dr. Andrey Krutov
Sokolovská 49/83, 186 75 Praha 8
Czech Republic
Emails: a.o.krutov at gmail dot com GPG key, andrey dot krutov at matfyz dot cuni dot cz
MR author ID: 912066, Google Scholar ID: UIOivHUAAAAJ, arXiv ID: krutov_a_1
I am a researcher at the Mathematical Institute of Charles University (Prague, Czechia). My research interests includes representation theory of Lie (super)algebra, geometry of integrable systems, quantum groups and noncommutative geometry. I got my PhD in June 2014 at University of Groningen, under supervision of Dr. Arthemy Kiselev and Prof. Dr. Jaap Top.
Publications
- A. O. Krutov, R. Ó Buachalla, K. R. Strung, Nichols algebras and quantum principal bundles, Int. Math. Res. Not. IMRN (2023), no. 23, 20076–20117. arXiv:1701.04394 [math.QA]
- F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Positive line modules over the irreducible quantum flag manifolds, Lett. Math. Phys. 112 (2022), no. 6, 33 p., arXiv:1912.08802 [math.QA] OWP-2020-01
- A. Krutov, A. Lebedev, D. Leites, I.Shchepochkina, Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2, Linear Algebra Appl. 649 (2022), 1–21, arXiv:2102.11653 Updated version of OWP-2020-02.
- F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Holomorphic relative Hopf modules over the irreducible quantum flag manifolds, Lett. Math. Phys. 111 (2021), no. 1, 24 p., arXiv:2005.09652 [math.QA] link
- A. V. Kiselev, A. O. Krutov, On the (non)removability of spectral parameters in \(\mathbb{Z}_2\)-graded zero-curvature representations and its applications, Acta Appl. Math. 160 (2019), no. 1, 129–167, arXiv:1301.7143 [math.DG] link
- A. Krutov, A. Lebedev, On gradings modulo 2 of simple lie algebras in characteristic 2, SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018), no. 130, 27 p., arXiv:1711.00638 [math.RT] link (Open access)
- S. Bouarroudj, A. Krutov, D. Leites, I. Shchepochkina, Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras, Algebr. Represent. Theory 21 (2018), no.5, 897–941, arXiv:1806.05505 [math.RT].
- A. V. Kiselev, A. O. Krutov, T.Wolf, Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment, Nonlinear Systems and Their Remarkable Mathematical Structures (N. Euler, ed.), vol. 1, CRC Press, Boca Raton, FL, 2018, pp. 390–407, arXiv:1805.12397 [nlin.SI]
- S. Bouarroudj, A. Krutov, A. Lebedev, D. Leites, I. Shchepochkina, On restricted Lie (super)algebras in characteristic 3, Funct. Anal. Appl. 52 (2018), no. 1, 49–52, arXiv:1809.08582 [math.RT] link
- A. V. Kiselev, A. O. Krutov, Gardner's deformation of the Krasil'shchik–Kersten system, J. Phys.: Conf. Ser. 621 (2015), no. 1, 19 p., Group Analysis of Differential Equations and Integrable Systems (GADEISVII) (June 15–19, 2014; Larnaca, Cyprus). arXiv:1409.6688 [nlin.SI], link (Open access)
- A. V. Kiselev, A. O. Krutov, Non-Abelian Lie algebroids over jet spaces, J. Nonlin. Math. Phys. 21 (2014), no. 2, 188–213, arXiv:1305.4598 [math.DG] link (Open access)
- A. V. Kiselev, A. O. Krutov, Gardner's deformations as generators of new integrable systems, J. Phys.: Conf. Ser. 482 (2014), no. 1, 6 p., Physics and Mathematics of Nonlinear Phenomena 2013, (June 22–29, 2013; Gallipoli, Italy). arXiv:1312.6941 [nlin.SI] link (Open access)
- A. V. Kiselev, A. O. Krutov, Gardner's deformations of the graded Korteweg–de Vries equations revisited, J. Math. Phys. 53 (2012), no. 10, 103511, 18 p., arXiv:1108.2211 [nlin.SI] link
- V. Hussin, A. V. Kiselev, A. O. Krutov, T. Wolf, N=2 supersymmetric a=4-Korteweg–de Vries hierarchy derived via Gardner's deformation of Kaup–Boussinesq equation, J. Math. Phys. 51 (2010), no. 8, 083507, 19 p., arXiv:0911.2681 [nlin.SI] link
Preprints
- J. Bhowmick, B. Ghosh, A. O. Krutov, R. Ó Buachalla, Levi-Civita connection on the irreducible quantum flag manifolds, 45 p. arXiv:2411.03102 [math.QA]
- A. Krutov, P. Pandžić, Quantised \(\mathfrak{sl}_2\)-differential algebras, 10 p. arXiv:2403.08521 [math.QA]
