Sergey Galkin

Associate Professor:Faculty of Mathematics

Sergey Galkin has been at HSE University since 2013.

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Education and Degrees

2008
Candidate of Sciences* (PhD) in Mathematical Logic, Algebra and Number Theory
Steklov Mathematical Institute of the Russian Academy of Sciences
Thesis Title: Toric degenerations of Fano manifolds
2004
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.

Professional Interests

mathematics mathematical physics experimental mathematics history of mathematics algebra arithmetics geometry topology algebraic geometry mirror symmetry Symplectic Geometry number theory representation theory ordinary differential equations

Young Faculty Support Program (Group of Young Academic Professionals)
Category "Future Professoriate" (2014-2015)

https://mccme.ru/~galkin/#papers

Publications

Articles and book chapters¹⁴

Article Coates T., Galkin S., Kasprzyk A., Strangeway A. Quantum Periods for Certain Four-Dimensional Fano Manifolds // Experimental Mathematics. 2020. Vol. 29. No. 2. P. 183-221. doi
Article Galkin S., Rybakov S. A Family of K3 Surfaces and Towers of Algebraic Curves over Finite Fields // Mathematical notes. 2019. Vol. 106. No. 6. P. 1014-1018. doi
Article Galkin S., Belmans P., Mukhopadhyay S. Examples Violating Golyshev’s Canonical Strip Hypotheses // Experimental Mathematics. 2019 doi (in press)
Chapter Galkin S., Iritani H. Gamma conjecture via mirror symmetry, in: Primitive Forms and Related Subjects — Kavli IPMU 2014. Tokyo : Mathematical Society of Japan, 2019. P. 55-115. doi
Article Galkin S., Golyshev V., Iritani H. Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures // Duke Mathematical Journal. 2016. Vol. 165. No. 11. P. 2005-2077. doi
Article Coates T., Corti A., Galkin S., Kasprzyk A. Quantum Periods for 3-Dimensional Fano Manifolds // Geometry and Topology. 2016. Vol. 20. No. 1. P. 103-256. doi
Chapter Galkin S. Degenerations, transitions and quantum cohomology, in: Tropical Aspects in Geometry, Topology and Physics. Oberwolfach : , 2015. doi P. 1269-1273. doi
Article Galkin S., Katzarkov L., Mellit A., Shinder E. Derived categories of Keum's fake projective planes // Advances in Mathematics. 2015. Vol. 278. P. 238-253. doi
Article Galkin S., Mellit A., Smirnov M. Dubrovin's conjecture for IG(2,6) // International Mathematics Research Notices. 2015. Vol. 2015. No. 18. P. 8847-8859. doi
Chapter Coates T., Corti A., Galkin S., Golyshev V., Kasprzyk A. Mirror Symmetry and Fano Manifolds, in: European Congress of Mathematics Kraków, 2 – 7 July, 2012. Zürich : European Mathematical Society Publishing house, 2014. Ch. 16. P. 285-300. doi
Article Galkin S., Shinder E. Exceptional collections of line bundles on the Beauville surface // Advances in Mathematics. 2013. Vol. 224. No. 10 September. P. 1033-1050. doi
Article Cruz Morales J. A., Galkin S. Upper Bounds for Mutations of Potentials // Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2013. Vol. 9. No. 005. P. 1-13. doi
Article Akhtar M., Coates T., Galkin S., Kasprzyk A. Minkowski Polynomials and Mutations // Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2012. Vol. 8. No. 094. P. 1-707. doi
Article Galkin S., Golyshev V. Quantum cohomology of Grassmannians and cyclotomic fields / Пер. с рус. // Russian Mathematical Surveys. 2006. Vol. 61. No. 1. P. 171-173. doi

Working papers¹¹

Preprint Galkin S., Belmans P., Mukhopadhyay S. Graph potentials and moduli spaces of rank two bundles on a curve / Cornell University. Series math "arxiv.org". 2020. No. 2009.05568.
Preprint Galkin S., Nagaraj D. S. Projective bundles and blow-ups of Projective spaces / Cornell University. Series math "arxiv.org". 2020. No. 2006.12112.
Preprint Galkin S. Fano-Mathieu correspondence / Cornell University. Series math "arxiv.org". 2018. No. 1809.02738.
Preprint Galkin S., Popov P. On pairs, triples and quadruples of points on a cubic surface / Cornell University. Series math "arxiv.org". 2018. No. 1810.07001.
Preprint Galkin S. Small toric degenerations of Fano threefolds / Cornell University. Series math "arxiv.org". 2018. No. 1809.02705.
Preprint Galkin S. Apéry constants of homogeneous varieties / Cornell University. Series math "arxiv.org". 2016. No. 1604.04652.
Preprint Galkin S., Karzhemanov I., Shinder E. On automorphic forms of small weight for fake projective planes / Cornell University. Series math "arxiv.org". 2016. No. 1602.06107.
Preprint Galkin S., Shinder E. On a zeta-function of a dg-category / Cornell University. Series math "arxiv.org". 2015. No. 1506.05831.
Preprint Galkin S., Shinder E. The Fano variety of lines and rationality problem for a cubic hypersurface / Cornell University. Series math "arxiv.org". 2014. No. 1405.5154.
Preprint Galkin S. The conifold point / Cornell University. Series math "arxiv.org". 2014. No. 1404.7388.
Preprint Galkin S., Katzarkov L., Mellit A., Shinder E. Minifolds and Phantoms / Cornell University. Series math "arxiv.org". 2013. No. 1305.4549v1.

