What's NEW:
- May 27: Counter-examples to Gamma conjecture I
(with Jianxun Hu, Hiroshi Iritani, Hua-Zhong Ke, Changzheng Li, Zhitong Su)
arXiv:2405.16979,
(v3 is coming!)
- June 7: 2024.2 -- Geometry of Algebraic Varieties, feat. Lucas Castello Branco, problem-centric graduate course, Aug - Dec 2024.
- Oct 23: 2025.1 -- Minimal Surfaces and Quantization, in proportion 60/40, Tue 9h-11h and Thu 9h-11h, March - July 2025.
24 VIDEOS
of
178 TALKS
(April 2008 - March 2020, many newer videos on graph potentials are available by request)
Written works
{legend:
title[fulltext]
citation[doi]
arxiv[abs]
link[other]
text[authors,date,etc]}, ordered by last update of preprint, publication or postprint:
- S. Galkin, J. Hu, H. Iritani, H. Ke, C. Li, Z. Su:
Counter-examples to Gamma conjecture I.
arXiv:2405.16979.
- P. Belmans, S. Galkin, S. Mukhopadhyay:
Decompositions of moduli spaces of vector bundles and graph potentials.
Forum of Mathematics, Sigma , 11 (2023) e16.
arXiv:2009.05568 (v3 and later).
- S. Galkin, I. Karzhemanov, E. Shinder:
On automorphic forms of small weight for fake projective planes.
Moscow Math Journal 23:1 (2023) 97--111.
arXiv:1602.06107.
IPMU 15-0202.
(2014.08, Trento)
- P. Belmans, S. Galkin, S. Mukhopadhyay:
Graph potentials and symplectic geometry of moduli spaces of vector bundles.
arXiv:2206.11584.
- P. Belmans, S. Galkin, S. Mukhopadhyay:
Graph potentials and topological quantum field theories.
arXiv:2205.07244.
- S. Galkin, G. Mikhalkin:
Singular symplectic spaces and holomorphic membranes.
European Journal of Mathematics 8 (2022) 932--951.
arXiv:2203.10043.
(2014.10, Petra)
- S. Galkin, D.S. Nagaraj:
Projective bundles and blow-ups of Projective spaces.
Annali di Matematica 201 (2022) 2707--2713.
arXiv:2006.12112.
- P. Belmans, S. Galkin, S. Mukhopadhyay:
Examples violating Golyshev's canonical strip hypotheses.
Experimental Mathematics 31:1 (2022) 233--237.
arXiv:1806.07648.
MPIM 18-32.
- P. Belmans, S. Galkin, S. Mukhopadhyay:
Combinatorial non-abelian Torelli theorem.
July 17, 2021.
Expanded in: Can one hear the shape of a random walk? (2024)
- T. Coates, S. Galkin, A. Kasprzyk, A. Strangeway:
Quantum periods for certain four-dimensional Fano manifolds.
Experimental Mathematics 29:2 (2020) 183--221.
arXiv:1406.4891.
- S. Galkin, S. Rybakov:
A family of K3 surfaces and towers of algebraic curves over finite fields.
Math. Notes 106:6 (2019) 1014--1018.
arXiv:1910.14379
- S. Galkin, H. Iritani:
Gamma conjecture via mirror symmetry.
Primitive Forms and Related Subjects --- Kavli IPMU 2014, Adv. Stud. Pure Math. 83 (2019) 55--115.
arXiv:1508.00719.
- S. Galkin, P. Popov:
On pairs, triples and quadruples of points on a cubic surface.
Russ. Math. Surv., to appear.
arXiv:1810.07001.
- S. Galkin:
Fano-Mathieu correspondence.
arXiv:1809.02738.
IPMU 10-0150.
- S. Galkin:
Degenerations, transitions and quantum cohomology.
in: Tropical Aspects in Geometry, Topology and Physics. Oberwolfach Report No. 23/2015, pp. 1269--1273.
arXiv:1809.02737
(2015.04, Oberwolfach)
- S. Galkin:
Small toric degenerations of Fano threefolds.
arXiv:1809.02705.
IPMU 12-0121.
Original (in Russian): Preprint VINITI 167-B, Feb 27, 2008, Moscow.
Part 3/3 of my PhD thesis.
- S. Galkin:
Apéry constants of homogeneous varieties.
arXiv:1604.04652.
