Workshop on Combinatorics, Number Theory and Dynamical Systems

Semestre Temático – Dynamics Beyond Uniform Hyperbolicity

IMPA, Rio de Janeiro, de 19/08 até 23/08

Financial Support:
The workshop has a limited number of grants to cover local expenses of students and young researchers. Applications must be submitted until July 29th, and the result will be released on August 5th. All applicants must register at the workshop’s homepage.
Students must also submit a short curriculum vitae and a recommendation letter from the advisor or equivalent. The letter must be sent directly by the recommender to, with subject line “Workshop on Combinatorics, Number Teory and Dynamical Systems”.




Rio de Janeiro has a large number of hotels. Lately, for the main congresses, we have been using Hotel Acapulco, Everest Rio Hotel, Everest Park Hotel, Hotel Debret, Hotel Vermont, among others. To take advantage of IMPA´s special rate, please contact Ms. Michele Leite at MMX Eventos – – phone: + 55 21 2210-1732 or visit their homepage at:

For other type of accommodation like hostels and bed and breakfast, we suggest the following:

Pouso Verde Bed & Breakfast (very close to IMPA and strongly recommended)
Rua Caminhoá, 14 – Jardim Botânico
Tel: + 55 21 2529-2942 , + 55 21 99971-0511



Meiai Hostel:
R. Guilhermina Guinle, 127 – Botafogo
Tel: 55(21) 3495-4481


Pousada Girassol
Travessa Angrense, 25 A – Copacabana (entre Santa Clara e Raimundo Correa)
Tel: 55(21)2256-6951 / Fax: 55(21) 2286-5652


Lagoa Guest House
Rua do Humaitá, 392 – Humaitá
Tel: 55(21) 3518-9000


Che Lagarto Ipanema
Rua Paul Redfern 48 – Ipanema
Tel: 55(21) 2512-8076

Leblon Spot (associado à Hostelling International)
Rua Dias Ferreira, 626 – Leblon
Tel: 55(21) 2137-0090

Please check availability and prices directly with them


Hotels and Flats – Rio de Janeiro








Invited Speakers

Boris Adamczewski (CNRS, France)
Pierre Arnoux (Université Aix-Marseille, France)
Artur Avila (IMPA, Brazil/CNRS, France)
Nilson Bernardes (UFRJ, Brazil)
Vitaly Bergelson (Ohio State University, USA)
Julien Cassaigne (CNRS, France)
Alex Eskin (University of Chicago, USA)
Sébastien Ferenczi (CNRS, France)
Albert Fisher (USP, Brazil)
Arek Goetz (San Francisco State University, USA)
Harald Helfgott (CNRS, France)
Yoshiharu Kohayakawa (USP, Brazil)
Elon Lindenstrauss (Hebrew University, Israel)
Ali Messaoudi (UNESP – S.J. do Rio Preto, Brazil)
János Pintz (Alfréd Rényi Institute of Mathematics, Hungary)
Miguel Walsh (Universidad de Buenos Aires, Argentina)
Barak Weiss (Tel Aviv University, Israel)
Maté Wierdl (University of Memphis, USA)


In the two weeks prior to the workshop, from August 5th to August 16th, there will be two minicourses. The purpose of the minicourses is to introduce Ph.D. students and researchers to two prominent areas of research in dynamical systems and ergodic theory, namely Ratner’s theory and Ergodic Ramsey Theory. The idea is to develop the basics and discuss the main results in these areas.

The lectures of the workshop will overlap many of the topics discussed in the minicourses, thus we encourage those interested in the workshop to attend the minicourses. Below we list the tentative syllabus.

Introduction to Ratner’s theory.

Speakers: Alex Eskin and Yuri Lima
3ª (08/06),4ª(08/07), 5ª(08/08) e 6ª(08/09) – 15:30 – 17:00 – Aud. R. Mañé
3ª(08/13) e 5ª(08/15) – 15:30 – 17:00 – Aud. 3

1.Dynamics on hyperbolic surfaces.

-The hyperbolic plane: Möbius transformations, geodesics, geodesic and horocycle flows.
-The group SL(2,R): its linear and hyperbolic actions, algebraic description of geodesic and horocycle flows, ergodic theory of Anosov flows.

2.Ratner’s theorems.

-Homogeneous spaces: group actions, Lie groups, Haar measures, quotient spaces and lattices.
-Unipotent actions: Lie algebras, the adjoint representation.
-Ratner’s theorems: orbit closure theorem, measure classification theorem, and equidistribution theorem.

3.Horocycle flows on hyperbolic surfaces.

-More on SL(2,R): KAN and Cartan decompositions, Haar measure.
-Hedlund’s theorem.
-Mautner phenomenon: representations, Mautner lemma, Mautner phenomenon on SL(2,R).
-Howe-Moore’s theorem.
-Furstenberg’s theorem.
-Dani-Smillie’s theorem.

4.Oppenheim’s conjecture.

-The moduli space SL(n,R)/SL(n,Z): Mahler compactness criterium.
-Raghunathan’s observation.
-Proof of Oppenheim’s conjecture.

Lecture notes

Introduction to Ergodic Ramsey Theory.

Speaker: Vitaly Bergelson
Title: Ergodic Ramsey theory
2ª (08/12), 3ª(08/13), 4ª(08/14) e 6ª(08/16) – 17:30 – 19:30 – Aud. 3

1.Three main principles of ergodic Ramsey theory.
2.Many facets of Poincaré recurrence theorem.
3.Uniform distribution and van der Corput sets.
4.Multiple recurrence, Szemeredi’s theorem and its extensions.
5.Topological algebra in the Stone-Cech compactifications and Ramsey theory.
6.Mild mixing, IP-sets and p-limits.
7.The nilpotent connection.
8.Ergodic Ramsey Theory and amenable groups.

Picture of the Group


Poster Session

Danilo Caprio (UNESP)
Fibonacci Adding Machine

Patricia Cirilo (UNESP)
Law of large numbers for certain cylinder flows

Pierre-Antoine Guihéneuf (Paris Sud 11)
What is the effect of spatial discretizations on dynamical systems?

Carlos Alberto Lima (USP-S.CARLOS)
Hausdorff Dimension Of Quasi-Arcs

Maurizio Monge (UNIPI)
On the failure of Kronecker’s density theorem for powers of an algebraic number

Tatiana Rodrigues (UNESP)
A class of Cubic Rauzy Fractal

Manuel Stadlbauer (UFBA)
A Ruelle theorem for transient random walks

Poster Submission

Posters should be sent to using Poster – Workshop in Combinatorics as subject. The standard adopted for posters is size A0 vertical.

Deadline for submission of posters: June 29,2013.



Registered Participants


Scientific and Organizing Committee

Yuri Lima (Weizmann, Israel)
Christian Mauduit (CNRS/Université Aix-Marseille, France)
Carlos Gustavo Moreira (IMPA, Brazil)
Enrique Pujals (IMPA, Brazil)
Carlos Matheus Santos (CNRS, France)
Marcelo Viana (IMPA, Brazil)
Jean-Christophe Yoccoz (Collège de France, France)



Visa Information

I wish to remind that US and Mexican citizens must apply for a visa to come to Brazil, concerning Europeans citizens it depends of the country, so please get in touch with the nearest Brazilian Consulate in your country in this direction.

A natural question would be the type of visa you need. Since you will not be receiving income or employment in Brazil, a tourist visa is just fine.

In order to avoid bureaucracy delays, I advise you to apply for the tourist visa as soon as possible.

Please let me know if you need an official letter of invitation sending an e-mail to