Misha Verbitsky

Deputy Laboratory Head:Laboratory of Algebraic Geometry and Its Applications
Professor:Faculty of Mathematics

Misha Verbitsky has been at HSE University since 2009.

Education and Degrees

2006
Degree
Independent University of Moscow
2006
Degree
Independent University of Moscow
1995
PhD
Harvard University
Thesis Title: Cohomology of compact hyperkaehler manifolds
1995
Doctoral programme
Harvard University

Professional Interests

complex manifold holomorphic symplectic manifold hyperkahler manifolds hypercomplex manifold

Research interests

Algebraic geometry, differential geometry, hyperkahler geometry, calibrations on manifolds quaternionic structures, locally conformally Kaehler manifolds, Yang-Mills theory, Hodge theory

Awards and Accomplishments

Best Teacher – 2020, 2012

Courses (2018/2019)

Research Seminar (Postgraduate course’s programme; 3 year, 1 semester)Rus
Research Seminar of Master’s Programme 1 (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Eng

Courses (2017/2018)

Complex Algebraic Geometry (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
Research Seminar (Postgraduate course’s programme; 2 year, 1 semester)Rus
Research Seminar "Geometric Structures on Manifolds 1" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
Research Seminar "Geometric Structures on Manifolds 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus

Editorial board membership

2017: Member of the Editorial Board, Épijournal de Géométrie Algébrique.
2016: Member of the Editorial Board, Journal of Geometry and Physics.
2013: Member of the Editorial Board, Complex Manifolds.
2007–2016: Member of the Editorial Board, Proceedings of the Edinburgh Mathematical Society.