(2008.10, Mainz, preprint SFB45)
- S. Galkin, V. Golyshev, H. Iritani:
Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures.
Duke Math. J. 165:11 (2016) 2005--2077.
arXiv:1404.6407.
IPMU 10-0200.
- T. Coates, A. Corti, S. Galkin, A. Kasprzyk:
Quantum periods for 3-dimensional Fano manifolds.
Geometry & Topology 20 (2016) 103--256.
arXiv:1303.3288.
IPMU 13-0113.
- S. Galkin, A. Mellit, M. Smirnov:
Dubrovin's conjecture for IG(2,6).
Int Math Res Notices 2015:18 (2015) 8847--8859.
arXiv:1405.3857.
- S. Galkin, L. Katzarkov, A. Mellit, E. Shinder:
Derived categories of Keum's fake projective planes.
Adv. Math. 278 (2015) 238--253.
(2013.06, Mainz)
- S. Galkin, E. Shinder:
On a zeta-function of a dg-category.
arXiv:1506.05831.
(2013.01, Saint Petersburg - Moscow)
- S. Galkin, E. Shinder:
The Fano variety of lines and rationality problem for a cubic hypersurface.
arXiv:1405.5154.
- S. Galkin:
The conifold point.
arXiv:1404.7388.
(2011, Split)
- S. Galkin, L. Katzarkov, A. Mellit, E. Shinder:
Minifolds and Phantoms.
2013. IPMU 13-0102.
arXiv:1305.4549.
- S. Galkin, E. Shinder:
Exceptional collections of line bundles on the Beauville surface.
Adv. Math. 244 (2013) 1033--1050.
arXiv:1210.3339.
MPIM 12-60.
- J. A. Cruz Morales, S. Galkin:
Upper bounds for mutations of potentials.
SIGMA 9:005 (2013) 1--13.
arXiv:1301.4541.
IPMU 12-0110.
- M. Akhtar, T. Coates, S. Galkin, A. Kasprzyk:
Minkowski Polynomials and Mutations.
SIGMA 8:094 (2012) 1--707.
arXiv:1212.1785.
IPMU 12-0120.
- T. Coates, A. Corti, S. Galkin, V. Golyshev, A. Kasprzyk:
Mirror Symmetry and Fano manifolds.
in: ECM Kraków, 2-7 July, 2012, pp. 285--300.
arXiv:1212.1722.
IPMU 12-0102.
- S. Galkin, A. Usnich:
Laurent phenomenon for Ginzburg-Landau potential.
2010. IPMU 10-0100.
- S. Galkin:
G-minimal varieties are quantum minimal.
IPMU 10-0101.
(2008.04, Mainz)
- S. Galkin:
Two instances of fake minimal Fano threefolds.
IPMU 11-0099.
(2008.05, Mainz-IHES, preprint SFB45)
- S. Galkin:
Del Pezzo surfaces and low ramified pencils of elliptic curves.
Preprint VINITI 168-B, Feb 27, 2008, Moscow.
In Russian, part 2/3 of my PhD thesis.
- S. Galkin, V. Golyshev:
Quantum cohomology of Grassmannians and cyclotomic fields.
Russ. Math. Surv. 61:1 (2006) 171--173.
In Russian + English . Part 1/3 of my PhD thesis.
(2004, Moscow)
- S. Galkin:
Derived categories of coherent sheaves on toric stacks.
ITEP-TH-105/04.
In Russian, a preprint version of my specialist (Master) thesis.
(2004.06, Moscow)
Older or superceded/overlapping versions
- P. Belmans, S. Galkin, S. Mukhopadhyay:
Graph potentials and moduli spaces of rank two bundles on a curve.
arXiv:2009.05568v2 (v1-v2 only).
Superceded by
arXiv:2009.05568v3 (v3 and later),
arXiv:2205.07244,
arXiv:2206.11584.
- S. Galkin, A. Mellit:
Minifolds 1: on the projective fourspace.
IPMU 11-0100.
(2011.02, Trieste)
In 2013 it was incorporated as the first half of preprint
arXiv:1305.4549,
but since second half of it was published separately,
an extended version of this paper is going to be released.
- S. Galkin:
Picard lattices of nodal toric Fano threefolds.
2008, in Russian, part 4/3 of my PhD thesis.
A supplementary computation for
arXiv:1809.02705,
of independent interest.
- S. Galkin:
Toric degenerations of Fano manifolds.