Grants

2015-2017: Dynasty foundation award for "Explicit constructions of interesting projective manifolds"

2015: Simons IUM-fellowship

Principal Investigator:

2016: RFBR grant 16-01-20250, organization of the conference "Monge--Ampere equation and Calabi--Yau manifolds"

2015: RFBR grant 15-01-20558, organization of the conference "Projective Algebraic Geometry" (celebrating Fyodor Zak's 65th birthday)

2014-2015: "Derived categories and mirror symmetry for Fano manifolds and moduli spaces", grant MK-1297.2014.1 from the Ministry of Education and Science of the Russian Federation.

2014-2015: "Phantoms in fake projective planes'', NRU HSE's Academic Fund Program, research grant No 14-01-0025

2009-2011: "Quantum topological invariants of Fano manifolds",
JSPS Grant-in-Aid for Scientific Research (Kakenhi) 10554503.

2009-2012: Start-Up Grant, World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

Participant:

2015-2016: "Categorical and analytic invariants in algebraic geometry", JSPS-RFBR grant 15-51-50045

2014-2016: "Algebraic geometry of symplectic varieties", key participant of the grant RSF 14-21-00053

2013-2017: AG Laboratory NRU-HSE, RF government grant, ag. 11.G34.31.0023

- "Algebraic geometry, homological algebra, algebraic number theory and mirror symmetry", NSh grants 2998.2014.1, 4713.2010.1, 1987.2008.1, 9969.2006.1