Conferences

2021
Семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Presentation: Hyperkahler manifolds with round Kahler cones
2017
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Presentation: Algebraic and Kahler dimension of nilmanifolds
Teichmüller Theory in Higher Dimension and Mirror Symmetry (Анжер). Presentation: Теория Тейхмюллера
Geometry and Topology Seminar (Technion) (Хайфа). Presentation: Ergodic complex structures
2016
Школа-конференция по теории струн, интегрируемым моделям и теории представлений (Москва). Presentation: Миникурс "Спиноры и формула Вайценбека"
Школа-конференция по теории струн, интегрируемым моделям и теории представлений (Москва). Presentation: Миникурс "Введение в теорию многообразий Калаби-Яу"
Еженедельный семинар Лаборатории алгебраической геометрии (Москва). Presentation: Факторы Кобаяши и эргодические комплексные структуры
Coloquio de Matematica UC (UC Mathematics Colloquium) (Сантьяго). Presentation: Automorphisms of hyperkahler manifolds
Geometry Over Nonclosed Fields (Мюнхен). Presentation: Constructing automorphisms of hyperkahler manifolds
The 1st International Conference on Differential Geometry (Фес). Presentation: Degenerate twistor families
Algebraic Geometry Seminar (Нью-Йорк). Presentation: Existence of automorphisms for hyperkahler manifolds
Geometry/Topology Seminar (Нью-Йорк). Presentation: Algebraic dimension of nilmanifolds
Complex Projective Geometry (Бухарест). Presentation: Birational contractions of hyperkaehler manifolds are diffeomorphic
Geometry and Topology seminar (Weizmann Institute) (Реховот). Presentation: Homogeneous dynamic, hyperbolic geometry and cone conjecture
Seminar in Real and Complex Geometry (Тель-Авив). Presentation: Pseudoholomorphic curves on 6-sphere and other nearly Kahler manifolds
The different faces of geometry, a workshop in honour of Fedor Bogomolov (Ноттингем). Presentation: Cousin groups and generalized Oeljeklaus-Toma manifolds
Derived categories and Chow groups of hyperkaehler and Calabi-Yau varieties (Нью-Йорк). Presentation: Perverse coherent sheaves on hyperkahler manifolds and Weil conjectures
2015
Hyperbolicity in algebraic geometry (Ilhabela). Presentation: Symplectic packing and hyperbolicity
Workshop on Hyperkaehler Geometry (Сеул). Presentation: Symplectic packing for Campana simple manifolds
Distribution of Rational and Holomorphic Curves in Algebraic Varieties Banff (Банфф). Presentation: MBM classes on hyperkahler manifolds
Geometry Over Nonclosed Fields: Geometry and Arithmetic of Holomorphic Symplectic Varieties (Нью-Йорк). Presentation: Proof of Morrison-Kawamata cone conjecture for holomorphically symplectic manifolds
2014
Differential Geometry Seminar (Brussels). Presentation: Ergodic complex structures and Kobayashi metric
Seminaire de geometrie algebrique (Angers). Presentation: Ergodic complex structures and Kobayashi metric
Moduli spaces of irreducible symplectic varieties, cubics and Enriques surfaces (Lille). Presentation: Hyperkähler manifolds are non-hyperbolic
Complex Geometry and Lie Groups (Турин (Torino)). Presentation: Hypercomplex manifolds of quaternionic dimension 2 and HKT-structures
Hebrew University topology and geometry seminar (Иерусалим (Jerusalem)). Presentation: Ergodic complex structures
Seminar in Geometry and Topology (Rehovot). Presentation: Kahler threefolds without subvarieties
International Congress of Mathematicians 2014 (Seoul). Presentation: Teichmuller spaces, ergodic theory and global Torelli theorem
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Presentation: Голоморфные кривые с границей на лагранжевых многообразиях в гиперкэлеровых многообразиях
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Симплектические упаковки и алгебраическая геометрия
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Теорема Агола и другие гипотезы трехмерной геометрии
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Гиперкэлерова структура на пространстве модулей локальных систем и поля Хиггса
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Контрпример к гипотезе Ходжа и группа Мамфорда-Тэйта
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Кватернионы, октавы, группа G_2
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Гипотеза Моррисона-Каваматы о кэлеровом конусе
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Однородные комплексные многообразия
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Полные симплектические упаковки
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Полиэдрально кэлеровы многообразия
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Почти комплексные 6-многообразия
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Симплектические упаковки произвольными телами и эргодическая теория
Научный семинар в Университете Тель-Авива (Тель-Авив (Tel-Aviv)). Presentation: Symplectic packing on simple Kahler manifolds, hyperkahler manifolds and tori
Научный семинар в Университете Тель-Авива (Тель-Авив (Tel-Aviv)). Presentation: Hypercomplex manifolds of quaternionic dimension 2 and HKT-structures
Seoul ICM 2014 Satellite Conference on Topology of Torus Actions and Applications to Geometry and Combinatorics (Тэджон (Daejeon)). Presentation: Complex subvarieties in homogeneous complex manifolds
The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles (Сингапур (Singapore)). Presentation: Holography principle and Moishezon twistor spaces
G2 manifolds (Нью-Йорк (New York)). Presentation: Kahler structure on the knot space of a G2-manifold
Real and Complex Differential Geometry (Бухарест (Bucharest)). Presentation: Kähler threefolds without subvarieties
Thematic session "Quaternion-Kähler manifolds and related structures in Riemannian and algebraic geometry" (Joint Meeting of the German Mathematical Society (DMV) and the Polish Mathematical Society (PTM) (Poznań). Presentation: Holography principle and Moishezon twistor spaces
Geometry, Topology and Integrability (Москва). Presentation: Симплектические упаковки в гиперкэлеровых многообразиях и торах
Lagrangian submanifolds and related topics (Милан (Milano)). Presentation: Pseudoholomorphic curves with boundaries on holomorphic Lagrangian subvarieties
Complex Geometry, Analysis and Foliations (Триест (Trieste)). Presentation: Kähler threefolds without subvarieties
2013
The 6th meeting of "The locally free geometry seminars" (Мадрид). Presentation: Ergodic complex structure on hyperkahler manifolds
International Conference on Analytic and Algebraic Geometry related to bundles (Мумбаи). Presentation: Instanton bundles on P3 and rational curves in twistor spaces of Nakajima quivers
Moduli Spaces and their Invariants in Mathematical Physics (Монреаль). Presentation: Holography principle and Moishezon twistor spaces
Special Lectures in Real and Complex Geometry (Тель-Авив). Presentation: Global Torelli theorem for hyperkaehler manifolds
Special Lectures in Real and Complex Geometry (Тель-Авив). Presentation: Ergodic complex structures
Seminar in Geometry and Topology (Rehovot). Presentation: Moduli of complex structures and Ratner theory
Séminaire de géométrie algébrique de Jussieu (Париж). Presentation: Ergodic complex structures and Kobayashi metric
Международная конференция «Геометрия алгебраических многообразий», посвященная памяти В.А.Исковских (Москва). Presentation: Towards the cone conjecture for hyperkaehler manifolds
Workshop ”Symplectic Algebraic Geometry” (Киото). Presentation: Ergodic complex structures and Kobayashi metric
Третья летняя математическая школа "Алгебра и геометрия" (Ярославль). Presentation: Курс "Симплектическая емкость"
Around Torelli's theorem for K3 surfaces. Arithmetic, Geometry and Dynamical aspects (Страсбург). Presentation: Global Torelli theorem for hyperkahler manifolds
Around Torelli's theorem for K3 surfaces. Arithmetic, Geometry and Dynamical aspects (Страсбург). Presentation: Ergodic complex structures
SCGP Weekly Talks (Нью-Йорк). Presentation: Moduli spaces and the mapping class group
Quiver Varieties Program Seminar (Нью-Йорк). Presentation: Towards the Cone Conjecture for Hyperkahler Manifolds
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Presentation: Эргодические комплексные структуры в пространстве Тейхмюллера
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Presentation: Особая квартика с кручением в третьих гомологиях

IMPA, Geometria Diferencial seminar, Rio de Janeiro
Moduli of symplectic structures
22 de janeiro de 2015, 15:30
http://seminarios.impa.br/visualizar?id=6135

