Sophie Morier-Genoud
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     Publications and preprints


  • q-deformations of the modular group and of the real quadratic irrational numbers, (with L.Leclere) submitted.
  • Quantum real numbers and q-deformed Conway-Coxeter friezes., (with V. Ovsienko), submitted.
  • Counting Coxeter's friezes over a finite field via moduli spaces, Algebraic Combinatorics, to appear.
  • q-deformed rationals and q-continued fractions., (with V. Ovsienko), Forum Math. Sigma 8 (2020), e13.
  • On q-deformed real numbers, (with V. Ovsienko) Experimental Mathematics, DOI: 10.1080/10586458.2019.1671922.
  • Symplectic frieze patterns, SIGMA Symmetry Integrability Geom. Methods Appl. 15 (2019), 089, 36 pages.
  • Farey Boat. Continued fractions and triangulations, modular group and polygon dissections., (with V. Ovsienko), Jahresber. Dtsch. Math. Ver. (2019) 121:91--136.
  • On tangent cones of Schubert varieties (with D. Fuchs, A. Kirillov, V.Ovsienko), Arnold Math. J. 3 (2017), no. 4, 451--482.
  • Extremal set theory, cubic forms on $\bbF_2^n$ and Hurwitz square identities (with V. Ovsienko), Integers 16 (2016), Paper No. A28, 9 pp.
  • Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics, Bull. London Math. Soc. 47 (2015) 895-938.
  • Introducing supersymmetric frieze patterns and linear difference operators, (with V. Ovsienko, S. Tabachnikov), Math. Z. 281 (2015) Issue 3-4, 1061-1087 .
  • SL_2(\Z)-tilings of the torus, Coxeter-Conway friezes and Farey triangulations, (with V. Ovsienko, S. Tabachnikov), Enseign. Math. 61 (2015), no. 1-2, 71--92.
  • Classification of the algebras O_{p,q}, (with M. Kreusch), Comm. Algebra 43 (2015), no. 9, 3799--3815.
  • Linear difference equations, frieze patterns and combinatorial Gale transform , (with V. Ovsienko, R. Schwartz, S. Tabachnikov), Forum Math., Sigma, Vol. 2 (2014).
  • A short survey of Lie antialgebras (with S. Leidwanger), J. Phys.: Conf. Ser. 532 (2014) 012015.
  • Orthogonal designs and a cubic binary function (with V.Ovsienko), IEEE Trans. Information Theory, vol. 59, n3 (2013),1583-1589.
  • Arithmetics of 2-friezes, J. Algebraic. Combin., 36 (2012) no 4, 515-539,
  • Superalgebras associated to Riemann surfaces: Jordan algebras of Krichever-Novikov type, (with S. Leidwanger),Int. Math. Res. Not. IMRN (2012), no. 19, 4449-4474 ,
  • 2-frieze patterns and the cluster structure of the space of polygons, (with V. Ovsienko, S. Tabachnikov), Ann. Inst. Fourier, 62, 3 (2012) 937-987.
  • Universal enveloping algebras of Lie antialgebras, (with S.Leidwanger), Algebr Represent Theor (2012) 15, 1--27,
  • New solutions of the Hurwitz problem on square identities, (with A. Lenzhen, V. Ovsienko), J. of Pure App. Alg., 215 (2011), 2903-2911,
  • A series of algebras generalizing the octonions and Hurwitz-Radon identity, (with V.Ovsienko), Comm. Math. Phys. 306 (2011), no. 1, 83-118,
  • Simple graded commutative algebras, (with V.Ovsienko), J. Algebra 323 (2010), 1649--1664,
  • Graded commutative algebras: examples, classification, open problems, (with V.Ovsienko), Proc. XXVIII Workshop Geometrical Methods in Math. Phys. (2010),
  • Well, Papa, can you multiply triplets?, (with V.Ovsienko), Math. Intelligencer: Volume 31, Issue 4 (2009), Page 1.
  • Representations of asl_2, Int. Math. Res. Not. IMRN (2009), no. 10, 1838--1859,
  • Geometric lifting of the canonical basis and semitoric degenerations of the Richardson varieties,
    Trans. Amer. Math. Soc. 360 (2008), no. 1, 215--235.
  • Realisation of Lusztig cones, (with P.Caldero, R.Marsh), Repres. Theory 8, 458-478, 2004
  • Relèvement géométrique de la base canonique et involution de Schützenberger, C.R. Acad.Sci. Paris. Ser. I337, 371-374, 2003


         Other texts


  • Integrable Systems and Friezes, Lecture notes (with the Exercise sheet by Max Glick in Appendix), Leicester (2017)

  • Frises et Algèbres non-associatives, Mémoire HDR (2014), abstract.

  • Relèvement géométrique de l'involution de Schützenberger et applications, Mémoire de Thèse (2006), abstract.


         Students dissertations


    Rapport Frises, par Adrien Laurent.




    Symmetries, Integrable Systems and Representations
    Editors: Kenji Iohara, Sophie Morier-Genoud, Bertrand Remy

    These are the proceedings of two international conferences, that took place in 2011 in Tokyo and Lyon, in honor of Professor Michio Jimbo.