# Research

**Proposition.** *The stabilizer of a generalized quaternion origami for the action of the group *GL(2,**Z**)* is a congruence subgroup of index 3 or 6.*

**Theorem.** *For any even natural n, the length of a shortest integer sequence on a circle containing all permutations of the set *{1,2,...,*n*}* as subsequences is at most n*^{2}/2.

**Scientific interests**

I am currently working in the following fields (in alphabetical order): Combinatorial and Geometric Group Theory, Dynamics, Graphs, Number Theory, Permutation Groups, Representation Theory, Teichmüller Theory, Translation Surfaces

**Papers**

8. *Even permutations with small support as commutators of generating pairs*, Preprint 2014 (PDF under construction)

7. *All even permutations with large support are commut-ators of generating pairs*, Preprint 2014, submitted (PDF)

6. *An average sum on SL*_{2}*(Z)-orbits of square-tiled surfaces in H(2)*, To appear in Discrete and Continuous Dynamical System - A (PDF)

5. [with Maksim Bezrukov]

*Growth competition on Cayley graphs of groups*,

Preprint 2013 (PDF under revision)

4. [with Carlos Matheus and Jean-Christophe Yoccoz]

*Homology of origamis with symmetries*, Annales de l'Institut Fourier, Volume 64, 2014 (PDF)

3. *The probability of generating the symmetric group with a commutator condition*, Preprint 2012 (PDF)

2. [with Emmanuel Lecouturier]

*On a conjecture of H. Gupta*, Discrete Mathematics, Volume 312, Issue 8, 28 April 2012, Pages 1444-1452 (PDF, reports)

1. *Interpolation by polynomials*, Belarusian State University, Minsk, 2003 (PDF - in Russian)

**Other works**

2. *Origamis and permutation groups*, Ph.D. thesis, University Paris-Sud, Orsay, 2011 (PDF, abstract, Jury, reports)

1. *Actions of groups on origamis*, Scientific Internship report, Ecole Polytechnique, France, 2006 (PDF - in French)

**Talks and presentations**

2000-2003 ● several talks on diophantine approximations, inequalities and algebraic interpolations, Belarus

2004-2006 ● presentations on Alexandroff's theorems, Knot Theory, Poincaré Duality and Picard's theorems, France

2007 ● Ergodic Theory and Dynamics seminar, Orsay, France

2008 ● workshop "Dynamique dans l'espace de Teichmüller", Roscoff, France

2008 and 2009 ● *Groups, graphs and matrices*, Lyceum Corot, Savigny-sur-Orge, France

January 2011 ● *Square-tiled surfaces and permutation groups*, Dynamical Systems seminar of Jussieu, Paris, France

March 2011 ● *Square-tiled surfaces and permutation groups*, "Le Teich" seminar, Marseille, France

May 2012 ● *Les maths, à quoi ça sert ?*, Collège Jean-Baptiste Dumas, Salindres, France

June 2012 ● *A survey on square-tiled surfaces*, Colloquium da UMI, IMPA, Rio de Janeiro, Brazil

June 2012 ● *Generating the symmetric group*, First Palis Balzan International Symposium on Dynamical Systems, IMPA, Rio de Janeiro, Brazil

October 2013 ● *An average sum on GL(2,Z)-orbits of square-tiled surfaces in H(2)*, IRMA, Strasbourg, France

November 2013 ● *An average sum on GL(2,Z)-orbits of square-tiled surfaces in H(2)*, University Paris 13, France

February 2014 ● A talk at the Jacobs University, Bremen, Germany

**Summer schools & workshops**

2003 ● Diophantine analysis, uniform distributions and applications, conference, Minsk, Belarus

Sept. 2006 ● Analytic aspects of low dimensional geometry, symposium, University of Warwick, Coventry, UK

June-July 2007 ● Clay Mathematics Institute Summer School on Homogeneous Flows, Moduli Spaces and Arithmetic, CRM: Ennio De Giorgi, Pisa, Italy

May 2008 ● Congress in memory of Adrien Douady, IHP, Paris, France

June 2008 ● Dynamique dans l'espace de Teichmüller, workshop, Roscoff, France

June-July 2008 ● Dynamical Systems, workshop, ICTP, Trieste, Italy

June 2009 ● Dynamics and Geometry of Teichmüller Space, CIRM, Luminy, France

April 2010 ● Dynamics and PDE's, Institute Mittag-Leffler, Stockholm, Sweden

May 2011 ● Billiards, Flat Surfaces, and Dynamics on Moduli Spaces, Mathematisches Forschungsinstitut Oberwolfach, Germany

June 2012 ● First Palis Balzan International Symposium on Dynamical Systems, IMPA, Rio de Janeiro, Brazil

September 2012 ● Algebraic Geometry for the Flats, school, Roscoff, France

February 2014 ● New trends in Teichmüller theory and mapping class groups, Mathematisches Forschungsinstitut Oberwolfach, Germany