Sergey Mironovich Natanzon
Education and Degrees
- 2000
Doctor of Sciences* in Geometry and Topology
Thesis Title: Topology of moduli spaces of Riemann supersurfaces and real algebraic supercurves - 1982
Candidate of Sciences* (PhD) in Geometry and Topology
Thesis Title: Finite groups of homeomorphisms of surfaces, and real forms of complex algebraic curves - 1974
Doctoral programme in Mathematics
Central Institute of Economics and Mathematics of the Academy of Sciences of the USSR
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Publications50
- Article Basalaev A., Dunin-Barkowski P., Natanzon S. M. Integrable hierarchies associated to infinite families of Frobenius manifolds // Journal of Physics A: Mathematical and Theoretical. 2021. Vol. 54. No. 11. P. 1-25. doi
- Article Kazaryan M., Lando S., Natanzon S. M. On framed simple purely real Hurwitz numbers // Izvestiya. Mathematics. 2021. Vol. 85. P. 1-30. doi
- Article Mironov A., Morozov A., Natanzon S. M. Cut-and-join structure and integrability for spin Hurwitz numbers // The European Physical Journal C - Particles and Fields. 2020. Vol. 80. No. 97. P. 1-16. doi
- Article Natanzon S. M., Orlov A. Y. Hurwitz number from Feynman diagrams / Пер. с рус. // Theoretical and Mathematical Physics. 2020. Vol. 204. No. 3. P. 1166-1194. doi
- Book Natanzon Sergey M. Complex Analysis, Riemann Surfaces and Integrable Systems / Пер. с рус. Cham : Springer, 2019. doi
- Article Costa A. F., Sergey Natanzon, Shapiro B. TOPOLOGICAL CLASSIFICATION OF GENERIC REAL MEROMORPHIC FUNCTIONS FROM COMPACT SURFACES // Annales Academiae Scientiarum Fennicae Mathematica. 2018. Vol. 43. P. 349-363. doi
- Book Натанзон С. М. Комплексный анализ, римановы поверхности и интегрируемые системы. М. : МЦНМО, 2018.
- Article Natanzon S. M., Orlov Aleksandr Yur'evich. BKP and projective Hurwitz numbers // Letters in Mathematical Physics. 2017. Vol. 107. P. 1065-1109. doi
- Article Felikson A., Natanzon S. M. Double pants decompositions revisited // Moscow Mathematical Journal. 2017. Vol. 17. No. 1. P. 51-58.
- Article Gusein-Zade S., Natanzon Sergey M. Klein foams as families of real forms of Riemann surfaces // Advances in Theoretical and Mathematical Physics. 2017. Vol. 21. No. 1. P. 231-241. doi
- Article Natanzon S. M., Pratoussevitch A. Moduli Spaces of Higher Spin Klein Surfaces // Moscow Mathematical Journal. 2017. Vol. 17. No. 2. P. 327-349.
- Article Natanzon S. M. Dispersionless 2D Toda hierarchy, Hurwitz numbers and Riemann theorem // Journal of Physics: Conference Series. 2016. Vol. 670. P. 1-6.
- Article S.M.Natanzon, A.V.Zabrodin. Formal solutions to the KP hierarchy // Journal of Physics A: Mathematical and Theoretical. 2016. Vol. 49. No. 14-22. doi
- Article Natanzon S. M., Pratoussevitch A. Higher Spin Klein Surfaces // Moscow Mathematical Journal. 2016. Vol. 16. No. 1. P. 95-124.
- Article Natanzon S. M., Pratoussevitch A. Классификация m-спин клейновых поверхностей / Пер. с рус. // Russian Mathematical Surveys. 2016. Vol. 71. No. 2. P. 382-384. doi
- Article Natanzon S. M., Zabrodin A. Symmetric solutions to dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics // International Mathematics Research Notices. 2015. Vol. 2015. No. 8. P. 2082-2110. doi
- Article Alexeevski A., Natanzon S. M. Algebras of conjugacy classes of partial elements // American Mathematical Society Translations. 2014. Vol. 234. P. 1-12. doi
- Article Mironov A., Morozov A., Natanzon S. M. Infinite-dimensional topological field theories from Hurwitz numbers // Journal of Knot Theory and Its Ramifications. 2014. Vol. 23. No. 6. P. 1-16.
- Article Alexandrov A., Mironov A., Morozov A., Natanzon S. On KP-integrable Hurwitz functions // Journal of High Energy Physics. 2014. Vol. 11. No. 80. P. 1-31.
- Article Mironov A., Morozov A., Natanzon S. M. A Hurwitz theory avatar of open-closed strings // The European Physical Journal C - Particles and Fields. 2013. Vol. 73. No. 2. P. 1-10.
