Home » Current Work / List of Papers

Current Work / List of Papers

AIM SQuaREs Work Group

Currently I’m a member of an AIM SQuaREs program, that allows our research group (Ruth Kellerhals, John Ratcliffe, Steve Tschantz, Bruno Martelli, Vincent Emery and me) meeting through the years of 2015-2017 at the American Institute of Mathematics (AIM) for collaborative research.

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 (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

You may also wish to access the list of my paper directly on arXiv or HAL. See also my ORCid.

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