Ruth Kellerhals

Ruth Kellerhals (born 17 July 1957) is a Swiss mathematician at the University of Fribourg, whose field of study is hyperbolic geometry, geometric group theory and polylogarithm identities.[1]

Prof. Dr.

Ruth Kellerhals
Born (1957-07-17) 17 July 1957
Hägendorf, Switzerland
NationalitySwiss
CitizenshipSwitzerland
Alma materUniversity of Basel
OccupationMathematician
EmployerUniversity of Fribourg
Known forHyperbolic geometry, Coxeter groups, polylogarithm identities

Biography

As a child, she went to a gymnasium in Basel and then studied at the University of Basel, graduating in 1982 with a diploma directed by Heinz Huber "On finiteness of the isometry group of a compact negatively curved Riemannian manifold". She received her PhD in 1988, from the same university, with a thesis entitled "On the volumes of hyperbolic polytopes in dimensions three and four". Her advisor was Hans-Christoph Im Hof. During the year 1983–84 she also studied at the University of Grenoble (Fourier Institute).

In 1995 she received her habilitation from the University of Bonn, where she worked at the Max Planck Institute for Mathematics since 1989 until 1995. There, she was an assistant with Professor Friedrich Hirzebruch. Since 1995 she has been an assistant professor at the University of Göttingen, and since 1999 a distinguished professor at the University of Bordeaux 1. In 2000 she became a professor at the University of Fribourg, Switzerland, where she was in 1998 and '99 as a visiting professor.

Research

Her main research fields include hyperbolic geometry, geometric group theory, geometry of discrete groups (especially reflection groups, Coxeter groups), convex and polyhedral geometry, volumes of hyperbolic polytopes, manifolds and polylogarithms. She does historical research into the works and life of Ludwig Schläfli, a Swiss geometer.[2]

She has been a guest researcher at MSRI, IHES, Mittag-Leffler Institute, the State University of New York at Stony Brook, RIMS in Kyoto, Osaka City University, ETH Zürich, the University of Bern and the University of Auckland. Also she visited numerous research institutes and universities in Helsinki, Berlin and Budapest.

