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Hopf monads generalize Hopf algebras to a non-braided setting, that is,
to arbitrary monoidal categories. The initial motivation to introduce
the notion of Hopf monad was to understand the Drinfeld-Joyal-Street
categorical center in Hopf algebraic terms. Such a description is useful
in quantum topology for comparing the Turaev-Viro and Reshetikhin-Turaev
invariants of 3-manifolds.

We will describe, by means of Bloch and Kriz's approach, the coLie algebra of mixed Tate motives over P^{^1} minus three points in terms of explicit algebraic cycles. In particular, to do so, we construct algebraic cycles corresponding to multiple polylogarithms with a specialization at the point 1 corresponding to multiple zeta values.

Singular curves over number fields have properties very different from those of smooth curves:
such a curve can have the trivial Brauer group, contain infinitely many adelic points, but only
finitely many rational points or none at all. Nevertheless, finite descent explains all counterexamples
to the Hasse principle on singular curves provided all the geometric irreducible components are rational.
Singular curves can be used to construct surfaces which are counterexamples to the Hasse

On March 15th, 2013 the Max Planck Institute for Mathematics will celebrate the 75th birthday of emeritus director Günter Harder. On this occasion there will be talks by two of his students and a special tea in honor of his important contributions to MPIM and Mathematics.