Ekaterina Amerik
- Research Fellow:Laboratory of Algebraic Geometry and Its Applications
- Professor:Faculty of Mathematics
- Ekaterina Amerik has been at HSE University since 2011.
Education and Degrees
- 2014
Doctor of Sciences*
- 2005
Candidate of Sciences* (PhD)
- 1997
PhD
Leiden University
Thesis Title: On the geometry of smooth hypersurfaces in the projective space - 1992
Degree
Lomonosov Moscow State University
* Candidate of Sciences
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.
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.
* Doctor of Sciences
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Research interests
Algebraic geometry and its interactions with dynamics; arithmetical dynamics; birational geometry; holomorphic symplectic manifolds and their fibrations.
Courses (2022/2023)
- Algebraic Geometry (Optional course (faculty); 1, 2 module)Rus
- Research Seminar "Algebraic Geometry 2" (Optional course (faculty); 3 module)Rus
- Past Courses
Courses (2019/2020)
- Galois Theory (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 3, 4 module)Rus
- Galois Theory (Bachelor’s programme; Faculty of Economic Sciences; 3 year, 3, 4 module)Rus
- Galois Theory (Bachelor’s programme; Faculty of Economic Sciences; 2 year, 3, 4 module)Rus
- Research Seminar "Geometric Structures on Manifolds 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2017/2018)
- Complex Algebraic Geometry (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Geometric Structures on Manifolds 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Conferences
- 2022Japanese-European symposium on symplectic varieties and moduli spaces (Bologna-Tokyo). Presentation: Parabolic automorphisms of hyperkahler manifolds
- 2021
Семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Presentation: К элементарному описанию экстремальных кривых и исключительных множеств на гиперкэлеровом многообразии типа К3
- Primorie Mathematical Fair (Владивосток). Presentation: Parabolic automorphisms of hyperkahler manifolds
- From Fano varieties to hyperKähler manifolds: geometry and derived categories (Версаль). Presentation: Sur une description de courbes extrémales sur les variétés hyperkaehleriennes de type K3
- Hodgefun -- Groupes Fondamentaux, Théorie de Hodge et Motifs (Флоренция). Presentation: Parabolic automorphisms of hyperkähler manifolds
- 2016
Topology of Complex Algebraic Varieties (Марсель (Люмини)). Presentation: Automorphisms of hyperkähler manifolds via lattice embeddings
- 2015Workshop of rationally connected varietes (Москва). Presentation: Characteristic foliation on a smooth hypersurface in a holomorphic symplectic manifold
- 2014Frontiers of Rationality (Longyearbyen). Presentation: The Kahler Cone of Hyperkahler Manifolds
- Workshop "Model Theory, Arithmetic Geometry and Number Theory" (Berkeley). Presentation: Some applications of Hrushovski's theorem about the Frobenius map to algebraic dynamics
- KAWA-NORDAN 2014. Winter School and a Workshop in Complex Analysis and Geometry (Luminy). Presentation: The kaehler cone of holomorphic symplectic manifolds
- Семинар А. Шварца (Davis). Presentation: О рациональных кривых на гиперкэлеровых многообразиях
- Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Presentation: Характеристическое слоение на гладких дивизорах в голоморфно симплектических многообразиях
- Vojta's Conjectures (Банфф (Banff)). Presentation: Characteristic foliation on smooth divisors in hyperkaehler manifolds
- Komplexe Analysis (Обервольфах (Oberwolfach)). Presentation: The Kahler cone of hyperkaehler manifolds
- Научный семинар (Université Paris-Sud) (Orsay). Presentation: Теория калибрации и голоморфные Лагранжевы расслоения. Комплексная геометрия многообразий Фано
- Fibrations on Algebraic Varieties and Related Topics (Милан (Milano)). Presentation: Characteristic foliation on a smooth divisor in a hyperkaehler manifold
- 2013Диофантова геометрия (Москва). Presentation: Some remarks about the dynamical Hasse principle
- Workshop "Rational Points, Rational Curves and Entire Holomorphic Curves on Projective Varieties" (Монреаль). Presentation: Some remarks about the dynamical Hasse principle
- Algebra Seminar (Лейден). Presentation: Some remarks about the dynamical Hasse principle
- Birational geometry of complex algebraic varieties (Марсель). Presentation: Negative classes and rational curves on hyperkähler manifolds
- Workshop "Foliation Theory in Algebraic Geometry" (Нью-Йорк). Presentation: On families of Lagrangian tori on hyperkaehler manifolds
- Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Presentation: O лагранжевых расслоениях на голоморфных симплектических многообразиях
Publications41
- 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 Amerik E., Verbitsky M. Contraction centers in families of hyperkähler manifolds // Selecta Mathematica, New Series. 2021. Vol. 27. Article 60. doi
- 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.
- 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 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
- Chapter Amerik E. Negative Rational Curves and Their Deformations on Hyperkähler Manifolds, in: Birational Geometry and Moduli Spaces Vol. 39. Springer, 2020. doi Ch. 1. P. 1-11. doi
- Preprint Verbitsky M., Amerik E. Contraction centers in families of hyperkahler manifolds / Cornell University. Series arXiv "math". 2019.
