Piotr Pragacz - Böcker

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, taken from a summer school in Thurnau, aim to give an introduction to these topics, and to describe late-1990s progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersections theory and algebraic geometry.

The articles in this volume study various cohomological aspects of algebraic varieties:- characteristic classes of singular varieties;- geometry of flag varieties;- cohomological computations for homogeneous spaces;- K-theory of algebraic varieties;- quantum cohomology and Gromov-Witten theory.The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before.Contributors:Paolo AluffiMichel BrionAnders Skovsted BuchHaibao DuanAli Ulas Ozgur KisiselPiotr PragaczJorg SchurmannMarek SzyjewskiHarry Tamvakis