Dynamical Systems seminar is supported by RFBR project 20-01-00420-a and Laboratory Poncelet.

Участник:Nataliya Goncharuk/CURRICULUM VITAE

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General information

Sex
Female
Born
15.07.1989 in Kharkiv, Ukraine
Nationality
Russia
Family status
Married, have two sons.
Address
Russia, 143983, Moscowskaya obl., Zheleznodorozhniy, Granichnaya street, 40, ap. 241
Address in USA
590 Malott hall, Cornell university, Ithaca, NY.
Contacts
natasha@urkud.name, ng432@cornell.edu, natalka@mccme.ru, +1 607 351 87 10 (USA), +7(909)952-64-03 (Russia)

Languages

Russian (native), English, Ukrainian. I can also read in French.

Current position

HC Wang Assistant professor, Cornell university, Ithaca, NY (2016-2019)

Next position

Post-doctoral student, University of Toronto, Canada.

Research interests

  • Dynamics on the circle
  • Complex dynamics
  • Complex foliations
  • Global bifurcations of planar vector fields

Publications

  • Thesis: Circle diffeomorphisms and complex dynamics, 2016. Doctoral advisor: Yu.Ilyashenko.

Mathematics

  • N. Goncharuk, «Rotation numbers and moduli of elliptic curves», Functional Analysis and Its Applications, 2012, 46:1, pp. 11–25. (translated from Russian)
  • X. Buff, N. Goncharuk, «Complex rotation numbers», Journal of Modern Dynamics, Volume 9 (2015), pp. 169-190.
  • N. Goncharuk, Yu. Kudryashov, «Bounded limit cycles of polynomial foliations in C^2» Bulletin of the Brazilian Mathematical Society, New Series (2017), Volume 48, Issue 1, pp 63–83. See also on arxiv.
  • N. Goncharuk, Yu. Kudryashov, “Cheap limit cycles” (arXiv:1702.00897), Nonlinearity, Volume 31, Number 3 (2018).
  • N. Goncharuk, Yu. Kudryashov, «Genera of non-algebraic leaves of polynomial foliations of C^2» (arXiv:1407.7878), Moscow Math. J., Volume 18, Issue 1, 2018, pp. 63–83.
  • N. Goncharuk, “Complex rotation numbers: bubbles and their intersections” (arXiv:1708.01077), Analysis and PDE, Volume 11, No 7 (2018), pp. 1787 – 1801.
  • N. Goncharuk, “Self-similarity of bubbles”, arxiv:1805.04769, accepted to Nonlinearity.
  • N.Goncharuk, Yu. Ilyashenko, N.Solodovnikov, “Global bifurcations in generic one-parameter families with a parabolic cycle on S2” ( arXiv:1707.09779).
  • N.Goncharuk, Yu. Ilyashenko, “Large bifurcation supports”, arXiv:1804.04596.
  • N. Goncharuk, Yu. Kudryashov, “Bifurcations of the polycycle "tears of the heart": multiple numerical invariants”, arXiv:1808.07459, submitted to Moscow Mathematical Journal; positive review received.

Teaching aids (in Russian)

A. I. Bufetov, N.B.Goncharuk, Yu.S.Ilyashenko, Lecture notes of the course «Ordinary differential equations», part I, Moscow: the Board of Trustees of the Department of Mechanics and Mathematics of MSU, 2012. — 120 p. (in Russian)

More complete version of the lecture notes is here.

Talks

Conference talks

International conference “Geometric aspects of modern dynamics” (Porto, Portugal, 2016),
Talk “Complex rotation numbers”
AMS - EMS - SPM joint meeting (Porto, Portugal), June 2015
Talk «Genera of non-algebraic leaves of polynomial foliations of CP^2»
International conference «Spectral Theory and Differential equations» dedicated to the Anniversary of B.M.Levitan (Moscow, Russia), June 2014
Talk «Geometry of non-algebraic solutions of polynomial vector fields in CP²».
International conference «Holomorphic foliations and complex dynamics» (Moscow, Russia), June 2012
Talk «Complex rotation numbers»
ESF conference «Algebraic Methods in Dynamical Systems» (Bedlewo, Poland), May 2010
Poster «The rotation number and the moduli of elliptic curves».

