MINI-SCHOOL AT THE BANACH CENTER
"CHARACTERISTIC CLASSES OF SINGULAR VARIETIES"
(partially supported by EAGER)
PAOLO ALUFFI (MPI Bonn) and JOERG SCHUERMANN (Uni - Muenster)
Place: Banach Center, Warsaw, Poland
Time: April 22. 2002 (arrival day) - April 28. 2002 (departure day)
Organizers: Piotr Pragacz and Andrzej Weber
SUMMARY OF LECTURES BY P. ALUFFI:The theme of the lectures will be the comparison between different notions of characteristic classes for singular spaces. Our initial motivation will come from concrete questions in projective and enumerative geometry, leading us to define an invariant by intersection theoretic means; this invariant will turn out to be closely related to the difference between the Chern-Schwartz-MacPherson classes and Fulton classes of hypersurfaces. We will explore different ways to realize Chern-Schwartz-MacPherson's classes, including an approach via differential forms with logarithmic poles, and an approach expressing Chern-Schwartz-MacPherson's classes of a hypersurface in terms of a new notion of `Chern class' for a coherent sheaf.
SUMMARY OF THE LECTURES BY J. SCHUERMANN:After recalling the basic notations of the theory of constructible functions, we will explain the isomorphism between constructible functions and Lagrangian cycles (in the embedded context), together with a translation of these operations into the context of Lagrangian cycles. Here we use the language of "stratified Morse theory for constructible functions". Based on these results, we give a new approach to the theory of characteristic classes of singular spaces, including a generalized Verdier-Riemann-Roch theorem for regular embeddings.
Apart of the two mini-courses by Paolo Aluffi and Joerg Schoermann there is a possibility to deliver some additional talks during afternoons. We are looking forward to possible proposals. So far we announce the following PROGRAM.
All correspondence about the mini-school should be sent by e-mail
to Piotr Pragacz firstname.lastname@example.org
Mathematicians from EU wishing to participate at the mini-school may apply for the support to their home nodes of EAGER.