Homepage for Charlene Kalle

Address

Mathematisch Instituut Universiteit Leiden Niels Bohrweg 1 2333 CA Leiden The Netherlands

Room 212 Email: kallecccj@math.leidenuniv.nl Tel: +31 71 5271590

Research

I'm an associate professor at Leiden University in the group of Frank den Hollander. Information about my former whereabouts can be found on my short CV.

Keywords

interval maps, ergodic theory, dynamical systems, numeration systems, number expansions, fractal geometry

PhD students

• Niels Langeveld: Matching, entropy, holes and expansions
• Marta Maggioni: Measures and matching for number systems
• Benthen Zeegers (started in November 2018)
• Jonny Imbierski (started in September 2020, joint with Dalia Terhesiu)

Books

A first course in ergodic theory (with Karma Dajani), CRC Press, 2021. Doortrapte getallen (with Irene Verstraten), Zebra Series Vol. 63, Epsilon Uitgaven Utrecht, 2021. Het gebruik van wiskunde in de Islam (with Natasja Bouwman), Zebra Series Vol. 13, Epsilon Uitgaven Utrecht, 2002.

Publications in international journals

• Critical intermittency in random interval maps (with Ale Jan Homburg, Marks Ruziboev, Evgeny Verbitskiy and Benthen Zeegers). To appear in Comm. Math. Phys. (arXiv)
• Random Lochs' Theorem (with Evgeny Verbitskiy and Benthen Zeegers). To appear in Studia Math. (arXiv)
• On approximation by random Lüroth expansions (with Marta Maggioni). Int. J. Number Theory 18(5): 1013-1046, 2022. (arXiv)
• Invariant densities for random continued fractions (with Valentin Matache, Masato Tsujii and Evgeny Verbitskiy). J. Math. Anal. Appl. 512(2): Paper no. 126163, 2022. (arXiv)
• Invariant densities for random systems of the interval (with Marta Maggioni). Ergodic Theory Dynam. Systems 42(1): 141-179, 2022. (arXiv)
• Matching for random systems with an application to minimal weight expansions (with Karma Dajani and Marta Maggioni). Nonlinearity 34(6): 3676-3708, 2021. (arXiv)
• The β-transformation with a hole at 0 (with Derong Kong, Niels Langeveld and Wenxia Li). Ergodic Theory Dynam. Systems 40(9): 2482-2514, 2020. (arXiv)
• Invariant measures, matching and the frequency of 0 for signed binary expansions (with Karma Dajani). Publ. Res. Inst. Math. Sci. 56(4): 701-742, 2020. (arXiv)
• Matching for a family of infinite measure continued fraction transformations (with Niels Langeveld, Marta Maggioni and Sara Munday). Discrete Contin. Dyn. Syst. 40(11): 6309-6330, 2020. (arXiv)
• On the bifurcation set of unique expansions (with Derong Kong, Wenxia Li and Fan Lü), Acta Arith. 188(4): 367-399, 2019. (arXiv)
• The random continued fraction transformation (with Tom Kempton and Evgeny Verbitskiy), Nonlinearity 30(3): 1182-1203, 2017. (arXiv)
• Matching for generalised β-transformations (with Henk Bruin and Carlo Carminati), Indag. Math. 28(1): 55-73, 2017. (arXiv)
• Natural extensions for piecewise affine maps via Hofbauer towers (with Henk Bruin), Monatsh. Math. 175(1): 65-88, 2014. (arXiv)
• Isomorphisms between positive and negative beta-transformations, Ergodic Theory Dynam. Systems 34(1): 153-170, 2014. (arXiv)
• Local dimensions for the random β-transformation (with Karma Dajani), New York J. Math. 19: 285-303, 2013. (arXiv)
• Beta-expansions, natural extensions and multiple tilings (with Wolfgang Steiner), Trans. Amer. Math. Soc. 364(5): 2281-2318, 2012. (arXiv)
• Transformations generating negative β-expansions (with Karma Dajani), Integers 11B, 2011, A5. (arXiv)
• A note on the greedy β-transformation with arbitrary digits (with Karma Dajani), in École de théorie ergodique, Sémin. Congr. 20, Soc. Math. France: 83-104, 2010. (PDF)
• Natural extensions for the Golden Mean (with Karma Dajani), in European Women in Mathematics, Proceedings of the 13th General Meeting, World Sci. Publ.: 113-123, 2010. (arXiv)
• A natural extension for the greedy β-transformation with three arbitrary digits (with Karma Dajani), Acta Math. Hungar. 125(1-2): 21--45, 2009. (PDF)
• Random β-expansions with deleted digits (with Karma Dajani), Discrete Contin. Dyn. Syst. 18(1): 199-217, 2007. (PDF)
• On the convergence of logarithmic first return times (with Karma Dajani), Rev. Roumaine Math. Pures Appl. 52(1): 35-46, 2007. (PDF)

Publications in Dutch

• De oorsprong van ergodentheorie (with Frank den Hollander), Nieuw Arch. Wiskd. (5), 22(1): 9-13, 2021. (PDF)
• Tegeltjeswijsheden, Eureka!, 49: 20-23, 2015. (PDF)
• Bewogen getallen, Nieuw Arch. Wiskd. (5), 12(1): 49-54, 2011. (PDF)

Preprint

• Decay of correlations for critically intermittent systems (with Benthen Zeegers). (arXiv)

Thesis

• Expansions and Extensions, 2009. (PDF)

Workshops

Together with Karma Dajani and Robbert Fokkink I am organising one-day meetings in Ergodic Theory and Fractals. Previously Tom Kempton and Cor Kraaikamp have also co-organised such meetings.

Together with Carlo Carminati, Sara Munday and Evgeny Verbitskiy I organised the conference 60 years of dynamics and number expansions from December 10 to 14, 2018 at the Centro Ennio de Giorgi in Pisa.

Together with Karma Dajani I organised the workshop on `Fractals, Ergodic Theory and Dynamical Systems' in Utrecht in 2016.

Together with Evgeny Verbitskiy I organised a workshop on `Ergodic Theory and Dynamical Systems' in honour of Prof. Yakov Sinai holding the Kloosterman Chair in Leiden in 2015.

I co-organised the school and workshop called Streams II at the Lorentz Center in Leiden in 2014.

Teaching

In the fall semester of 2021-2022 I will be teaching the bachelor/master course Ergodic Theory and Fractals together with Evgeny Verbitskiy.
I will also be tutoring a group of first year mathematics students for the course Wiskundige Structuren.

In the spring semester of 2021-2022 I will be teaching Dynamics and Chaos for second year mathematics students together with Martina Chirilus-Bruckner.

Foundation Compositio Mathematica

Starting January 2022 I am a board member and the secretary of the Foundation Compositio Mathematica.