- A. Krutov, D. Leites, I. Shchepochkina, Non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries, 51 p. arXiv:2309.16370 [math.DG]
- A. O. Krutov, R. Ó Buachalla, Curvature of positive relative line module over the quantum projective spaces, 18 p. arXiv:2309.16612 [math.QA]
- A. Krutov, P. Pandžić, Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\), 14 p. arXiv:2209.09591 [math.RT]
- A. Krutov, D. Leites, J. Shang, Duflo-Serganova homology for exceptional modular Lie superalgebras with Cartan matrix, 20 p. arXiv:2008.12033 [math.RT]
SuperLie
I'm a current maintener of the SuperLie package for Mathematica. SuperLie was originally developed by Pavle Grozman. The details can be found at the github page of the package. The new release is expecting soon!Talks at conferences, workshops, and research seminars
- 2024
- "Clifford alagebra analogue of the Cartan theorem for symmetric pairs" (poster) Poisson 2024, Accademia Pontaniana, Napoli, Italy. (July 8-12)
- "Nichols algebras and quantum principal bundles", Noncommutative Geometry Seminar, SISSA, Trieste, Italy. (19 Jun)
- "Clifford algebra analogue of the Cartan theorem for symmetric pairs", CaLISTA 2nd Annual Meeting, Bulgarian Academy of Sciences, Sofia, Bulgaria. (May 27 - 31)
- "Quantised \(\mathfrak{sl}_2\)-differential algebres", Representation theory seminar, University of Zagreb, Croatia. (21 May)
- "Clifford algebra analogue of the Cartan theorem", Séminaire "Groupes de Lie et espaces de modules", Université de Genève, Switzerland. (30 April)
- "Quantised \(\mathfrak{sl}_2\)-differential algebres", Central European Seminar, Masaryk University, Brno, Czech Republic. (14 March)
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", Miniworkshop on Manifolds, (C*-)Algebras and Quantization, Naples, Italy. (31 January - 2 February)
- "Structure of Clifford algebras of isotropy representations associated to symmetric pairs", 44th Winter School Geometry and Physics, Srni, Czechia. (13 - 20 January)
- 2023
- "Structure of Clifford algebras of isotropy representations associated to symmetric pairs", Séminaire "Groupes de Lie et espaces de modules", Université de Genève, Switzerland. (5 December)
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", Journées SL2R: en l'honneur du 60e anniversaire de Pavle Pandžić, Université de Lorraine, Institut Élie Cartan de Lorraine, Metz, France. (9 November)
- "Transgressions in the relative Weil algebra", Central European Seminar, Masaryk University, Brno, Czech Republic. (13 October)
- "Schubert calculus for the quantum Grassmannians", Quantum Groups and Noncommutative Geometry in Prague, Prague, Czech Republic. (11th to 15th September)
- "Non-integrable distributions with simple infinite-dimensional Lie (super)algebras of symmetries", Training school on Cartan Geometry, Brno, Czech Republic. (September 4 - 8)
- "Schubert calculus for the irreducible quantum flag manifolds", Representation Theory XVIII, Dubrovnik, Croatia. (June 18 - 24)
- "Transgression in the relative Weil algebra", CaLISTA Kick-off meeting, University of Bologna, Italy. (June 5 - 9)
- "Noncommutative differential geometry of the quantum Grassmannians", Séminaire "Groupes de Lie et espaces de modules", Université de Genève, Switzerland. (4 April)
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", Prague Mathematical Physics Seminar, Mathematical Institute of Charles University, Czech Republic (16 March)
- "Schubert calculus for the quantum Grassmannians", Representation theory seminar, University of Zagreb, Croatia. (28 February)
- "Schubert calculus for the quantum Grassmannians", 43th Winter School Geometry and Physics, Srni, Czechia. (14 - 20 January)
- 2022
- "Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2", IV International Workshop on Non-Associative Algebras in Covilhã, Portugal. (25 October)
- "Nichols algebras and quantum principal bundles", Central European Seminar, Masaryk University, Brno, Czech Republic. (22 October)
