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== General information == * '''Scientific interests''' Dynamical systems: slow-fast systems, limit cycles, attractors. * '''Current affiliation''' National Research University — Higher School of Economics. * '''Languages''' Russian (native), English (advanced). == Ph.D. thesis == * '''Topic''' Canard solutions in slow-fast systems on the two-torus. (Рус.: «Решения-утки в быстро-медленных системах на торе»; [http://ilya.schurov.com/f/thesis-schurov.pdf text] (Russian), [http://mech.math.msu.su/%7Esnark/files/vak/arr3.pdf abstract] (Russian), [http://ilya.schurov.com/f/thesis-schurov-slides.pdf slides] (Russian) ** Классификатор ВАК: 01.01.02 (differential equations, dynamical systems and optimal control). ** УДК: 517.925.42 + 517.928.4 + 517.938 ** AMS MSC 2010: [http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=34E15&btn=Search&ls=s 34E15], [http://www.ams.org/mathscinet/msc/msc2010.html?t=70K70&s=37G15&btn=Search&ls=Ct 37G15]. * '''Thesis adviser''' prof. Yulij Sergeevich Ilyashenko. * '''Defended''' June 18, 2010. Department of mechanics and mathematics, Lomonosov Moscow State University. Ph. D. thesis is devoted to the study of the new phenomena in the slow-fast systems on the two-torus. It is shown that generic slow-fast systems with only one (time-scaling) parameter on the two-torus have attracting canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parameter families. The number of canard cycles in such systems is determined by the geometric properties of the system and can be effectively computed. Explicit estimate on the number of cycles is given. It shown that the estimate is sharp for every system from some explicitly constructed open set. Limit cycle bifurcation scenario is described. Main results of the thesis and outline of the proofs are presented in paper [4] (see section [[#Papers]] below), detailed proofs are presented in papers [1] and [2]. == Education == * 2006 — 2009. Moscow State University, Department of Mechanics and Mathematics. Ph.D. student. Differential equations, under supervision of Yulij Sergeevich Ilyashenko. * 2001 — 2006, Moscow State University, Department of Mechanics and Mathematics. Student. Graduated cum laude. == Papers == [1] I. V. Schurov. [http://dx.doi.org/10.1007/s10883-010-9093-9 ''Ducks On The Torus: Existence and Uniqueness'']. Journal of Dynamical and Control Systems, '''16''':2 (2010), 267—300. Preprint: [http://arxiv.org/abs/0910.1888 arXiv:0910.1888v1 (math.DS)] [2] Щуров И.В. [http://dyn-sys.org/public/ducks-nonconvex-trudy.pdf ''Уточные циклы в типичных быстро-медленных системах на торе.''], Труды ММО '''71''' (2010), 200-234 : Translation: I. V. Shchurov. ''[http://aimsciences.org/journals/doIpChk.jsp?paperID=7132&mode=full Canard cycles in generic fast-slow systems on the torus.]'' Transactions of the Moscow Mathematical Society, '''2010''', 175-207 [http://www.dyn-sys.org/public/ducks-nonconvex-trudy-en.pdf PDF] [3] П. И. Каледа, И. В. Щуров. [http://www.dyn-sys.org/public/kaleda-schurov-HA.pdf «Цикличность элементарных полициклов с фиксированным числом особых точек в типичных k-параметрических семействах»]. Алгебра и анализ. '''22''':4 (2010), 57—75) : Translation: P. I. Kaleda; I. V. Shchurov. [http://www.ams.org/journals/spmj/2011-22-04/S1061-0022-2011-01158-6/home.html ''Cyclicity of elementary polycycles with fixed number of singular points in generic k-parameter families'']. St. Petersburg Math. J. '''22''' (2011), 557-571. [4] I. V. Schurov. ''[http://aimsciences.org/journals/doIpChk.jsp?paperID=7132&mode=full Duck farming on the two-torus: multiple canard cycles in generic slow-fast systems]'', Discrete and Continuous Dynamical Systems, '''Supplement 2011''', 1289–1298 [http://arxiv.org/abs/1008.0133 arXiv:1008.0133 (Math.DS)]. [5] A. A. Glutsyuk, V. A. Kleptsyn, D. A. Filimonov, I. V. Schurov. ''On the adjacency quantization in the equation modelling the Josephson effect''. To appear in Funktsionalnyj analiz i priolozheniya (in Russian). See also [http://arxiv.org/abs/1301.7159 