennsylvania - 215-898-8627.