Hyperbolicity 2015
Holomorphic dynamics school
Hyperbolicity in algebraic geometry conference
January 5 to January 15
Ilhabela, Sao Paulo, Brazil
http://verbit.ru/MATH/TALKS/Ergo/Ilhabela/Ergo1-Ilhabela-Jan-6-2015.pdf
http://verbit.ru/MATH/TALKS/Ergo/Ilhabela/Ergo2-Ilhabela-Jan-7-2015.pdf
http://verbit.ru/MATH/TALKS/Ergo/Ilhabela/Ergo1-Ilhabela-Jan-8-2015.pdf
Misha Verbitsky, Mapping class group and moduli spaces (3 lectures)
http://verbit.ru/MATH/TALKS/Symplectic-Packing-Ilhabela-2015.pdf
Misha Verbitsky, Symplectic packing and hyperbolicity

Workshop on Hyperkaehler Geometry,
March 2-6, 2015, KIAS, Seoul
http://home.kias.re.kr/MKG/h/WHG2015/
http://verbit.ru/MATH/TALKS/Symplectic-Packing-Seoul-2015.pdf

http://www.birs.ca/events/2015/5-day-workshops/15w5169
Distribution of Rational and Holomorphic Curves in
Algebraic Varieties Banff, Alberta, Canada, March 15-20, 2015
"MBM classes on hyperkahler manifolds"
http://verbit.ru/MATH/TALKS/MBM-Banff-2015.pdf

Geometry Over Nonclosed Fields: Geometry and Arithmetic of
Holomorphic Symplectic Varieties
March 22С28, 2015
http://verbit.ru/MATH/TALKS/Mor-Kaw-SimonsS-2015.pdf
Proof of Morrison-Kawamata cone conjecture
for holomorphically symplectic manifolds
https://www.simonsfoundation.org/mathematics-and-physical-science/simons-symposia/geometry-over-non-closed-fields-2015/

Publications

Books²

Book Вербицкий М. С. Начальный курс топологии. Задачи и теоремы. М. : МЦНМО, 2017. (in press)
Book Kaledin D., Verbitsky M. Hyperkahler manifolds Vol. 12. Somerville : International Press, 1999.