arXiv:1301.7159 (Math.DS)] (with English summary). [6] O. L. Romaskevich, I. V. Schurov, V. A. Kleptsyn. Josephson effect and slow-fast systems. Nanostructures. Mathematical Physics and Modelling. '''8''':1 (2013), pp. 31-46 (in Russian). See also [http://arxiv.org/abs/1305.6755 arXiv:1305.6755 (Math.DS)]. [7] Ilya Schurov and Nikita Solodovnikov. ''Duck factory on the two-torus: multiple canard cycles without geometric constraints''. [http://arxiv.org/abs/1405.3251 arXiv:1405.3251 (Math.DS)] == Conference talks == * Petrovskii Conference: Differential Equations and Related Topics, Moscow State University, 2007. Abstract: ''Ducks on the torus existence and uniqueness'', Международная конференция, посвященная памяти И.Г.Петровского, тезисы докладов. — М.: Издательство МГУ, 2007 — с. 358. * Summer school "Dynamical Systems" under supervision of Yu. S. Ilyashenko, Slovakia, 2009. ''Slow-fast systems on the two-torus''. * [http://www.pdmi.ras.ru/EIMI/2010/tgd/ Topology, Geometry, and Dynamics]: Rokhlin Memorial, January 11-16, 2010. Saint Petersburg, Russia. ''Canard cycles in generic slow-fast systems on the two-torus'' [[:File:Ducks on torus (Rokhlin memorial abstract, 2010).pdf|<nowiki>[abstract]</nowiki>]][http://commons.wikimedia.org/wiki/File:Canard_cycles_on_the_two-torus_%28slides,_I._Schurov%29.pdf <nowiki>[slides]</nowiki>] * [http://www.aimsciences.org/AIMS-Conference/2010/ The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications], Dresden University of Technology, Dresden, Germany, May 25—28, 2010. [http://www.aimsciences.org/AIMS-Conference/conf-reg2010/ss/detail.php?abs_no=255 Canard cycles in generic slow-fast systems on the two-torus] [[:File:Canard cycles in generic slow-fast systems on the two-torus (AIMS2010).pdf|<nowiki>[slides]</nowiki>]]. * [http://www.lboro.ac.uk/departments/ma/equadiff/symposia.html Equadiff 2011], August 1-5, 2011, Loughborough University, Loughborough, UK. ''Polynomial growth of cyclicity for elementary polycycles and Hilbert-Arnold problem.'' [http://atlas-conferences.com/c/b/d/b/37.htm <nowiki>[abstract]</nowiki>] [http://dyn-sys.org/public/slides-equadiff2011-schurov.pdf <nowiki>[slides]</nowiki>] * [http://www.math.fu-berlin.de/hsfs2011 International Workshop on Hysteresis and Slow-Fast Systems], Wittenberg, Germany, December 12-14, 2011. ''Canard cycles in generic slow-fast systems on the two-torus. '' [http://www.math.fu-berlin.de/hsfs2011/abstracts_hsfs2011.pdf <nowiki>[abstracts]</nowiki>] (see p. 18) [http://www.math.fu-berlin.de/hsfs2011/Presentations/Shurov_Presentation.pdf <nowiki>[slides]</nowiki>] * [http://mishchenko90.mi.ras.ru/ Differential Equations and Optimal Control], dedicated to the 90th anniversary of E. F. Mishchenko (April 16–17, 2012, Steklov Mathematical Institute, Moscow). Talk: ''Canard Cycles in Generic Slow–Fast Systems on the Two-Torus'' [http://mishchenko90.mi.ras.ru/abstr_book_double.pdf abstracts] (see p. 153). * [http://www.dyn-sys.org/wiki/Summer_School_2012 Summer school "Dynamical Systems"] under supervision of Yu. S. Ilyashenko, Dubna, 2012. ''Slow-fast systems and Josephson effect''. == Scientific schools participation == * [http://wiki.dynsys.org/Summer_school Summer schools "Dynamical Systems"] under supervising of Yu. S. Ilyashenko: Dubna, Bezengi, Solovki, Slovakia (2003-2012). * [http://www.dance-net.org/rtns2010/ Recent trends in nonlinear sciences] (RTNS 2010). 25 January 2010 — 29 January 2010, Segovia, Spain. == Event organization == * [http://leconf.mccme.ru/ Lyapunov Exponents and Related Topics in Dynamics and Geometry], French-Russian International Conference. Independent University of Moscow, Laboratoire Jean-Victor Poncelet, Moscow, January 24-28, 2005. Member of the organizing committee. * Summer School "Dynamical Systems" under supervision of Yu. S. Ilyashenko (Laboratoire Jean-Victor Poncelet, Independent University of Moscow) in [http://www.dyn-sys.org/wiki/Summer_School_2011 2011] and [http://www.dyn-sys.org/wiki/Summer_School_2012 2012], member of the organizing committee. == Teaching experience == * 2011-2012 