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Current Work / List of Papers

Équipe de recherche “Géométrie hyperbolique et structures combinatoires”

C’est l’équipe de recherche (dirigée par moi) au sein de l’Université de Neuchâtel qui est principalement financée par le projet PP00P2_170560 du Fonds National Scientifique.

En ce moment, j’ai besoin de mains libres pour rendre aide à mes recherches, et pour compléter la tache importante de formation de nouvelle génération de chercheuses et chercheurs. Donc, j’ai besoin de deux thésards et une chercheuse / un chercheur postdoctorant(e).

Research Unit “Hyperbolic Geometry and Combinatorial Structures”

This is a research unit which I’m supervising within the University of Neuchâtel. It is primarily financed by the Swiss National Science Foundation project PP00P2_170560.

At the moment, I need some free hands to help me carrying out research and also educating new researchers. Thus, I’m currently hiring two graduate students and one post-doctoral fellow.

Work in Progress

  • with Alan Reid and Leone Slavich: geometric cobordisms of hyperbolic manifolds, embeddability of codimension one manifolds
  • with Laura Ciobanu: enumeration problems for triangulations, polytopal decompositions and other geometric objects
  • with Jun Murakami: correspondences between hyperbolic volumes and quantum invariants of graphs, links and knots
  • with Sinai Robins: number-theoretic properties of hyperbolic/spherical volumes


Published/Accepted papers

  • “Volume formulae for fibred cone-manifolds with spherical geometry”, Sbornik: Mathematics, 2016 (issue dedicated to the 150th Anniversary of the Journal); link
  • with Jun Murakami: “Combinatorial decompositions, Kirillov-Reshetikhin invariants and the Volume Conjecture for hyperbolic polyhedra”, Experimental Math., 2016; hal-01396113
  • with Leone Slavich: “Hyperbolic four-manifolds, colourings and mutations”, Proc. London Math. Soc., 2016; hal-01396108
  • with Laura Ciobanu: “Geodesic growth of RACGs based on trees”, Journal of Algebraic Combinatorics, 2016; hal-01141141
    • a SAGE worksheet enclosed with the manuscript
    • see Appendix in hal-01141141 for the details of the worksheet’s Python code
  • with Jun Murakami: “The dual Jacobian of a generalised tetrahedron, and volumes of prisms”, Tokyo Journal of Mathematics, 2016; hal-01396110
  • with Leone Slavich: “Symmetries of hyperbolic four-manifolds”, Int. Math. Res. Notices, 2015; hal-01163571
    • a SAGE worksheet enclosed with the manuscript
  • with Bruno Martelli & Steven Tschantz: “Some hyperbolic three-manifolds that bound geometrically”, Proc. Amer. Math. Soc., 2015; hal-01287540
    • a Mathematica notebook enclosed with the manuscript
  • with Bruno Martelli: “Hyperbolic four-manifolds with one cusp”, Geom. and Funct. Anal., 2013; hal-00837649
  • with Ruth Kellerhals: “The minimal growth rate of cocompact Coxeter groups in hyperbolic 3-space”, Canadian J. Math., 2013; authors’ draught
  • “Examples of rigid and flexible Seifert fibred cone-manifolds”, Glasgow Math. Journal, 2013; hal-00726613
  • “On the optimality of the ideal right-angled -cell”, Algebr. Geom. Topol., 2012; hal-00751349
  • with Jun Murakami: “Volume of a doubly truncated hyperbolic tetrahedron”, Aequationes Mathematicae, 2012; hal-00713381
  • “Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers”, European J. Comb., 2012; hal-00699562
  • with Sasha Mednykh & Marina Pashkevich: “Volume formula for a Z_2-symmetric spherical tetrahedron through its edge lengths”, Arkiv för Matematik, 2011; hal-00605572
  • with Sasha Mednykh: “Spherical structures on torus knots and links”, Siberian Math. Journal, 2009; hal-00606856

Some of the above papers and pre-prints are a part of the AIM Pre-print series.

AIM SQuaREs Work Group

An AIM SQuaREs program, that provided a research group of Ruth Kellerhals, John Ratcliffe, Steve Tschantz, Bruno Martelli, Vincent Emery, Matthieu Jacquemet and me an opportunity of meeting and collaborating for three 1-week periods through the years of 2015-2017 at the American Institute of Mathematics (AIM) is where a significant part of the research produced in 2015-2017 was originated and much discussed.

You may also wish to access the list of my paper directly on arXiv or HAL. See also my ORCid. (All sources are updated intermittently)

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