Schubert varieties and degeneracy loci have a long history in
mathematics, starting from questions about loci of matrices with
given ranks. These notes, from a summer school in Thurnau, aim to
give an introduction to these topics, and to describe recent
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 intersection theory and
algebraic geometry.
General
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