Department/Division Human and Environmental Studies/Mathematical and Information Sciences
Undergraduate School Division of Cognitive and Information Sciences
Other Affiliation
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Personal Page Website
Research areas Mathematics, Complex dynamical systems, Random complex dynamical systems, Fractals, Ergodic theory
Keywords Chaos, Fractals, Randomness-induced phenomena, Complex singular functions
Themes I am working on (random) complex dynamical systems and fractal geometry. Especially, I am interested in randomness-induced phenomena ( new phenomena in random dynamical systems which cannot hold in deterministic dynamical systems).
Major publications H. Sumi, Interaction cohomology of forward or backward self-similar systems, 47 pages, 9 figures. Adv. Math., 222 (2009), no. 3, 729--781.
H. Sumi, Random complex dynamics and semigroups of holomorphic maps, published in Proc. London. Math. Soc. (2011), 102 (1), 50--112.
R. Stankewitz and H. Sumi, Dynamical properties and structure of Julia sets of postcritically bounded polynomial semigroups, Trans. Amer. Math. Soc., 363 (2011), no. 10, 5293--5319.
H. Sumi, Cooperation principle, stability and bifurcation in random complex dynamics, 40 pages, 6 figures. Advances in Mathematics 245 (2013) 137--181.
H. Sumi and M. Urbanski, Transversality family of expanding rational semigroups, Advances in Mathematics, 234 (2013) 697--734.
H. Sumi, The space of 2-generator postcritically bounded polynomial semigroups and random complex dynamics, Adv. Math. 290 (2016) 809--859.
J. Jaerisch and H. Sumi, Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method, Trans. Amer. Math. Soc.
369 (2017), no. 9, 6147–6187.
J. Jaerisch and H. Sumi, Pointwise Hoelder exponents of the complex analogues of the Takagi function in random complex dynamics, Adv. Math. 313 (2017) 839--874.

Professional societies/Research and synergic activities Mathematical Society of Japan
Teaching Areas
  • Undergraduate courses
  • Graduate courses (Master's program)
  • Graduate courses (Doctor's program)
  • Undergraduate courses open to all departments
Background 1989-1994 Faculty of Science, Kyoto University (majoring mathematics)
1999 Ph.D. (Graduate School of Human and Environmental Studies, Kyoto University)
1999-2005 Assistant Professor, Department of Mathematics, Tokyo Institute of Technology
2005-2017 Associate Professor, Department of Mathematics, Osaka University
2017- Professor, Graduate School of Human and Environmental Studies, Kyoto University

2000 The MSJ Takebe Katahiro Prize for Encouragement of Young Researchers (from The Mathematical Society of Japan)
2012 Osaka University President Award for Encourgement (for research)

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