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Curriculum Vitae of Nataliya Goncharuk

 

Publications

 

ORCID https://orcid.org/0000-0002-4270-0510

Positions

• 2022 – now: Assistant Professor, Department of Mathematics, Texas A&M University,  College Station, TX.

• 2019-2022: Postdoctoral fellow, Department of Mathematics, University of Toronto, Canada.

• 2016-2019: HC Wang Assistant Professor, Department of Mathematics, Cornell University, Ithaca, NY.

• 2015-2016: Junior researcher, Laboratory of Algebraic geometry and its Applications, Higher school of Economics, Moscow, Russia.

Degrees

• 2012–2016: Postdoctoral studies, Higher School of Economics and Independent University of Moscow.

 2016: Defended PhD thesis “Circle diffeomorphisms and complex dynamics”
at Institute for Information Transmission Problems, Moscow.
Doctoral advisor: Yulij S. Ilyashenko.

• 2007-2012 Lomonosov Moscow State University, Department of Mechanics and Mathematics, Diploma with highest honors.
• 2007-2012 Independent University of Moscow, Diploma with highest honors.

 

Research interests

•  global bifurcations of planar vector fields;

•  circle dynamics;

•  renormalizations;

•  one-dimensional complex dynamics;

•  polynomial foliations in С².

Prizes and Awards

•  2018 Prize of the Moscow Mathematical Society given to young mathematicians.  For the series of works "New fractal set 'bubbles' and complex rotation numbers"

• Simons foundation grant for undergraduate and doctoral students in Mathematics, 2013, 2015.

• August Möbius Contest Winner in nomination “Undergraduates”, 2012.

• Open Contest of research works held by Higher School of Economics, Winner in nomination “Mathematics”, 2011.

• Dobrushin scholarship spring 2010 – spring 2012 (all semesters).

• International Mathematical Olympiad: Gold medal, 2006 (Ukranian team)

• National Ukrainian Mathematical Olympiad: diploma of 1st degree, 2003–2006.

Organization, service

Organized the 1-day workshop ``Groups and dynamics'' in Texas A&M (with R.Grigorchuk), Mar 1, 2024

Scientific committee member, workshop ``Anti-classification results in dynamical systems and smooth manifolds'' (Oct 13-31, 2025), Institute Henri Poincare, Paris, France.

Outreach

• SEE-Math summer school, TAMU, 2024 and 2025: Hands-on mini-courses on Platonic solids and Euler numbers,
• Math Circles, Fall 2024: 3 hands-on sessions on Fractals
• Power teams exam, TAMU: Author of the problems (2023, 2024)

Teaching experience

• Texas A& M University (2022-present): Differential equations MATH308; Putnam Challenge MATH490; Complex Variables MATH617, 618; Dynamical Systems and Chaos MATH614; Complex Dynamics and the Mandelbrot set MATH663.

• University of Toronto (2019-2022): Differential equations 1 MAT244 (3 times); Complex Variables MAT334.

• Cornell university (2016-2019): Real analysis (6110), Dynamical systems (6260), Honors introduction to Analysis I (4130), Intro to Analysis (3110), Introduction to Differential equations(3120) – 3 times, Calculus II (1120).

•  "Bachelor of Arts in Economics" joint program of NES and HSE, Moscow (2013-2016): Calculus-1 (large lecture course), Introduction to modern topology (lectures and practice), Calculus-2 (practical session).

• Summer school “Modern Mathematics” (Dubna, Russia), mini-courses (2010-2017): Bifurcations of planar vector fields (2017); with Yury Kudryashov: Schottky groups (2015), Arnold's cat (2013), Maps of the circle and continuous fractions (2011), Deterministic Chaos (2010).

• Russian–Japanese mathematical winter school (2013), Moscow, Higher School of Economics, Mini-course “Complex rotation numbers”

•  Independent university of Moscow (2011), Course “Rotation numbers and moduli of elliptic curves”

• Moscow State University (2011): organized the undergraduate seminar “Dynamical systems” (with A. Bufetov and O. Romaskevich).

• Moscow State School #57 , High school (2011-2012): Teacher (selected topics of Calculus, Algebra, and Mathematical logic).

Selected invited talks

• AMS 2025 Central Sectional Meeting: Special Session on Current trends in complex dynamics I, University of Kansas, ``Renormalization and smoothness of irrational Arnold tongues'', March 2025

• Semi-annual Workshop in Dynamical Systems and Related Topics, Penn State University, ``Renormalization operators and Arnold tongues'', November 2024

• Geometry Topology Dynamical Systems seminar, UT Dallas, ``Renormalization operators and irrational Arnold tongues'', October 2024

• Analysis seminar, Rice University, Houston, ``Renormalization operators and Arnold tongues'', February 2024

• Seminário de Sistemas Dinâmicos e Teoria Ergódica, IMPA, Rio-de-Janeiro, Brazil, ``Oscillations of irrational Arnold tongues'', January 2024

• 7th Brazilian School of Dynamical systems, Universidade Federal do Ceará, Brazil, ``Renormalization and Arnold tongues'', October 2023.