Articles and book chapters⁸⁵

Article Amerik E., Verbitsky M. MBM classes and contraction loci on low-dimensional hyperkähler manifolds of K3[n] type // Algebraic Geometry. 2022. Vol. 9. No. 3. P. 252-265. doi
Article Bogomolov F. A., Déev R., Verbitsky M. Sections of Lagrangian fibrations on holomorphically symplectic manifolds and degenerate twistorial deformations // Advances in Mathematics. 2022. Vol. 405. Article 108479. doi
Article Ornea L., Verbitsky M. Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds // Manuscripta Mathematica. 2022 doi
Article Ornea L., Verbitsky M. Twisted Dolbeault cohomology of nilpotent Lie algebras // Transformation Groups. 2022. Vol. 27. P. 225-238. doi
Article Corrêa M., Ferreira A. M., Verbitsky M. Classification of holomorphic Pfaff systems on Hopf manifolds // European Journal of Mathematics. 2021. Vol. 7. P. 729-740. doi
Article Ornea L., Verbitsky M. Closed orbits of Reeb fields on Sasakian manifolds and elliptic curves on Vaisman manifolds // Mathematische Zeitschrift. 2021. Vol. 299. P. 2287-2296. doi
Article Amerik E., Verbitsky M. Contraction centers in families of hyperkähler manifolds // Selecta Mathematica, New Series. 2021. Vol. 27. Article 60. doi
Article Kamenova L., Verbitsky M. Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kahler geometry // European Journal of Mathematics. 2021 doi
Chapter Amerik E., Verbitsky M. Rational Curves and MBM Classes on Hyperkähler Manifolds: A Survey, in: Rationality of Varieties. Birkhäuser, 2021. P. 75-96. doi
Article Bogomolov F. A., Kamenova L., Verbitsky M. Algebraically hyperbolic manifolds have finite automorphism groups // Communications in Contemporary Mathematics. 2020. Vol. 22. No. 2. Article 1950003. doi
Article Amerik E., Verbitsky M. Collections of Orbits of Hyperplane Type in Homogeneous Spaces, Homogeneous Dynamics, and Hyperkähler Geometry // International Mathematics Research Notices. 2020. Vol. 2020. No. 1. P. 25-38. doi
Article Verbitsky M., Liviu O. Hopf surfaces in locally conformally Kahler manifolds with potential // Geometriae Dedicata. 2020. Vol. 207. P. 219-226. doi
Article Verbitsky M., Birbrair L., Fernandes A., Sampaio J. E. Multiplicity of singularities is not a bi-Lipschitz invariant // Mathematische Annalen. 2020. Vol. 377. No. 1-2. P. 115-121. doi
Article Verbitsky M., Vuletescu V., Ornea L. Flat affine subvarieties in Oeljeklaus–Toma manifolds // Mathematische Zeitschrift. 2019. Vol. 292. No. 3-4. P. 839-847. doi
Article Kurnosov N., Soldatenkov A., Verbitsky M. Kuga-Satake construction and cohomology of hyperkähler manifolds // Advances in Mathematics. 2019. Vol. 351. P. 275-295. doi
Article Verbitsky M., Solomon J. P. Locality in the Fukaya category of a hyperkähler manifold // Compositio Mathematica. 2019. Vol. 155. No. 10. P. 1924-1958. doi
Article Angella D., Tomassini A., Verbitsky M. On non-Kähler degrees of complex manifolds // Advances in Geometry. 2019. Vol. 19. No. 1. P. 65-69. doi
Article Ornea L., Verbitsky M. Positivity of LCK Potential // Journal of Geometric Analysis. 2019. Vol. 29. No. 2. P. 1479-1489. doi
Article Verbitsky M., Kamenova L. Pullbacks of hyperplane sections for Lagrangian fibrations are primitive // Communications in Contemporary Mathematics. 2019. Vol. 21. No. 8. P. 1850065- . doi
Article Verbitsky M., Mehrotra S., Markman E. Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkähler manifold // European Journal of Mathematics. 2019. Vol. 5. No. 3. P. 964-1012. doi
Article Verbitsky M., Fino A., Grantcharov G. Algebraic dimension of complex nilmanifolds // Journal de Mathématiques Pures et Appliquées. 2018. Vol. 9. No. 118. P. 204-218. doi
Article Biswas I., Mj M., Verbitsky M. Stable Higgs bundles over positive principal elliptic brations // Complex Manifolds. 2018. Vol. 5. No. 1. P. 195-201. doi
Article Verbitsky M., Entov M. Unobstructed symplectic packing by ellipsoids for tori and hyperkahler manifolds // Selecta Mathematica, New Series. 2018. Vol. 24. No. 3. P. 2625-2649. doi
Article Verbitsky M., Liviu O., Vuletescu V. Weighted Bott-Chern and Dolbeault cohomology for LCK-manifolds with potential // Journal of the Mathematical Society of Japan. 2018. Vol. 70. No. 1. P. 409-422. doi
Article Kamenova L., Verbitsky M. Algebraic nonhyperbolicity of hyperkähler manifolds with Picard rank greater than one // New York Journal of Mathematics. 2017. Vol. 23. P. 489-495.
Article Amerik E., Verbitsky M. Construction of automorphisms of hyperkähler manifolds // Compositio Mathematica. 2017. Vol. 153. No. 8. P. 1610-1621. doi
Article Verbitsky M., Grantcharov G., Lejmi M. Existence of HKT metrics on hypercomplex manifolds of real dimension 8 // Advances in Mathematics. 2017. Vol. 320. P. 1135-1157. doi
