Special year in dynamical systems, Laboratoire CNRS J.-V. Poncelet
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Preparatory school for non-specialists

1–3 December 2011, Poncelet Laboratory, Moscow, Russia

Flows on surfaces, symbolic dynamics and dynamics on moduli spaces

5–9 December 2011, Poncelet Laboratory, Moscow, Russia

Having a core in dynamics, the subject of the conference is located at the frontier between dynamics, geometry, topology, combinatorics, and representation theory. Certain classical problems of one-dimensional dynamics, of dynamics on surfaces, of billiards in polygons, of surface foliations, can be solved using the recent knowledge about the moduli spaces. Reciprocally, dynamical and geometric methods produce results about the moduli spaces which were difficult to obtain through pure algebro-geometric or complex-analytic approaches.

The conference is intended to put into contact experts in different aspects of the area (dynamics in moduli spaces, surface dynamics, surface foliations, horocyclic flow, symbolic dynamics, billiards in polygons), which, hopefully, would enrich everybody. It is expected that the talks would be accessible to graduate students and to non-specialists. The conference is preceded by a brief school for graduate students. The mini-courses of A. Bufetov, of J.-F. Quint, and of A. Zorich are intended to help to the graduate students get prepared for the conference.

Algebra and Geometry

June 4-9, 2012

Holomophic foliations and complex dynamics

11–15 June 2012, Poncelet Laboratory, Moscow, Russia

Theory of holomorphic foliations takes its origin in the study of the Hilbert 16-th problem concerning limit cycles of real planar polynomial vector fields: is it true that the number of limit cycles is bounded from above by a function of the degrees of its components? Now holomorphic foliations and complex dynamics are quickly developing areas on the crossing of several domains in mathematics, including dynamical systems, analysis, complex and Riemannian geometry, ergodic theory.

For example, both foliations and holomorphic dynamics arise in classification problems in complex geometry and in some problems of mathematical physics.

The conference is intended to put together specialists working in different aspects of holomorphic foliations and dynamics (analytic extension of holonomy, uniformization of leaves, complete vector fields, minimal sets, complex geometry, local complex dynamics, rational iterations) and their relation to mathemathical physics (Izing model). This would certainly enrich everybody.

See details on the conference homepage.

Ergodic theory and Lie groups

September 10-15, 2012