Selected works

  • Publications
    • R. Kellerhals, Algebraic aspects of hyperbolic volume, MFO Report 2017.
    • J. Nonaka, R. Kellerhals, The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space, Tokyo J. of Math. 40 (2017), 379-391.
    • R. Kellerhals, On minimal covolume hyperbolic lattices, in: Special Issue "Geometry of Numbers", MDPI Mathematics 2017, vol. 5, 16 pp.
    • R. Guglielmetti, M. Jacquemet, R. Kellerhals, Commensurability of hyperbolic Coxeter groups: theory and computation, RIMS Kôkyûroku Bessatsu B66 (2017), 57-113.
    • R. Guglielmetti, M. Jacquemet, R. Kellerhals, On commensurable hyperbolic Coxeter groups, Geom. Dedicata 183 (2016), 143-167.
    • R. Kellerhals, Commensurability of hyperbolic Coxeter groups, MFO Report No. 38/2014, DOI 10.4171/OWR/2014/38, 29-32.
    • R. Kellerhals, Hyperbolic orbifolds of minimal volume, Comput. Methods Funct. Theory 14 (2014), 465-481.
    • R. Kellerhals, A. Kolpakov, The minimal growth rate of cocompact Coxeter groups in hyperbolic 3-space, Canad. J. Math. 66 (2014), 354-372.
    • R. Kellerhals, Cofinite hyperbolic Coxeter groups, minimal growth rate and Pisot numbers, Algebr. Geom. Topol. 13 (2013), 1001-1025.
    • V. Emery, R. Kellerhals, The three smallest compact arithmetic hyperbolic 5-orbifolds, Algebr. Geom. Topol. 13 (2013), 817-829.
    • R. Kellerhals, Scissors congruence, the golden ratio and volumes in hyperbolic 5-space, Discrete and Computational Geometry 47 (2012), 629-658.
    • R. Kellerhals, G. Perren, On the growth of cocompact hyperbolic Coxeter groups, European Journal of Combinatorics 32 (2011), 1299-1316.
    • R. Kellerhals, Ludwig Schläfli - ein genialer Schweizer Mathematiker, Elem. Math. 65 (2010), 165-177.
    • T. Hild, R. Kellerhals, The fcc lattice and the cusped hyperbolic 4-orbifold of minimal volume, J. Lond. Math. Soc. 75 (2007), 677-689.
    • V. Kac, R. Kellerhals, F. Knop, P. Littelmann, D. Panyushev, Special issue in honour of Ernest Borisovich Vinberg, J. Algebra 313 (2007), 1-3.
    • R. Kellerhals, On the structure of hyperbolic manifolds, Israel J. Math. 143 (2004), 361-379.
    • R. Kellerhals, Hyperbolic Coxeter groups and space forms, in: Proceedings Symposium "The Coxeter Legacy: Reflections and Projections", Toronto, 2004, E. Ellers (ed.), Fields Institute.
    • R. Kellerhals, Quaternions and some global properties of hyperbolic 5-manifolds, Canad. J. Math. 55 (2003), 1080-1099.
    • N. Johnson, R. Kellerhals, J. Ratcliffe, S. Tschantz, Commensurability classes of hyperbolic Coxeter simplex reflection groups, Linear Algebra Appl. 345 (2002), 119-147.
    • R. Kellerhals, Collars in PSL(2,H), Annales Academiae Scientiarum Fennicae 26 (2001), 51-72.
    • R. Kellerhals, T. Zehrt, The Gauss-Bonnet formula for hyperbolic manifolds of finite volume, Geometriae Dedicata 84 (2001), 49-62.
    • R. Kellerhals, Old and New about Hilbert's Third Problem. European women in mathematics (Loccum, 1999), 179-187, Hindawi Publ. Corp., Cairo, 2000.
    • N. Johnson, R. Kellerhals, J. Ratcliffe, S. Tschantz, The size of a hyperbolic Coxeter simplex, Transformation Groups 4 (1999), 329-353.
    • R. Kellerhals, Ball packings in spaces of constant curvature and the simplicial density function, J. reine angew. Math. 494 (1998), 189-203.
    • R. Kellerhals, Volumes of cusped hyperbolic manifolds, Topology 37 (1998), 719-734.
    • R. Kellerhals, Nichteuklidische Geometrie und Volumina hyperbolischer Polyeder, Math. Semesterber. 43 (1996), 155-168.
    • R. Kellerhals, Der Mathematiker Ludwig Schläfli (15.01.1814 - 20.03.1895), DMV-Mitteilungen 4 (1996), 35-43.
    • R. Kellerhals, Regular simplices and lower volume bounds for hyperbolic n-manifolds, Annals of Global Analysis and Geometry 13 (1995), 377-392.
    • R. Kellerhals, Shape and size through hyperbolic eyes, The Mathematical Intelligencer 17 (2) (1995), 21-30.
    • R. Kellerhals, Volumes in hyperbolic 5-space, Geom. Funct. Anal. 5 (1995), 640-667.
    • R. Kellerhals, Volumina von hyperbolischen Raumformen, Habilitationsschrift, Universität Bonn, April 1995, Preprint MPI 95-110, 100 pp.
    • R. Kellerhals, On volumes of non-Euclidean polytopes, in: "Polytopes: Abstract, Convex and Computational", 231-239, T. Bisztriczky et al. (eds.), Proceedings NATO ASI 440, Kluwer, Dordrecht, 1994.
    • R. Kellerhals, On the volumes of hyperbolic 5-orthoschemes and the Trilogarithm, Comm. Math. Helv. 67 (1992), 648-663.
    • R. Kellerhals, The dilogarithm and volumes of hyperbolic polytopes, in: "Structural properties of Polylogarithms", Leonard Lewin (ed.), AMS Mathematical Surveys and Monographs, vol. 37 (1991), 301-336.
    • R. Kellerhals, On Schläfli's reduction formula, Math. Z. 206 (1991), 193-210.
    • R. Kellerhals, On the volume of hyperbolic polyhedra, Math. Ann. 285 (1989), 541-569.
    • R. Kellerhals, Über den Inhalt hyperbolischer Polyeder in den Dimensionen drei und vier, Dissertation, Universität Basel 1988, 78 pp.
gollark: You can stop the space pirates by politely asking them to go away, via the `Writer` monad.
gollark: However, if your spacesuit is eaten by bees, you can use the `Applicative` function `pure`, a dependency (available via `npm install applicative-pure`) to summon a new one from the burrito shop (they make spacesuits).
gollark: This is of course part of the monad, similarly to how a group is strictly some set and an operation on it.
gollark: Anyway, the burrito is kind of like a spacesuit containing apples, with a box which converts them to oranges.
gollark: Monad tutorials.

References
  1. Freiburger Nachrichten 16. März 2000
  2. Der Mathematiker Ludwig Schläfli (15.01.1814 – 20.03.1895), DMV-Mitteilungen 4 (1996), 35–43, Ludwig Schläfli – ein genialer Schweizer Mathematiker, Elem. Math. 65 (2010), 165–177
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