Bas Lemmens

        School of Mathematics, Statistics and Actuarial Science
        University of Kent
        Sibson Building, Canterbury
        Kent CT2 7FS, United Kingdom

        Office: 355
        E-mail: B.Lemmens@kent.ac.uk
        Phone: +44 1227 823651 (Office)

      Research Interests:

      Geometric and Nonlinear Functional Analysis
      Monotone Dynamical Systems Theory
      Metric Geometry


      Editorial duties:

    • Associate editor of Linear Algebra and Its Applications (2010--2018)

      Activities:

    • Hilbert Geometries Workshop, CIRM Luminy, 9-13 January, 2012.
    • POSTA2012, Maynooth, September 2-4, 2012
    • LAA lecture, University of Wisconsin at Madison, USA, 2012.
    • Mini-symposium ``Linear and Nonlinear Perron-Frobenius Theory'' at the 18th Conference of the International Linear Algebra Society (ILAS), Providence, Rhode Island, USA on June 3-7, 2013
    • Geometry and Dynamics of Finsler manifolds, CIRM Luminy, 16-20 June, 2014.
    • Jordan Geometric Analysis and Applications, Queen Mary University of London, 3-5 September, 2014.
    • SIAM Conference on Control and Its Applications, Paris, 8-10 July, 2015.
    • Order structures, Jordan algebras and geometry workshop, Lorentz Center, Leiden, May 29 -June 2, 2017.
    • Positivity X, University of Pretoria, South Africa, July 2019.
    • Advances in the Geometric and Analytic Theory of Convex Cones, Jeju, Korea, May 2019.

      Grants:

      Talent fellowship by the Netherlands Organization for Scientific Research, 2003-2004.
      Marie Curie Intra-European fellowship, 2005-2007.
      EPSRC 1st grant (EP/J008508/1) ''From hyperbolic geometry to nonlinear Perron-Frobenius theory'' 2012-2013.
      EPSRC grant (EP/R044228/1) ''Jordan Algebras, Finsler Geometry and Dynamics'' with Co-I Cho-Ho Chu at Queen Mary University of London, 2018-2021.

      Research supervision:

      Mark Roelands (PhD) 2012-2016, Post-doc (2018)-present
      Marten Wortel (Post-doc) 2013-2014
      Hent van Imhoff (PhD, Leiden, co-supervisor with Onno van Gaans) 2015-2019.
      Floris Claassens (PhD) 2016- 2020

      Book:



    • Nonlinear Perron-Frobenius Theory,
      B. Lemmens and R. Nussbaum, Cambridge Tracts in Mathematics 189,
      Cambridge Univ. Press, 2012.

      Some reviews of the book:

    • by Yongdo Lim for LAA
    • by Peter Zabreiko for Zentralblatt
    • by Bjorn Ruffer for MathSciNet

      Papers:

    • A metric version of Poincare's theorem concerning biholomorphic inequivalence of domains, (pdf)
      B. Lemmens, arXiv, (2020), submitted.

    • On the linearity of order-isomorphisms, (pdf)
      B. Lemmens, Hent van Imhoff, and Onno van Gaans, Canadian J. Math., (2020), to appear.

    • Hilbert and Thompson isometries on cones in JB-algebras, (pdf)
      B. Lemmens, Mark Roelands and Marten wortel, Mathematische Zeitschrift, 292(3), (2019), 1511-1547. (Open Access)

    • Inverses of disjointness preserving operators in finite dimensional pre-Riesz spaces, (pdf)
      Anke Kalauch B. Lemmens, and Onno van Gaans, Quaest. Math., 42(4), (2019), 423-430. (Open Access)

    • Isometries of infinite dimensional Hilbert geometries, (pdf)
      B. Lemmens, M. Roelands, and M. Wortel, J. Topology and Analysis, 10(4), (2018), 941-959.

    • Monotone dynamical systems with dense periodic points, (pdf)
      B. Lemmens, Onno van Gaans and Hent van Imhoff, J. Differential Equations, 265(11), (2018), 5709-5715.

    • Detecting fixed points of nonexpansive maps by illuminating the unit ball, (pdf)
      B. Lemmens, Brian Lins, and Roger Nussbaum, Israel J. Math., 224(1), (2018), 231-262.

    • Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces, (pdf)
      B. Lemmens, B. Lins, R. Nussbaum, and M. Wortel, J. d'Analyse Math., 134(2), (2018), 671-718.

    • An order theoretic characterization of spin factors, (pdf)
      B. Lemmens, Mark Roelands and Hent van Imhoff, Quarterly J. Math., 68(3), (2017), 1001-1017.

    • Midpoints for Thompson's metric on symmetric cones, (pdf)
      B. Lemmens and Mark Roelands. Osaka J. Math., 154(1), (2017), 197-208. (Open Access).

    • Unique geodesics for Thompson's metric, (pdf)
      B. Lemmens and M. Roelands, Ann. Inst. Fourier (Grenoble), 65(1), (2015), 315-348. (Open Access)

    • Bands in partially ordered vector spaces with order unit, (pdf)
      A. Kalauch, B. Lemmens, and O. van Gaans, Positivity, 9(3), (2015), 1385-1292. (Open Access)

    • Riesz completions, functional representations and anti-lattices, (pdf)
      A. Kalauch, B. Lemmens, and O. van Gaans, Positivity, 18(1), (2014), 201-218.