Article Amerik E., Verbitsky M. Morrison-Kawamata cone conjecture for hyperkahler manifolds // Annales Scientifiques de l'Ecole Normale Superieure. 2017. Vol. 50. No. 4. P. 973-993. doi
Article Verbitsky M. Transcendental Hodge algebra // Selecta Mathematica, New Series. 2017. Vol. 23. No. 3. P. 2203-2218. doi
Article Panov T., Ustinovskiy Y., Verbitsky M. Complex geometry of moment-angle manifolds // Mathematische Zeitschrift. 2016. Vol. 284. No. 1. P. 309-333. doi
Article Amerik E., Verbitsky M. Hyperbolic geometry of the ample cone of a hyperkähler manifold // Research in the Mathematical Sciences. 2016. Vol. 3. No. 7. P. 1-9. doi
Article Ornea L., Verbitsky M. LCK rank of locally conformally Kähler manifolds with potential // Journal of Geometry and Physics. 2016. Vol. 107. P. 92-98. doi
Article Ornea L., Verbitsky M. Locally conformally Kähler metrics obtained from pseudoconvex shells // Proceedings of the American Mathematical Society. 2016. No. 144. P. 325-335. doi
Chapter Bogomolov F. A., Kamenova L., Lu S., Verbitsky M. On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds, in: Geometry Over Nonclosed Fields. Springer, 2016. doi (in press)
Article Entov M., Verbitsky M. Unobstructed symplectic packing for tori and hyper-Kähler manifolds // Journal of Topology and Analysis. 2016. Vol. 08. No. 4. P. 589-626. doi
Article Verbitsky M. Degenerate twistor spaces for hyperkahler manifolds // Journal of Geometry and Physics. 2015. Vol. 91. P. 2-11. doi
Article Verbitsky M. Ergodic complex structures on hyperkahler manifolds // Acta Mathematica. 2015. Vol. 215. No. 276. P. 161-182. doi
Article Soldatenkov A., Verbitsky M. Holomorphic Lagrangian Fibrations on Hypercomplex Manifolds // International Mathematics Research Notices. 2015. Vol. 2015. No. 4. P. 981-984. doi
Article Amerik E., Verbitsky M. Rational Curves on Hyperkähler Manifolds // International Mathematics Research Notices. 2015. Vol. 2015. No. 23. P. 13009-13045. doi
Article Amerik E., Verbitsky M. Teichmüller space for hyperkähler and symplectic structures // Journal of Geometry and Physics. 2015. Vol. 97. P. 44-50. doi
Article Ananʼin S., Verbitsky M. Any component of moduli of polarized hyperkähler manifolds is dense in its deformation space // Journal de Mathématiques Pures et Appliquées. 2014. Vol. 101. No. 2. P. 188-197.
Article Campana F., Demailly J., Verbitsky M. Compact Kahler 3-manifolds without nontrivial subvarieties // Algebraic Geometry. 2014. Vol. 2. P. 131-139.
Article Kamenova L., Verbitsky M. Families of Lagrangian fibrations on hyperkahler manifolds // Advances in Mathematics. 2014. Vol. 260. P. 401-413.
Article Verbitsky M. Holography principle for twistor spaces // Pure and Applied Mathematics Quarterly. 2014. Vol. 10. No. 2. P. 325-354. doi
Article Kamenova L., Lu S., Verbitsky M. Kobayashi pseudometric on hyperkähler manifolds // Journal of London Mathematical Society. 2014. Vol. 90. No. 2. P. 436-450.
Article Verbitsky M. Rational curves and special metrics on twistor spaces // Geometry and Topology. 2014. Vol. 18. No. 2. P. 897-909. doi
Chapter Verbitsky M. Teichmuller spaces, ergodic theory and global Torelli theorem, in: Proceedings of the International Congress of Mathematicians, Seoul 2014 Vol. 2. Seul : Kyung Moon Sa Co. Ltd, 2014. P. 793-811.
Article Jardim M., Verbitsky M. Trihyperkähler reduction and instanton bundles on CP^3 // Compositio Mathematica. 2014. Vol. 150. No. 11. P. 1836-1868.
Article Soldatenkov A. O., Verbitsky M. k-symplectic structures and absolutely trianalytic subvarieties in hyperkahler manifolds // Journal of Geometry and Physics. 2014 (in press)
Article Ornea L., Verbitsky M., Vuletescu V. Blow-ups of locally conformally Kahler manifolds // International Mathematics Research Notices. 2013. No. 12. P. 2809-2821.
Article Grantcharov G., Verbitsky Misha. Calibrations in hyper-Kähler geometry // Communications in Contemporary Mathematics. 2013. Vol. 15. No. 2. P. 1-27. doi
Article Soldatenkov A. O., Verbitsky M. Holomorphic Lagrangian fibrations on hypercomplex manifolds // International Mathematics Research Notices. 2013
Article Ornea L., Verbitsky M. Locally conformally Kahler manifolds admitting a holomorphic conformal flow // Mathematische Zeitschrift. 2013. Vol. 273. No. 3-4. P. 605-611.
Article Verbitsky M. Mapping class group and a global Torelli theorem for hyperkahler manifolds // Duke Mathematical Journal. 2013. Vol. 162. No. 15 (2013). P. 2929-2986.
Article Verbitsky M. Pseudoholomorphic curves on nearly Kahler manifolds // Communications in Mathematical Physics. 2013. Vol. 324. No. 1. P. 173-177.
Article Verbitsky M. A Formally Kahler structure on a knot space of a G₂-manifold // Selecta Mathematica, New Series. 2012. Vol. 18. No. 3. P. 539-555.
