Group theory, topology and dynamics: Russian-Swiss collaboration

The main goal of this proposal is to organize a strong multi-disciplinary research group working in a rapidly developing area at the intersection of  dynamical systems, low-dimensional topology and geometric group theory. The group will include several leading mathematicians from Switzerland and Russia, as well as young researchers and graduate students from both countries.

Historically, since the work of Poincaré in the beginning of the 20th century, there was a fruitful interaction between dynamics, topology and geometric group theory. Multi-disciplinary approach combining algebraic, geometric and dynamical intuition and techniques continues to be extremely productive and has led in recent years to spectacular developments in all these subjects. Areas of front-line research include Teichmüller dynamics, ergodic theory, measurable group theory, theory of groups of homeomorphisms and so on.

Mathematical ties between Russia and Switzerland have a long and successful history, and there currently exist many active mathematical collaborations between our two countries. In the same time, Swiss Universities and Russian counterparts have established global cooperation programs and many students have benefited from existing exchanges. In this beneficial situation for further development of contacts and mobility,  our project aims at creating a solid framework for more regular and active research collaboration.

Given the scope of the present call for proposals, we have decided, as the first step, to concentrate our efforts on the creation of  a "triangle" including one cluster in Switzerland (with PA and her group at the University of Geneva and a former collaborator now starting independent research at the University of Neuchâtel) and two clusters in Russia: in Moscow (with PA and her group at the Higher School of Economics in Moscow and  one senior participant and his group at Steklov Institute) and at the St.Petersburg State University. All these departments are centers of excellence in the area of the project, and there is high potential for further development. Indeed, based on the present proposal, we plan to extend our collaboration beyond the funded period and to seek other funds and also to expand it by eventually including other colleagues from Geneva and St.Petersburg, as well as another cluster at the University of Zurich.

An important part of the proposal consists in enhancing mobility and contacts among young members of the participating research centers. In particular, we plan such activities as internships for advanced students, doctoral school and a monthly joint online seminar. We hope that an opportunity to learn from actively working leading mathematicians and to collaborate with them in the frame of this project will allow the young talents not only to get their first results, but also to extend their scientific horizons and to form a useful network of contacts for their future academic career.

To summarize, active and regular contacts and collaboration in the frame of this project will  be beneficial for the global scientific cooperation between our two countries, for development of young researchers and for the advancement of research in Russia and in Switzerland.

Participants:

University of Geneva:

High School of Economics:

Steklov Mathematical Institute of RAS:

University of Neuchâtel:

St. Petersburg State University :