• EDAI seminar PUC Rio, Rio de Janeiro, Brazil, ``Complex rotation numbers’’, October 2023.

• Workshop on Mathematical Billiards, U T Dallas, USA, Complex rotation numbers, August 2023.

• Inaugural CNAM Fields Nonlinear Days: Renormalization and Toronto, Canada, ``Renormalization and Arnold tongues'', August 2023.

• Workshop ``Adventurous Berkeley Complex Dynamics’’, MSRI, Berkeley, California, ``Complex rotation numbers and renormalization’’, May 2022.

•  Introductory Workshop on Tame Geometry, Transseries and Applications to Analysis and Geometry, Fields Institute for Research in Mathematical Sciences, Toronto, Canada, ``Complex rotation numbers’’, Jan 2022.

•  Dynamical Systems Seminar, Universite Paul Sabatier, Toulouse, France (zoom), ``Complex rotation numbers and renormalization’’, Jan 2022.

•  Seminaire Teich, Institut de mathematiques de Marseille,``Nombres de rotation complexes et des jolies images dans l’espace des paramètres’’ (zoom, Dec 2021).

•  Dynamical systems seminar, Stony Brook university, Institute for Mathematical Sciences,  “Renormalization and irrational Arnold tongues” (Oct 2021)

•  The Budapest-Wien Dynamics seminar (zoom, Mar 2021), ``Complex rotation numbers and bubbles’’.

•  Virtual Workshop Many faces of renormalization (zoom, Mar 2021; Simons Center for Geometry and Physics, Stony Brook University), ``Bubbles and renormalization’’

•  Séminaire de Systèmes Dynamiques, Institut de Mathematiques de Jussieu-Paris Rive Gauche (zoom; Jan 2021) ``Complex rotation numbers and bubbles’’.

•  Seminário do Grupo de Sistemas Dinâmicos, Universidade Federal do Rio de Janeiro (zoom, Nov 2020), ``Structurally unstable families of planar vector fields’’ (with Yury Kudryashov).

•  Geomtop Weizmann Seminar (zoom; Rehovot, Israel, 2020) ``Complex rotation numbers’’

•  Resistencia Dinamica (zoom; Rio de Janeiro, Brazil, 2020) ``Complex rotation numbers’’

•  Analytic Low-Dimensional Dynamics: a celebration of Misha Lyubich's 60th birthday (Toronto, Canada, 2019) “Complex rotation numbers”

•  Meeting of the Moscow Mathematical Society (Moscow, 2018), “Complex rotation numbers and bubbles”.

•  Dynamical systems seminar, Stony Brook university, Institute for Mathematical Sciences (2017) “Complex rotation numbers” .

•  International conference “Geometric aspects of modern dynamics” (Porto, Portugal, 2016), “Complex rotation numbers”

•  CAPA seminar , Uppsala University (2016), “Bubbles”.

•  AMS - EMS - SPM joint meeting (Porto, Portugal, 2015), “Genera of non-algebraic leaves of polynomial foliations of CP^2”.

•  Oliver club, Cornell university (2015), “Bubbles”.

•  Seminario de foliaciones y singularidades UNAM, Instituto de Matemáticas (Mexico, 2014), “Complex rotation numbers”

•  Seminar “Sistemas Dinámicos” UNAM, Instituto de Matemáticas (Cuernavaca, 2014), “The topology of solutions of polynomial vector fields in C2”.

•  International conference “Spectral Theory and Differential equations” dedicated to the Anniversary of B.M.Levitan (Moscow, Russia, 2014), “Geometry of non-algebraic solutions of polynomial vector fields in CP2”.

•  International conference “Holomorphic foliations and complex dynamics” (Moscow, 2012), “Complex rotation numbers”.

•  Seminar of the Department of Differential Equations, Steklov Mathematical Institute (Moscow, 2011, 2010), “Rotation numbers and moduli of elliptic curves”.

•  Séminaire à l’UMPA de géométrie et dynamique, ENS Lyon (2011), “The limit behavior of complex rotation number”.

•  Séminaire à l’UMPA de géométrie et dynamique, ENS Lyon (2010), “The rotation number and the moduli of elliptic curves”.

•  ESF conference “Algebraic Methods in Dynamical Systems” (Bedlewo, Poland, 2010) Poster “The rotation number and the moduli of elliptic curves”.

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