Article Liviu O., Verbitsky M. Automorphisms of locally conformally Kahler manifolds // International Mathematics Research Notices. 2012. No. 4. P. 894-903.
Article Markushevich D., Tikhomirov A. S., Verbitsky M. Editors' preface for the topical issue "Instantons, coherent sheaves and their moduli spaces'' // Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1185-1187.
Article Tikhomirov A. S., Markushevich D., Verbitsky M. Editors’ preface for the topical issue “Instantons, coherent sheaves and their moduli spaces” // Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1185-1187.
Article Soldatenkov A. O., Verbitsky M. Subvarieties of hypercomplex manifolds with holonomy in SL(n,H) // Journal of Geometry and Physics. 2012. Vol. 62. No. 11. P. 2234-2240.
Article Verbitsky M. A CR twistor space of a G2-manifold. // Differential Geometry and its Application. 2011. Vol. 29. No. 1. P. 101-107.
Chapter Ornea L., Verbitsky M. A report on locally conformally Kaehler manifolds, in: Harmonic Maps and Differential Geometry. A Harmonic Map Fest in Honour of John C. Wood's 60th Birthday September 7-10, 2009 Cagliari, Italy Vol. 542. NY : American Mathematical Society, 2011. Ch. 10. P. 135-151.
Article Verbitsky M. Hodge theory on nearly Kaehler manifolds // Geometry and Topology. 2011. Vol. 15. P. 2111-2133.
Article Verbitsky M. Hyperholomorpic connections on coherent sheaves and stability // Central European Journal of Mathematics. 2011. Vol. 9. No. 3. P. 535-557.
Article Verbitsky M. Manifolds with parallel differential forms and Kähler identities for G2-manifolds. // Journal of Geometry and Physics. 2011. Vol. 61. No. 6. P. 1001-1016. doi
Article Jardim M., Verbitsky M. Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2 // Advances in Mathematics. 2011. Vol. 227. P. 1526-1538.
Article Ornea L., Verbitsky M. Oeljeklaus-Toma manifolds admitting no complex subvarieties // Mathematical Research Letters. 2011. Vol. 18. No. 4. P. 747-754.
Article Verbitsky M. Hyperkahler SYZ conjecture and semipositive line bundles // Geometric and Functional Analysis. 2010. Vol. 19. No. 5. P. 1481-1493.
Article Verbitsky M., Ornea L. Locally conformally Kaehler manifolds with potential // Mathematische Annalen. 2010. No. 248 (1). P. 25-33.
Article Verbitsky M. Plurisubharmonic functions in calibrated geometry and q-convexity // Mathematische Zeitschrift. 2010. Vol. 264. No. 4. P. 939-957.
Article Verbitsky M. Positive forms on hyperkahler manifolds // Osaka Journal of Mathematics. 2010. Vol. 47. No. 2. P. 353-384.
Article Alesker S., Verbitsky M. Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds // Israel Journal of Mathematics. 2010. Vol. 176. No. 1. P. 109-138.
Article Moraru R., Verbitsky M. Stable bundles on hypercomplex surfaces // Central European Journal of Mathematics. 2010. Vol. 8. No. 2. P. 327-337.
Article Ornea L., Verbitsky M. Topology of locally conformally Kahler manifolds with potential // International Mathematics Research Notices. 2010. No. 4. P. 717-726.
Article Verbitsky M. Balanced HKT metrics and strong HKT metrics on hypercomplex manifolds // Mathematical Research Letters. 2009. Vol. 16. No. 4. P. 735-752.
Article Barberis M. L., Dotti I. G., Verbitsky M. Canonical bundles of complex nilmanifolds, with applications to hypercomplex geometry // Mathematical Research Letters. 2009. Vol. 16. No. 2. P. 331-347.
Article Verbitsky M., Ornea L. Morse-Novikov cohomology of locally conformally Kahler manifolds // Journal of Geometry and Physics. 2009. Vol. 59. No. 3. P. 295-305.
Article Verbitsky M. Positive toric fibrations // Journal of London Mathematical Society. 2009. Vol. 79. No. 2. P. 294-308.
Article Verbitsky M. An intrinsic volume functional on almost complex 6-manifolds and nearly Kähler geometry // Pacific Journal of Mathematics. 2008. Vol. 235. No. 2. P. 323-344.
Article Verbitsky M. Coherent sheaves on general K3 surfaces and tori // Pure and Applied Mathematics Quarterly. 2008. Vol. 4. No. 3/2. P. 651-714.
Article Verbitsky M., Ornea L. Embeddings of compact Sasakian manifolds // Mathematical Research Letters. 2007. Vol. 14. No. 4. P. 703-710.
Article Verbitsky M. Quaternionic Dolbeault complex and vanishing theorems on hyperkahler manifolds // Compositio Mathematica. 2007. Vol. 143. No. 6. P. 1576-1592.
Article Alesker S., Verbitsky M. Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry. // Journal of Geometric Analysis. 2006. Vol. 16. No. 3. P. 375-399.
Article Вербицкий М. С. Голоморфные расслоения на диагональных многообразиях Хопфа // Известия РАН. Серия математическая. 2006. Т. 70. № 5. С. 13-30.
Article Verbitsky M. Hypercomplex structures on Kähler manifolds // Geometric and Functional Analysis. 2005. Vol. 15. No. 6. P. 1275-1283.