academic year: assistant professor in Higher School of Economics (see my [http://www.hse.ru:6060/org/persons/23534663 homepage] at HSE, in Russian). ** Calculus and probability theory for students of political sciences (lectures and seminars). See details [http://math-hse.info/2011-12/%D0%9D%D0%B0%D1%87%D0%B0%D0%BB%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8B_%D0%B8_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0 here] and [http://math-hse.info/2011-12/%D0%94%D0%BE%D0%BF%D0%BE%D0%BB%D0%BD%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D0%B5_%D0%B3%D0%BB%D0%B0%D0%B2%D1%8B_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8B_%D0%B8_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0 here] (in Russian) ** Game theory for students of political sciences (seminars). [http://math-hse.info/2011-12/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%B8%D0%B3%D1%80 Details] (in Russian) ** Calculus for economists (seminars). [http://math-hse.info/2011-12/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7 Details] (in Russian) ** Linear algebra for economists (seminars). [http://math-hse.info/2011-12/%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0 Details] (in Russian) ** Discrete mathematics for linguists (seminars). [http://math-hse.info/2011-12/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%B4%D0%BB%D1%8F_%D0%BB%D0%B8%D0%BD%D0%B3%D0%B2%D0%B8%D1%81%D1%82%D0%BE%D0%B2 Details] (in Russian) * 2010-2011 academic year: assistant professor in Higher School of Economics. ** Calculus and probability theory for students of political sciences (lectures and seminars). See details [http://math-hse.info/2010-11/%D0%9D%D0%B0%D1%87%D0%B0%D0%BB%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8B_%D0%B8_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0 here], [http://math-hse.info/2010-11/%D0%94%D0%BE%D0%BF%D0%BE%D0%BB%D0%BD%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D1%8B%D0%B5_%D0%B3%D0%BB%D0%B0%D0%B2%D1%8B_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8B_%D0%B8_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0 here] and [http://math-hse.info/2010-11/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_(%D0%B2%D0%B2%D0%BE%D0%B4%D0%BD%D1%8B%D0%B9_%D0%BA%D1%83%D1%80%D1%81) here] (in Russian) ** Calculus and probability theory for students of history (lectures and seminars). [http://math-hse.info/2010-11/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%B4%D0%BB%D1%8F_%D0%B8%D1%81%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%BE%D0%B2 Details] (in Russian) ** Probability theory for students of logistics (seminars) * 2009-2010 academic year ** ''[http://www.mccme.ru/ium/f09/cycles.html Limit cycles]'' special course in Independent University of Moscow (jointly with A. Fishkin, D. Filimonov, G. Golutsky), 2009. ** ''Ordinary differential equations'' course in [http://www.mccme.ru/mathinmoscow/ Math in Moscow] program, Independent University of Moscow & State University — Higher School of Economics (jointly with Yury Kudryahov), Spring 2010, in English. [http://www.dyn-sys.org/wiki/Math_in_Moscow/2010-spring Details] (in English). * [http://mmmf.math.msu.su/ Junior mechanics and mathematics faculty] («Малый мехмат МГУ»), 2001-2007, senior teacher. == Writings == * ''[http://www.encyclopedia.rosman.ru/books/math.php Modern Illustrated Encyclopedia: Mathematics, Informatics'']. (Рус.: Современная Иллюстрированная Энциклопедия: Математика, Информатика. Росмэн, 2007. ISBN 978-5-353-02884-0.) Author of several articles on calculus, differential equations and discrete math. (See incomplete list [http://ru.wikipedia.org/wiki/%D0%A3%D1%87%D0%B0%D1%81%D1%82%D0%BD%D0%B8%D0%BA:Ilya_Voyager/%D0%9C%D0%AD%D0%A8 here].) * [http://ru.wikipedia.org/ Wikipedia, the free encyclopedia]. Author of several articles on math and other topics (in Russian), see [http://toolserver.org/~soxred93/pages/index.php?name=+Ilya+Voyager&lang=ru&wiki=wikipedia&namespace=0&redirects=noredirects&getall=1 this] automatically generated list.
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