INTAS grant 05-100000-8118

RFBR grants 08-01-00395-a, 04-01-00613, 04-01-00702

ERC grant GEMIS

FWF grants P 24572-N25, P2077

NSF grants DMS0600800, FRG DMS-0652633, FRG DMS-0854977, DMS-0901330

Soshiki Wakate from Japan Society for Promotion of Science

In 2008: "Periods, moduli spaces and arithmetic of algebraic varieties", SFB45

https://www.mccme.ru/~galkin/talks

Conferences

2017
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Presentation: The conifold point
Конференция "Алгебра и теория чисел в Калининграде" (Калининград). Presentation: Точки, прямые, квадраты, и кубики
Конференция "Алгебра и теория чисел в Калининграде" (Калининград). Presentation: Представления колчана Кронекера и детерминантальные представления кубических форм
Inagurational conference for Gökova Geometry/Topology Institute (Гёкова (Gökova)). Presentation: Cubic forms and related geometries (3 talks)
Geometry of String and Gauge Theories (CERN). Presentation: Two Gauged Linear Sigma Models for non-spherical Calabi-Yau manifolds
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Presentation: Fano threefolds, K3 surfaces, Mathieu group, and Brav-Dyckerhoff relative Calabi-Yau structures
Международный семинар по бирациональной геометрии и семинар Гиперкэлерова суббоота (Москва). Presentation: Beauville-Donagi and Debarre-Voisin as symmetric squares of Kummer-Kahler-Kodaira-Kuznetsov
2016
miniPAGES (Polish Algebraic GEometry mini-Semester) (Бедлево). Presentation: Hyperkahler manifolds and modular forms
23 GÖKOVA GEOMETRY / TOPOLOGY CONFERENCES (Гокова). Presentation: Hyperkähler manifolds and mirror symmetry
2015
New Techniques in Birational Geometry (Stony Brook). Presentation: A tentative integer-valued birational invariant of threefolds
Amplitudes, Motives and Beyond (Mainz). Presentation: Exceptional minuscule graphs and motives
Mathematics of Physics: Geometry and Topology (Engelberg). Presentation: Refined counting of holomorphic discs bounded on Lagrangian torus on a surface
Magadan Algebraic Geometry International Conference (Магадан (Magadan)). Presentation: Counting rational curves on abelian varieties
Tropical Aspects in Geometry, Topology and Physics (Oberwolfach). Presentation: Degenerations, transitions and quantum cohomology
Algebraic Geometry Seminar (Stony Brook). Presentation: An explicit construction of Miura's varieties
Categorical and analytic invariants in algebraic geometry II (Токио, Кашива). Presentation: Counting rational curves on abelian varieties is a moonshine with delightful byproducts
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва). Presentation: Quantum, refined, tropical, real, and homotopic
2014
Calabi-Yau Geometry and Mirror Symmetry (臺北 (Taipei)). Presentation: On positive aspects of mirror symmetry
Hong Kong Geometry Colloquium (香港 (Hong Kong)). Presentation: Cubics, squares and lines
IMS Algebraic Geometry seminar (香港 (Hong Kong)). Presentation: Mirror symmetry for Fano manifolds
Introductory Workshop on Tropical Geometry in its Complex and Symplectic aspects (Lausanne). Presentation: Mini-course "Geometry of surfaces with geometric genus zero" (4 lectures)
Workshop on B-model aspects of Gromov-Witten Theory (Ann Arbor). Presentation: Gamma conjectures for Fano manifolds
Workshop on Calabi-Yau Manifolds, Mirror Symmetry and Related Topics (東京 (Tokyo)). Presentation: An explicit construction of Miura's varieties
The 10th meeting of "The locally free geometry seminars" (London). Presentation: Cubics: lines, squares, and irrationality
2nd International School on TQFT, Langlands and Mirror Symmetry (Playa del Carmen). Presentation: Cubics: lines, squares, and irrationality
Landau-Ginzburg Theory and Fano Varieties (경주시 (Gyeongju)). Presentation: On conjectures of Dubrovin and Ostrover-Tyomkin
Tropical Geometry in Europe (İstanbul). Presentation: Rational cubic fourfolds, their lines, and associated K3 surfaces
Seminar on Mirror Symmetry (Genève). Presentation: Rationality problems, with special regard to cubic hypersurfaces
Seminar on Mirror Symmetry (Genève). Presentation: Grothendieck's constructor and irrationality of cubic fourfolds
Tropicalization, Realization, and Algebraic-Tropical Correspondence (אילת (Eilat)). Presentation: Monotone Lagrangian tori in the plane
Calabi-Yau Manifolds and their Moduli (Edmonton). Presentation: Calabi-Yau threefolds from elliptic curves, Grassmannians, sextonions,...
Tropical Geometry in Europe (Marseille). Presentation: Dolgachev surfaces and ball quotients
A workshop on the Chow group of holomorphically symplectic manifolds (Москва (Moscow)). Presentation: Lines on rational cubic fourfolds, and associated K3 surfaces
Derived Categories, Motives and Zeta-functions (Edinburgh). Presentation: Derived categories, motives, symmetric powers, zeta-functions
Tropical Geometry (Saas Fee). Presentation: Polynomial relations between holomorphic curves and discs
Mathematics Inspired by String Theory (三亞 (Sānyà)). Presentation: A symplectic version of Dubrovin's conjectures
Complex manifolds, dynamics and birational geometry (Москва (Moscow)). Presentation: Acyclic line bundles on fake projective planes
One-day conference dedicated to the memory of V. A. Iskovskikh (Москва (Moscow)). Presentation: New Fano manifolds, new questions
Еженедельный семинар "Геометрические структуры на многообразиях" (Москва (Moscow)). Presentation: Grothendieck's LEGO and birational geometry
2013
Special Seminar IPMU, University of Tokyo (柏市 (Kashiwa)). Presentation: Exceptional collections on punctual Hilbert schemes of surfaces, and cateorical zeta-functions
Special Program "Tropical Geometry and Topology" (Bonn). Presentation: Mini-course "Geometry of Fano manifolds" (4 lectures)
Séminaire de Géométrie Tropicale (Paris). Presentation: The conifold point
MIPT's DM seminar at Moscow (Москва (Moscow)). Presentation: Bartender's guide to wandering drunkards
Seminar of Lie groups, Riemann surfaces, and mathematical physics (Москва (Moscow)). Presentation: Mirror symmetry for elliptic curves (after Polishchuk and Zaslow)
Seminar of Max Planck Institute for Mathematics (Bonn). Presentation: The quantization of mirror symmetry for del Pezzo surfaces
Seminar of the Steklov Math. Institute (Москва (Moscow)). Presentation: Пары точек и прямые на кубиках (Pairs of points and lines on cubics)
Seminar of the Institute of Mathematics of the Johannes Gutenberg University (Mainz). Presentation: Zeta-functions of perfect categories, symmetric powers and Hilbert schemes
Еженедельный семинар Лаборатории алгебраической геометрии и ее приложений (Москва (Moscow)). Presentation: Малообразия
2012
Workshop Homological Projective Duality and Quantum Gauge Theory (東京 (Tokyo)). Presentation: Projective duality, quantum cohomology and exceptional approximations
Первая международная конференция по алгебраической геометрии, теории элементарных частиц и теории струн «Relation of String Theory to Gauge Theories and Moduli Problems of Branes» (Москва (Moscow)). Presentation: Exceptional collections of four line bundles on Beauville's quotient-product surface
Workshop «Birational Geometry and Derived Categories» (Wien (Vienna)). Presentation: Minifolds and phantoms
Itinerant Seminar "Tropical Geometry in Europe" (Bonn). Presentation: Mutations of potentials and their upper bounds
Nakajima seminar (京都市 (Kyoto)). Presentation: Phantom categories
Hodge theoretic aspects of mirror symmetry (Mainz). Presentation: Exceptional non-commutative Hodge structures and Diophantine approximations
International School on TQFT, Langlands and Mirror Symmetry (Huatulco). Presentation: Homologically minimal fourfolds
Birational and Affine Geometry (Москва). Presentation: Minifolds