- Preprint Amerik E., Verbitsky M. MBM loci in families of hyperkahler manifolds and centers of birational contractions / Cornell University. Series arXiv "math". 2018.
- Article Amerik E., Guseva L. On the characteristic foliation on a smooth hypersurface in a holomorphic symplectic fourfold // Moscow Mathematical Journal. 2018. Vol. 18. No. 2. P. 193-204.
- Preprint Amerik E., Campana F. Specialness and Isotriviality for Regular Algebraic Foliations / Cornell University. Series arXiv "math". 2018.
- Article Campana F., Amerik E. Specialness and isotriviality for regular algebraic foliations // Annales de l'Institut Fourier. 2018. Vol. 68. No. 7. P. 2923-2950. doi
- Article Amerik E., Campana F. Characteristic foliation on non-uniruled smooth divisors on hyperkahler manifolds // Journal of London Mathematical Society. 2017. Vol. 95. No. 1. P. 115-127. doi
- Article Amerik E., Verbitsky M. Construction of automorphisms of hyperkähler manifolds // Compositio Mathematica. 2017. Vol. 153. No. 8. P. 1610-1621. doi
- Article Amerik E., Kuznetsova A. Endomorphisms of projective bundles over a certain class of varieties // Bulletin of the Korean Mathematical Society. 2017. Vol. 54. No. 5. P. 1743-1755. 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
- 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 Amerik E., Kuznetsova A. Endomorphisms of projective bundles over a certain class of varieties / Cornell University. Series arXiv "math". 2016.
- Article Amerik E., Kurlberg P., Nguyen K., Towsley A., Viray B., Voloch J. F. Evidence for the Dynamical Brauer-Manin Criterion // Experimental Mathematics. 2016. Vol. 25. No. 1. P. 54-65. 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
- Preprint Amerik E., Guseva L. On the characteristic foliation on a smooth hypersurface in a holomorphic symplectic fourfold / Cornell University. Series arXiv "math". 2016.
- Preprint Amerik E., Verbitsky M. Hyperbolic geometry of the ample cone of a hyperkahler manifold / Cornell University Library. 2015. No. 1511.02403.
- 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. Some applications of p-adic uniformization to algebraic dynamics // Contemporary Mathematics Series. 2015. No. 654. P. 3-21. 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
- Preprint Amerik E., Campana, F. Characteristic foliation on non-uniruled smooth divisors on projective hyperkaehler manifolds / Cornell University. Series math "arxiv.org". 2014. No. 1405.0539.
- Preprint Ekaterina Amerik, Misha Verbitsky. Morrison-Kawamata cone conjecture for hyperkahler manifolds / Cornell University. Series math "arxiv.org". 2014.
- Preprint Amerik E. Some applications of p-adic uniformization to algebraic dynamics / Cornell University. Series math "arxiv.org". 2014.
- Preprint Amerik E., Kurlberg P., Nguyen K., Towsley A., Viray B., Voloch J. F. Evidence for the Dynamical Brauer-Manin Criterion / Cornell University. Series math "arxiv.org". 2013. No. 1305.4398.
- Preprint Amerik E., Campana F. On families of lagrangian tori on hyperkaehler manifolds / Cornell University library. Series arxiv.org "algebraic geometry". 2013. (in press)
- Article Amerik, E., Campana, F. On families of lagrangian tori on hyperkähler manifolds // Journal of Geometry and Physics. 2013. Vol. 71. No. September. P. 53-57. doi
- Article Amerik E. A remark on a question of Beauville about Lagrangian fibrations // Moscow Mathematical Journal. 2012. Vol. 12. No. 4. P. 701-704.
- Chapter Amerik E. Iteration of rational self-maps with fixed points, in: Oberwolfach Reports 2012. European Mathematical Society Publishing house, 2012. P. 1862-1864.
- Article Amerik E. Existence of non-preperiodic algebraic points for a rational self-map of infinite order // Mathematical Research Letters. 2011. Vol. 18. No. 2. P. 251-256.
- Article Amerik E. On an automorphism of Hilb[2] of certain K3 surfaces // Proceedings of the Edinburgh Mathematical Society. 2011. Vol. 51. No. 1. P. 1-7.
- Article Bogomolov F. A., Amerik E., Rovinsky M. Remarks on endomorphisms and rational points // Compositio Mathematica. 2011. Vol. 148. No. 6. P. 1819-1842. doi
- Book Америк Е. Ю. Гиперболичность по Кобаяси: некоторые алгебро-геометрические аспекты. М. : МНЦМО, 2010.
- Article Voisin C., Amerik E. Density of rational points on the variety of lines of a cubic fourfold // Duke Mathematical Journal. 2008. No. 145(2). P. 379-408.
- Article Campana F., Amerik E. Fibrations meromorphes sur certaines varietes a fibre canonique trivial // Pure and Applied Mathematics Quarterly. 2008. No. 4(2). P. 1-37.