    • Continuity of the cone spectral radius, (pdf)
      B. Lemmens and R. Nussbaum, Proc. Amer. Math. Soc. 141(8), (2013), 2741-2754.

    • Isometries of polyhedral Hilbert geometries, (pdf)
      B. Lemmens and C. Walsh, J. Topology and Analysis 3(2), (2011), 213-241.

    • Non-expansive mappings on Hilbert's metric spaces, (pdf)
      B. Lemmens, Topological Methods in Nonlinear Analysis 38(1), (2011), 45-58.

    • Stability and convergence in discrete convex monotone dynamical systems, (pdf)
      M. Akian, S. Gaubert, and B. Lemmens, J. Fixed Point Theory Appl. 9(2), (2011), 295-325.

    • Dynamics of non-expansive maps on strictly convex normed spaces, (pdf)
      B. Lemmens and O. van Gaans, Israel J. Math., 171, (2009), 425-442.

    • Second derivatives of norms and contractive complementation in vector-valued spaces, (pdf)
      B. Lemmens, B. Randrianantoanina, and O.W. van Gaans, Studia Math., 179(2), (2007), 149-166.

    • Transitive actions of finite abelian groups of sup-norm isometries, (pdf)
      B. Lemmens, M. Scheutzow, and C. Sparrow, European J. Combin., 28(4) (2007), 1163-1179.

    • Variations of a combinatorial problem on finite sets, (pdf)
      B. Lemmens. Elemente der Math., 62(2), (2007), 59--67.

    • On one-complemented subspaces of Minkowski spaces with smooth Riesz norms, (pdf)
      B. Lemmens and O.W. van Gaans. Rocky Mountain J. Math., 6(6) (2006), 1937--1955.

    • A note on periodic points of order preserving subhomogeneous maps, (pdf)
      B. Lemmens and C. Sparrow. Proc. Amer. Math. Soc., 134(5) (2006), 1513--1517.

    • Iteration of order preserving subhomogeneous maps on a cone, (pdf)
      M. Akian, S. Gaubert, B. Lemmens, and R.D. Nussbaum. Math. Proc. Cambridge Philos. Soc., 140(1) (2006), 157-176.

    • On the dynamics of sup-norm nonexpansive maps, (pdf)
      B. Lemmens and M. Scheutzow. Ergodic Theory Dynam. Systems, 25(3) (2005), 861-871.

    • Periods of order-preserving nonexpansive maps on strictly convex normed spaces, (pdf)
      B. Lemmens and O.W. van Gaans. J. Nonlinear Convex Anal., 4(3) (2003), 353-363.

    • A characterization of the periods of periodic points of 1-norm nonexpansive maps, (pdf)
      B. Lemmens and M. Scheutzow. Selecta Math. (New Series), 9(4) (2003), 557-578.

    • Iteration of linear p-norm nonexpansive maps, (pdf)
      B. Lemmens and O.W. van Gaans. Linear Algebra Appl. 317 (2003), 265--280.

    • Periods of periodic points of 1-norm nonexpansive maps, (pdf)
      B. Lemmens. Math. Proc. Cambridge Philos. Soc. 135(1) (2003), 165--180.

    • Lower and upper bounds for omega-limit sets of nonexpansive maps, (pdf)
      B. Lemmens, R.D. Nussbaum, and S.M. Verduyn Lunel. Indag. Mathem. (New Series) 12(2) (2001), 191--211.

    • Integral rigid sets and periods of nonexpansive maps, (pdf)
      B. Lemmens. Indag. Mathem. (New Series) 10(3) (1999), 437--447.

      In books/proceedings/expository:

    • Order structures, Jordan algebras, and geometry (pdf)
      B. Lemmens and Onno van Gaans, Nieuw Archief voor Wiskunde., June, 111-114, 2018.

    • Birkhoff's version of Hilbert's metric and applications (pdf)
      B. Lemmens and R. Nussbaum. In A. Papadopoulos and M. Troyanov editors,
      Handbook of Hilbert geometry, European Mathematical Society Publishing House, Zurich. 2014.

    • Nonlinear Perron-Frobenius theory and dynamics of cone maps, (pdf)
      B. Lemmens, In Positive Systems, Lecture Notes in Control and Inform. Sci. 341, Springer, Berlin, 2007.

    • Periodic points of nonexpansive maps: a survey, (pdf)
      B. Lemmens. In S. Bezuglyi and S. Kolyada, editors, Topics in Dynamics and Ergodic Theory,
      London Math. Soc. Lecture Note Ser. 310, Cambridge Univ. Press, 2003.

      Undergraduate Research

    • On the number of pairwise touching simplices, (pdf)
      B. Lemmens and C. Parsons, Involve: a journal of mathematics, 8(3), (2015), 513-520.

    • On the complexity of detecting positive eigenvectors of nonlinear cone maps, (pdf)
      B. Lemmens and L. White, Involve: a journal of mathematics. 12(1), (2019), 141-150.