Ph.D. Thesis (Steklov Math Institute, April 3, 2008).
(in Russian).
Main results correspond to three papers above.
Mini-courses:
-
Decompositions in Algebraic and Symplectic Geometry, Gamma Conjectures, Mirror Symmetry, and their applications.
TIFR Mumbai, India, January-February 2020.
- Cubic forms and related geometries,
Gökova GTI, Turkey, June 2017.
- Cubic forms (with N. Kurnosov),
Dubna, Russia, July 2016.
- Geometry of surfaces with geometric genus zero,
EPFL Lausanne, Switzerland, January 2014.
- Geometry of Fano manifolds,
MPIM Bonn, Germany, September 2013.
[Notes, Photos]
- From classical geometry to mirror symmetry,
IPMU Kashiwa, Japan, May 2012.
- Reflecting Fano,
Geneva University, Switzerland, March 2012.
- Mirror constructions for Fano varieties,
KIAS summer school on Mirror Symmetry for Fano Varieties, Anmyendo, Korea, June 2011.
Organization of seminars:
Organization of conferences, workshops, schools, minicourses:
- Mirror Symmetry and applications,
December 13-18, 2017, Moscow (with C. Brav, L. Katzarkov, V. Przyjalkowski)
- Hyperkähler Saturday,
November 25, 2017, Moscow (with N. Kurnosov)
- Monge-Ampere equation and Calabi-Yau manifolds,
May 23-27, 2016, Moscow (with M. Verbitsky)
- Projective Algebraic Geometry (celebrating Fyodor Zak's 65th birthday),
September 7-12, 2015, Moscow (with K.Shramov and N.Kurnosov)
- Derived categories, Motives and Zeta-functions,
June 9-11, 2014, Edinburgh (with E. Shinder and M. Wemyss)
- Curves and categories in geometry and physics,
October 31 - November 4, 2011, Kashiwa (with T. Milanov, A. Bondal, K. Hori and K. Saito)
- Fuchsian differential equations and holomorphic connections,
April 25-28, 2011, Kashiwa (with A. Getmanenko and T. Milanov)
Lecture courses:
Minimal Surfaces, and Quantization (25.1),
(Numerical) Linear Algebra "2" / Álgebra Linear 2 (25.1, basic cycle),
Geometry of Algebraic Varieties (24.2),
Complex Geometry (24.1),
Linear Algebra / Álgebra Linear (24.1, 23.1),
Quantum Topology: an introduction (24.0),
Representation Theory / Teoria da Representação (23.2),
Riemann Surfaces /
Superfícies de Riemann (23.1-23.2),
Modular Forms (23.0 (summer), 15.1),
Algebraic Geometry and Statistical Learning Theory (22.2),
Complex Variable / Análise Complexa (22.2),
Introduction to Topology / Introdução à Topologia (22.1),
Algebra / Estruturas Algébricas I/II (22.1, 21.2, 21.1, 20.2, 20.1),
Logics, Proofs and LEAN / Lógica, Provas e LEAN (21.2),
Geometry of Robotics (21.1),
Algebraic Geometry (20.2, 17.2),
Commutative Algebra / Álgebra Comutativa (20.1),
Topics in Geometry / Tópicos em Geometria (19.2),
Symmetries and Moduli Spaces (16.2),
Algebraic Surfaces / Алгебраические поверхности (15.2-16.1, a year course),
Proofs of Irrationality / Доказательства иррациональности (15.2),
Projective Geometry / Проективная геометрия (14.1).
Coauthors:
Mohammad AKHTAR,
Pieter BELMANS,
Alexey BONDAL,
Tom COATES,
Alessio CORTI,
John Alexander CRUZ MORALES,
Ronaldo GARCIA,
Vasily GOLYSHEV,
Jianxun HU,
Hiroshi IRITANI,
Ilya KARZHEMANOV,
Al KASPRZYK,
Ludmil KATZARKOV,
Huazhong KE,
Changzheng LI,
Anton MELLIT,
Grigory MIKHALKIN,
Swarnava MUKHOPADHYAY,
D.S. Nagaraj,
Pavel POPOV,
Dan REZNIK,
Sergey RYBAKOV,
Evgeny SHINDER,
Constantin SHRAMOV,
Maxim SMIRNOV,
Andrew STRANGEWAY,
Zhitong SU,
Alexandr USNICH.
Some useful links.
