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 n2/2.
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 SL2(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