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Alexander Blokh

Professor, Director of Math Department Outreach Program This email address is being protected from spambots. You need JavaScript enabled to view it.
(205) 934-2154
University Hall 4018

Research and Teaching Interests: Dynamical systems, Topology

Education:

  • B.S., Kharkiv University (Ukraine), Mathematics
  • M.S., Kharkiv University (Ukraine), Mathematics
  • Ph.D., Kharkiv University (Ukraine), Mathematics

I was born in Ukraine, in the former Soviet Union. My native language is Russian. I grew up in Kharkiv, a city of 1.5 million in Eastern Ukraine. My family and I moved to Moscow and lived there until 1991, when we moved to the U.S.

I mostly do research in Dynamical Systems. It uses maps applied over and over (iterations of maps as these are called) to model processes and investigate how the latter can develop. I like this field of math because it is beautiful. If you ever come across the concepts or pictures of Julia sets or the Mandelbrot set, these are closely related to my area of interest. I am also interested in Topology, mainly planar Topology.

I teach Calculus, including Honors Calculus I, as well as graduate courses and Honors seminars. I am a Red Cross donor. In the past I volunteered at Birmingham Humane Society and Children's Hospital and tutored at local middle schools; these days I support charitable efforts of the local Ukrainian community. With the help of Department of Mathematics at UAB I organize an annual UAB Math Talent Search contest that started in 2001.

  • Research Interests
    1. Beautiful results.
    2. Surprising discoveries.
    3. Less machinery needed.
    4. The fields are very intuitive and visual.
  • Recent Courses

    Recently I have taught a few Calculus I classes and a graduate class of Topology. My teaching style includes strong student participation (including Honors Calculus and graduate courses such as Topology).

  • Select Publications

    I have published over 110 scientific articles. The list of all of them as well as the majority of articles themselves can be found on my personal website. Whenever possible I provide links to the papers in pdf format. Below please find the list of nine of my most interesting (in my view) publications.

    • A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin. "Quadratic-like dynamics of cubic polynomials," Communications in Mathematical Physics, 341 (2016), 733-749.
    • A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin. "Combinatorial models for spaces of cubic polynomials," C. R. Math. (Acad. Sci., Paris), 355 (2017), issue 5, 590-595.
    • A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin. "Models for spaces of dendritic polynomials," Trans. Amer. Math. Soc., 372 (2019), 4829-4849.
    • A. Blokh, M. Misiurewicz. "Renormalization towers and their forcing," Trans. Amer. Math. Soc., 372 (2019), 8933–8953.
    • A. Blokh, L. Oversteegen, R. Ptacek, V. Timorin. "Laminational models for some spaces of polynomials of arbitrary degree," Memoirs of the AMS, 265 (2020), No. 1288.
    • A. Blokh, L. Oversteegen, V. Timorin. "Upper bounds for the moduli of polynomial-like maps," 24 pages, 3 figures, Paper No. 035003 published online in Nonlinearity, 37 (2024).
    • A. Blokh, P. Haissinsky, L. Oversteegen, V. Timorin. "On critical renormalization of complex polynomials," 28 pages, 3 figures, Paper No. 109135 published online in Advances in Mathemaics, 428 (2023).
    • S. Bhattacharya, A. Blokh, D. Schleicher. "Unicritical Laminations," Fundamenta Mathematicae, 258 (2022), 25-63.
    • A. Blokh, L. Oversteegen, V. Timorin. "Slices of the Parameter Space of Cubic Polynomials," Trans. Amer. Math. Soc., 375 (2022) Number 8, 5313-5359.