Working papers⁶⁴

Preprint Verbitsky M., Ornea L. A Calabi-Yau theorem for Vaisman manifolds / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Ornea L. Algebraic cones of LCK manifolds with / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Liviu O., Vuletescu V. Do products of compact complex manifolds admit LCK metrics? / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Ornea L. Mall bundles and flat connections on Hopf manifolds / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Ornea L. Non-linear Hopf manifolds are locally conformally Kahler / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Liviu O. Principles of Locally Conformally Kahler Geometry / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Grantcharov G., Fino A. Special Hermitian structures on suspensions / Cornell University. Series arXiv "math". 2022.
Preprint Verbitsky M., Abasheva A. Algebraic dimension and complex subvarieties of hypercomplex nilmanifolds / Cornell University. Series arXiv "math". 2021.
Preprint Verbitsky M., Ornea L. Compact homogeneous locally conformally Kahler manifolds are Vaisman. A new proof / Cornell University. Series arXiv "math". 2021.
Preprint Verbitsky M., Liviu O. Lee classes on LCK manifolds with potential / Cornell University. Series arXiv "math". 2021.
Preprint Amerik E., Verbitsky M. MBM classes and contraction loci on low-dimensional hyperkahler manifolds of K3 / Cornell University. Series arXiv "math". 2021.
Preprint Amerik E., Verbitsky M. Parabolic automorphisms of hyperkahler manifolds / Cornell University. Series arXiv "math". 2021.
Preprint Verbitsky M., Entov M. Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces / Cornell University. Series arXiv "math". 2021.
Preprint Verbitsky M., Kamenova L. Roundness of the ample cone and existence of double Lagrangian fibrations on hyperkahler manifolds / Cornell University. Series arXiv "math". 2021.
Preprint Verbitsky M., Soldatenkov A. The Moser isotopy for holomorphic symplectic and C-symplectic structures / Cornell University. Series arXiv "math". 2021.
Preprint Verbitsky M., Amerik E. Contraction centers in families of hyperkahler manifolds / Cornell University. Series arXiv "math". 2019.
Preprint Verbitsky M., Kurnosov N. Deformations and BBF form on non-Kahler holomorphically symplectic manifolds / Cornell University. Series arXiv "math". 2019.
Preprint Verbitsky M., Kamenova L. Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kahler geometry / Cornell University. Series arXiv "math". 2019.
Preprint Verbitsky M., Ornea L. Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds / Cornell University. Series arXiv "math". 2019.
Preprint Verbitsky M., Ornea L. Twisted Dolbeault cohomology of nilpotent Lie algebras / Cornell University. Series arXiv "math". 2019.
Preprint Verbitsky M., Vuletescu V., Ornea L. Classification of non-Kahler surfaces and locally conformally Kahler geometry / Cornell University. Series math "arxiv.org". 2018.
Preprint Verbitsky M., Vuletescu V., Ornea L. Flat affine subvarieties in Oeljeklaus-Toma manifolds / Cornell University. Series arXiv "math". 2018.
Preprint Verbitsky M., Solomon J. P. Locality in the Fukaya category of a hyperkähler manifold / Cornell University. Series arXiv "math". 2018.
Preprint Amerik E., Verbitsky M. MBM loci in families of hyperkahler manifolds and centers of birational contractions / Cornell University. Series arXiv "math". 2018.
Preprint Verbitsky M., Sampaio J. E., Birbrair L., Fernandes A. Multiplicity of singularities is not a bi-Lipschitz invariant / Cornell University. Series arXiv "math". 2018.
Preprint Verbitsky M., Mj M., Biswas I. Stable Higgs bundles over positive principal elliptic fibrations / Cornell University. Series arXiv "math". 2018.
Preprint Verbitsky M., Bogomolov F. A., Kamenova L. Algebraically hyperbolic manifolds have finite automorphism groups / Cornell University. Series arXiv "math". 2017.
Preprint Ornea L., Verbitsky M. Embedding of LCK manifolds with potential into Hopf manifolds using Riesz-Schauder theorem / Cornell University. Series arXiv "math". 2017.
Preprint Verbitsky M. Ergodic complex structures on hyperkahler manifolds: an erratum / Cornell University. Series arXiv "math". 2017.
Preprint Kurnosov N., Soldatenkov A., Verbitsky M. Kuga-Satake construction and cohomology of hyperkahler manifolds / Cornell University. Series arXiv "math". 2017.
Preprint Verbitsky M., Ornea L. Positivity of LCK potential / Cornell University. Series arXiv "math". 2017.
Preprint Verbitsky M., Markman E., Mehrotra S. Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkahler manifold / Cornell University. Series arXiv "math". 2017.
Preprint Entov M., Verbitsky M. Unobstructed symplectic packing by ellipsoids for tori and hyperkahler manifolds / Cornell University. Series arXiv "math". 2017.
Preprint Fino A., Grantcharov G., Verbitsky M. Algebraic dimension of complex nilmanifolds / Cornell University. Series arXiv "math". 2016.
Preprint Kamenova L., Verbitsky M. Algebraic non-hyperbolicity of hyperkahler manifolds with Picard rank greater than one / Cornell University. Series arXiv "math". 2016.
Preprint Amerik E., Verbitsky M. Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry / Cornell University. Series arXiv "math". 2016.
