12th Internet Seminar 2008/09

Ergodic Theory – An Operator-Theoretic Approach

The 12th Internet Seminar on Evolution Equations is devoted to an operator-theoretic approach to the long-term behaviour of dynamical systems on topological and/or measure spaces. The field itself – Ergodic Theory – arose from Boltzmann's work on statistical mechanics and is classical by now. During the 1970s Furstenberg developed an interesting and powerful link with combinatorial number theory, a link that also established a new field in mathematics – multiple ergodic theory whose later development forms a cornerstone in the proof of the stunning recent results of Tao and Green on arithmetic progressions in the primes. Beside these striking applications, ergodic theory comprises a lot of beautiful results from functional analysis.

The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis.

The Internet Seminar is organised by the German-Italian consortium "International School on Evolution Equations", the annual Internet Seminars introduce PhD students and postdocs to varying subjects related to Evolution Equations. The course consists of three phases.

• Phase 1 (October–February): a weekly lecture is provided via the ISEM website.
• Phase 2 (March–May): the participants from small international groups to work on projects. The Projects complement the theory of Phase 1 and provide some applications of it.
• Phase 3 (7–13 June 2009): the final one-week workshop in Blaubeuren (Germany). The teams present their projects, and lectures will be delivered by leading experts in the field.