Seminar talks

Oliver club, Cornell university, March 2019. Meeting of the Moscow mathematical society, Moscow. December 2018.

Dynamical systems seminar, Institute for Mathematical Sciences, Stony Brook university. September 2017
Talk “Complex rotation numbers”.
Dynamical systems seminar, Department of Mathematics, Cornell university. October 2017
Talk “Complex rotation numbers”.
Topological seminar, Department of Mathematics, Cornell university. November 2016
Talk “Large bifurcation supports for vector fields on S^2”.
Dynamical systems seminar, Department of Mathematics, Cornell university. October 2016
Talk “Complex rotation numbers”.
CAPA seminar , Uppsala, Sweden, May 2016
Talk “Bubbles”
Oliver Mathematical club
Cornell university, Department of Mathematics, October 2015
Talk “Bubbles”
Seminar “Riemann surfaces, Lie algebras, and mathematical physics” (S.M.Natanzon, O.V.Schwarzman, O.K.Sheinman)
Independent university of Moscow, November 2014
Talk «Genera of non-compact leaves of polynomial foliations in CP^2»
Seminar “Sistemas Dinámicos”
UNAM, Instituto de Matemáticas, Cuernavaca, 22.05.2014
Talk “The topology of solutions of polynomial vector fields in ℂ²”
“Seminario de foliaciones y singularidades”
UNAM, Instituto de Matemáticas, Mexico, 27.02.2014
Talk «Complex rotation numbers»
Seminar “Riemann surfaces, Lie algebras, and mathematical physics” (S.M.Natanzon, O.V.Schwarzman, O.K.Sheinman)
Independent university of Moscow, November 2012
Talk «Complex rotation numbers»
Weekly seminar of Laboratory of Algebraic Geometry and its Applications
Moscow, Higher school of economics, April 2012
Talk «Rotation numbers and moduli of elliptic curves»
Seminar «Complex analysis in several variables» (Vitushkin Seminar)
Moscow, MSU, March 2012
Talk «Rotation numbers and moduli of elliptic curves»
Seminar of the Department of Differential Equations
Moscow, Steklov Mathematical Institute
April 2011: Talk «Rotation numbers and moduli of elliptic curves»
April 2010: Talk «Rotation numbers and the moduli of elliptic curves»`
Séminaire à l’UMPA de géométrie et dynamique, ENS Lyon
April 2011: Talk «The limit behaviour of complex rotation number»
February 2010: Talk «The rotation number and the moduli of elliptic curves»

Teaching

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”, July 2017
«Schottky groups» (with Yury Kudryashov), July 2015
«Arnold's cat» (with Yury Kudryashov), July 2013
«Maps of the circle and continuous fractions» (with Yury Kudryashov), July 2011.
«Deterministic Chaos» (with Yury Kudryashov), July 2010.
Russian–Japaneze 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)
organizing 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).

Personal grants and scholarships

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

(I’m the first woman who ever received this award).

Simons Foundation grant for students and postgraduates mathematicians

2013 and 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 (ru)
spring 2010 – spring 2012 (all semesters).

Education

Mainline

2012–2015, PhD student
Higher School of Economics, Mathematical department;
Independent University of Moscow
Science advisor (both universities): Yulij S. Ilyashenko
2007–2012, student
Lomonosov Moscow State University, Department of Mechanics and Mathematics;
Independent University of Moscow
Science advisor: Yulij S. Ilyashenko
Master thesis «Rotation numbers and moduli of elliptic curves»
Graduated with honours
2006–2007, student
Karazin Kharkiv National University, Department of Mechanics and Mathematics.
1999–2006, secondary school student
Kharkiv Physics and Mathematics Lyceum No 27

Summer schools

Secondary school achievements

Olympiads

International Mathematical Olympiad
Gold medal, 2006 (Ukranian team)
National Ukranian Mathematical Olympiad
diploma of 1st degree, 2003–2006.

Team contests

Ural Tournament of Mathsfights (captain of the team)
2nd team place, 2003
International Mathematical Tournament «The cup in memory of A. N. Kolmogorov», hightest junior league (captain of the team)
3rd team place, 2003
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