- Article A. Mironov, A. Morozov, S. Natanzon. Cardy–Frobenius extension of the algebra of cut-and-join operators // Journal of Geometry and Physics. 2013. Vol. 73. P. 243-251. doi
- Article Sergey Natanzon, Pratoussevitch A. Topological Invariants and Moduli of Gorenstein Singularities // Journal of Singularities. 2013. Vol. 7. P. 61-87. doi
- Article Mironov A., Morozov A., Natanzon S. M. Algebra of differential operators associated with Young diagrams // Journal of Geometry and Physics. 2012. Vol. 62. P. 148-155. doi
- Preprint Felikson А., Natanzon S. M. Double pants decompositions of 2-surfaces / Max Planck Institute for Mathematics. Series MPIM "MPIM". 2012.
- Article Alexandrov A., Mironov A., Morozov A., Natanzon S. M. Integrability of Hurwitz Partition Functions // Journal of Physics A: Mathematical and Theoretical. 2012. No. 45. P. 1-10. doi
- Article Felikson А., Natanzon S. M. Moduli via double pants decompositions // Differential Geometry and its Application. 2012. Vol. 30. No. 5. P. 490-508.
- Preprint Natanzon S. M., Pratoussevitch А. Topological invariants and moduli spaces of Gorenstein quasi-homogeneous surface singularities. / Institut des Hautes 'Etudes Scientifiques, Institut des Hautes ´Etudes Scientifiques (IHES) . Series IHES "09/2010". 2012.
- Book С.М. Натанзон Курс комплексного анализа. М. : Московский центр непрерывного математического образования, 2012.
- Article Феликсон А. А., Natanzon S. M. Double pants decompositions of 2-surfaces // Moscow Mathematical Journal. 2011. Vol. 11. No. 2. P. 231-258.
- Article Mironov A., Morozov A., Natanzon S. M. Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations // Journal of High Energy Physics. 2011. No. 11(097). P. 1-31. doi
- Article Loktev S., Natanzon S. M. Klein Topological Field Theories from Group Representations // Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2011. Vol. 7. No. 70. P. 1-15. doi
- Article Costa A., Gusein-Zade S., Natanzon S. M. Klein foams // Indiana University Mathematics Journal. 2011. Vol. 60. No. 3. P. 985-995. doi
- Article Феликсон А. А., Natanzon S. M. Labeled double pants decompositions // Moscow Mathematical Journal. 2011. Vol. 11. No. 3. P. 505-519.
- Article S.M. Natanzon, Pratusevich A. Moduli spaces of Gorenstein Quasi-Homogeneous Surface Singularities / Пер. с рус. // Russian Mathematical Surveys. 2011. No. 66:5(401). P. 1009-1010. doi
- Article А.Д. Миронов, А.Ю. Морозов, С.М. Натанзон Полный набор операторов разрезания и склейки в теории Гурвица-Концевича // Теоретическая и математическая физика. 2011. Т. 166. № 1. С. 3-27.
- Article С.М. Натанзон, Пратусевич А. Пространство модулей горенштейновых квазиоднородных особенностей поверхностей // Успехи математических наук. 2011. Т. 66. № 5. С. 189-190.
- Article Natanzon S. M. Cyclic Foam Topological Field Theories // Journal of Geometry and Physics. 2010. Vol. 60. No. 6-8. P. 874-883.
- Article Natanzon S. M. Simple Hurwitz numbers of a disk // Functional Analysis and Its Applications. 2010. Vol. 44. No. 1. P. 44-58.
- Book Натанзон С. М. Введение в пучки, расслоения и классы Черна. Московский центр непрерывного математического образования, 2010.
- Article Натанзон С. М. Дисковые одинарные числа Гурвица // Функциональный анализ и его приложения. 2010. Т. 44. № 1. С. 44-58.
- Article Natanzon S. M., Pratoussevitch A. Higher Arf Functions and Moduli Space of Higher Spin Surfaces // Journal of Lie Theory. 2009. Vol. 19. No. 1. P. 107-148.
- Article Natanzon S. M., Costa A. Poincar\'{e}'s theorem for the modular group of real Riemann surfaces // Differential Geometry and its Application. 2009. Vol. 27. No. 5. P. 680-690.
- Article Natanzon S. M., Алексеевский А. Hurwitz numbers for regular coverings of surfaces by seamed surfaces and Cardy-Frobenius algebras of finite groups // Translations of the American Mathematical Society. 2008. Vol. 224. P. 1-27.