Preprint Amerik E., Verbitsky M. Construction of automorphisms of hyperkahler manifolds / Cornell University. Series arXiv "math". 2016.
Preprint Ornea L., Verbitsky M. Hopf surfaces in locally conformally Kahler manifolds with potential / Cornell University. Series arXiv "math". 2016.
Preprint Ornea L., Verbitsky M. LCK rank of locally conformally Kahler manifolds with potential / Cornell University. Series arXiv "math". 2016.
Preprint Angella D., Tomassini A., Verbitsky M. On non-Kähler degrees of complex manifolds / Cornell University. Series arXiv "math". 2016.
Preprint Kamenova L., Verbitsky M. Pullbacks of hyperplane sections for Lagrangian fibrations are primitive / Cornell University. Series arXiv "math". 2016.
Preprint Ornea L., Verbitsky M. Compact pluricanonical manifolds are Vaisman / Cornell University. Series math "arxiv.org". 2015.
Preprint Amerik E., Verbitsky M. Hyperbolic geometry of the ample cone of a hyperkahler manifold / Cornell University Library. 2015. No. 1511.02403.
Preprint Verbitsky M. Transcendental Hodge algebra / Cornell University. Series math "arxiv.org". 2015.
Preprint Ornea L., Verbitsky M., Vuletescu V. Weighted Bott-Chern and Dolbeault cohomology for LCK-manifolds with potential / Cornell University. Series math "arxiv.org". 2015.
Preprint Verbitsky M., Grantcharov G., Lejmi M. Existence of HKT metrics on hypercomplex manifolds of real dimension 8 / Cornell University. Series math "arxiv.org". 2014.
Preprint Entov M., Verbitsky M. Full symplectic packing for tori and hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2014.
Preprint Ekaterina Amerik, Misha Verbitsky. Morrison-Kawamata cone conjecture for hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2014.
Preprint Verbitsky M. Teichmuller spaces, ergodic theory and global Torelli theorem / Cornell University. Series math "arxiv.org". 2014.
Preprint Andrey Soldatenkov, Misha Verbitsky. k-symplectic structures and absolutely trianalytic subvarieties in hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2014.
Preprint Campana F., Demailly J., Misha Verbitsky. Compact Kahler 3-manifolds without non-trivial subvarieties / Cornell University. Series math "arxiv.org". 2013.
Preprint Panov T., Ustinovsky Y., Verbitsky M. Complex geometry of moment-angle manifolds / Cornell University. Series math "arxiv.org". 2013.
Preprint Verbitsky M. Degenerate twistor spaces for hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2013.
Preprint Verbitsky M. Ergodic complex structures on hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2013.
Preprint Andrey Soldatenkov, Verbitsky M. Holomorphic Lagrangian fibrations on hypercomplex manifolds / Cornell University. Series math "arxiv.org". 2013.
Preprint Kamenova L., Lu S., Verbitsky M. Kobayashi pseudometric on hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2013.
Preprint Kamenova L., Verbitsky M. Families of Lagrangian fibrations on hyperkaehler manifolds / Cornell University. Series math "arxiv.org". 2012.
Preprint Verbitsky M. Holography principle for twistor spaces (with appendix by Dmitry Kaledin) / Cornell University. Series math "arxiv.org". 2012.
Preprint Ornea L., Verbitsky M. Locally conformally Kahler metrics obtained from pseudoconvex shells / Cornell University. Series math "arxiv.org". 2012.
Preprint Verbitsky M. Pseudoholomorphic curves on nearly Kahler manifolds / Cornell University. Series math "arxiv.org". 2012.
Preprint Verbitsky M. Rational curves and special metrics on twistor spaces / Cornell University. Series math "arxiv.org". 2012.
Preprint Soldatenkov A. O., Verbitsky M. Subvarieties of hypercomplex manifolds with holonomy in SL(n,H) / Cornell University. Series math "arxiv.org". 2012. No. 1202.0222v1.
Preprint Verbitsky M. A CR twistor space of a G2-manifold / Cornell University. Series math "arxiv.org". 2010. No. 1003.3174.
Preprint Liviu O., Verbitsky M. A report on locally conformally Kahler manifolds / Cornell University. Series math "arxiv.org". 2010. No. 1002.3473.

Apr

2021

‘We Managed to Create Another Centre of Mathematical Life in Moscow’

In celebration of Russia’s Year of Science and Technology, we continue our series about HSE University’s international laboratories, which are headed by world-class scientists and scholars. The first of these, the Laboratory of Algebraic Geometry and Its Applications, was established in October 2010. Below, Laboratory Head Dmitry Kaledin discusses the Lab’s history, research, achievements, and current activities.

Jan

2018

Young Stars of Mirror Symmetry Come Together in Moscow

Mirror symmetry is a relatively new field of mathematics which came into being in the 1990s. In 2017, HSE opened the International Laboratory for Mirror Symmetry and Automorphic Forms. The December conference, ‘Mirror Symmetry and Applications’, was a commemoration of its first year of operation.

Jun

2015

‘Studying with Enthusiastic People Around is Fun’

In 2015 eight graduates from the HSE Faculty of Mathematics started PhD programmes at MIT, McGill, Caltech, Pennsylvania State University and other top universities. HSE 4th year student Dmitry Pirozhkov who has got a place at Columbia University talked to the HSE News Service about how to get onto a prestigious PhD programme and about his expectations and academic plans.