Abstracts:
- Course of Paul Balmer:
We shall define triangulated categories and describe examples,
mainly in algebraic geometry and modular representation theory. We
shall discuss how much geometry one can try to develop for such
objects and we shall indicate applications, for instance to
quadratic forms via triangular Witt groups.
- Course of Jean-Pierre Tignol:
Valuations on division algebras are an indispensable tool to get
insights into the finer points of their structure; they play a
central role in the construction of noncrossed products and
counterexamples to the Kneser-Tits conjecture. An ongoing joint
work with Adrian Wadsworth aims to give a new foundation for the
theory of noncommutative valuations based on a more flexible
notion, which applies to semisimple algebras and not just to
division algebras. This series of lectures will give a survey of
this new approach and its applications to hermitian forms and
classical groups.
- Course of Alexander Vishik:
We will
define and describe the main properties of the, so-called,
Symmetric operations in Algebraic Cobordism, their connection to
Landweber-Novikov and Steenrod operations. Among the applications:
the computation of Algebraic Cobordism and Chow rings of Pfister
quadric, questions of k-rationality of cycles. The latter is
applied for the construction of fields with u-invariant
2^{r} + 1.