- Article Costa A., Natanzon S. M. Classification of $\mathbb{Z}_{pA{k}}A{m}$ orientation preserving actions on surfaces // Moscow Mathematical Journal. 2007. No. 7(3). P. 419-424.
- Article Натанзон С. М. Особенности и некоммутативные фробениусовы многообразия // Труды Математического института им. В.А. Стеклова РАН. 2007. № 259. С. 143-155.
- Book Natanzon S. M. Moduli of Riemann surfaces, real algebraic curves, and their superanalogs Vol. 225. American Mathematical Society, 2004.
Conferences
- 2020
Integrable Systems andAutomorphic Forms (Сочи). Presentation: Formal solution to the h-KP hierarchy
Théorie de Teichmüller : classique, supérieure, super et quantique (Марсель, Люмини). Presentation: Moduli space of Klein foams
- 2018
Group Analysis of Differential Equations and Integrable Systems (Ларнака). Presentation: Formal solution to the h-KP hierarchy
- 2017
Meeting of the Catalan, Spanish, Swedish Math Societies (CAT-SP-SW-MATH) (Умео). Presentation: Klein foams
- МЕЖДУНАРОДНАЯ КОНФЕРЕНЦИЯ, ПОСВЯЩЕННАЯ 65-ЛЕТИЮ Г.Б. ШАБАТА (Москва). Presentation: Клейновы пены
- Workshop on Algebraic Geometry "Singularities, Real and Tropical Geometry, and beyond" (Эйлат). Presentation: DISPERSIONLESS 2D TODA HIERARCHY, HURWITZ NUMBERS AND RIEMANN THEOREM
- Conference Contemporary mathematics in honor of the 80th birthday of Vladimir Arnold (1937-2010) (Москва). Presentation: Dispersionless 2D Toda Hierarchy, Hurwitz Numbers and Riemann Theorem
- 20165th Workshop on Combinatorics of Moduli Spaces, Hurwitz numbers, and cohomological field theories (Москва). Presentation: Formal solution to the h-KP hierarchy
- 7th European Congress of Mathematics (Берлин). Presentation: Symmetric solutions to dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics
Group Analysis of Differential Equations & Integrable Systems (Ларнака). Presentation: Dispersionless 2D Toda hierarchy, Hurwitz numbers and Riemann theorem
Infinite Analysis 16 Summer School (Нагоя). Presentation: Formal solutions to integrable hierarchies - 3 lections
- MCM2016: Moduli space, conformal field theory and matrix models (Окинава). Presentation: Moduli space of N=2 Riemann super surfaces and super real algebraic curves.
- Pre-conference MCM2016 Tokyo (Токио). Presentation: Moduli space of N=1 Riemann super surfaces.
- 2015XXIIIth International Colloquium on Integrable Systems (Прага). Presentation: Symmetric solutions of the dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics
- Quantum Topology (Санкт-Петербург). Presentation: SYMMETRIC SOLUTIONS OF THE DISPERSIONLESS 2D TODA HIERARCHY, HURWITZ NUMBERS AND CONFORMAL DYNAMICS
- Международная конференция по математической теории управления и механике (Суздаль). Presentation: Симметричные решения бездисперсионной 2D иерархии, числа Гурвица и конформная динамика
- 20144th Workshop on Combinatorics of Moduli Spaces, Cluster Algebras, and Topological Recursion (Москва (Moscow)). Presentation: Symmetric solutions to dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics
- Дни геометрии в Новосибирске (Новосибирск). Presentation: Симметричные решения бездисперсионной 2D Тода иерархии, числа Гурвица и конформная динамика
- Embedded Graphs (Сантк-Петербург). Presentation: Symmetric solutions of the dispersionless 2D Toda hierarchy, Hurwitz numbers and conformal dynamics.
- Geometric Control Theory and Analysis on Metric Structures (Lake Baikal). Presentation: Construction of conformal maps via integrable systems
- 2013XXXII Workshop on Geometric Methods in Physics (Bialowieza). Presentation: A Hurwitz theory avatar of open-closed strings.
- Synthesis of integrabilities in the context of duality between the string theory and gauge theories (Москва). Presentation: Symmetric dispersionless 2D Toda hierarchy and double Hurwitz numbers
- Hamiltonian PDEs, Frobenius manifolds and geometry of Deligne Mumford moduli spaces (Triest). Presentation: Symmetric solutions dispersionless of Toda hierarchy and Hurwitz numbers
‘The Programme is Unique not Only for Russia, but also for the Best Universities of the World’
Sergey Lando, Dean of the HSE Faculty of Mathematics and Head of the master’s programme in Mathematics, told us about some innovations in the Faculty’s master’s courses.