- "Quantum symmetric pairs: an overview", Representation theory seminar, University of Zagreb, Croatia. (11 October)
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", Representation Theory XVII, Dubrovnik, Croatia, (October 3 - 8) Slides:
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", Differential Geometry and its Applications, University of Hradec Králové, Czechia. (July 17 - 23)
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", Representation theory seminar, University of Zagreb, Croatia. (17 May)
- "Nichols algebras and quantum principal bundles", Prague Mathematical Physics Seminar, Mathematical Institute of Charles University, Czech Republic (14 April)
- "Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2", Seminar Cohomology in algebra, geometry, physics and statistics, IMCAS, Czech Republic (30 March)
- "Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\)", NCG&T Prague, IMCAS, Czech Republic. (25 January)
- "Holomorphic relative Hopf modules over the irreducible quantum flag manifolds", 42th Winter School Geometry and Physics, Srni, Czechia. (15 - 22 January)
- 2021
- "Holomorphic relative Hopf modules over the irreducible quantum flag manifolds", Diffieties, Cohomological Physics, and Other Animals. Alexandre Vinogradov Memorial Conference, Independent University of Moscow, Moscow State University. (13 - 17 December)
- Mini course "Introduction to dynamical systems", Summer school "Algebra, Topology and Analysis: \(C^*\) and \(A_\infty\) algebras", Gonio, Batumi, Georgia. (August 30 - September 3)
- Short course "Kostant conjecture for Clifford algebras", Representation theory seminar, University of Zagreb, Croatia. (29 April, 20 May, 26 May)
- 2020
- "Dufo-Serganova functor: exceptional modular Lie superalgebras with Cartan matrix", Representation theory seminar, University of Zagreb, Croatia. (22 December)
- Lecture course "Quantum Groups and Quantum Flag Manifolds", Representation theory seminar, University of Zagreb, Croatia. (January - July)
- 40th Winter School Geometry and Physics, Czech Republic, Srni (11-18 January) (attended)
- 2019
- "Nichols algebras and irreducible quantum flag manifolds", Supergeometry, supersymmetry and quantization, University of Luxembourg. (invited speaker) (16 - 20 December)
- Lecture course "Quantum Groups and Quantum Flag Manifolds", Representation theory seminar, University of Zagreb, Croatia. (October - December)
- "Nichols Algebras From Quantum Principal Bundles Over Quantum Flag Manifolds", Quantum Flag Manifolds in Prague, Czech Republic. (invited speaker) (16 - 20 September)) Slides:
- "Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic \(2\)", Representation theory seminar, University of Zagreb, Croatia. (10 September)
- "Dolbeault-Dirac Operators on the Standard Podle's Sphere I", Representation theory seminar, University of Zagreb, Croatia. (2 July)
- "On classification of simple Lie superalgebras in characteristic \(2\) and \(\mathbb{Z}/2\)-grading of simple Lie algebras", Representation theory seminar, University of Zagreb, Croatia. (11 June)
- "Schubert Calculus for Quantum Irreducible Flagmanifolds", Seminar on Quantum groups, Hopf algebras and monoidal categories, Université Libre de Bruxelles, Belgium. (5 April)
- 2018
- Lecture series "Introduction to geometry of PDEs", School of Mathematical Sciences, National Institute of Science Education and Research Bhubaneswar, India. (invited lecturer) (April - May)
- "On \(\mathbb{Z}/2\)-gradings of simple Lie algebra in characteristic \(2\) and its applications", Seminar "Riemann surfaces, Lie algebras and mathematical physics", Independent University of Moscow. Russia. (13 April)
- "Schubert Calculus for Quantum Grassmannians", Séminaire Groupes et Quantification, University of Riems Champange-Ardenne, France. (6 March)
- "Schubert Calculus for Quantum Grassmannians", Quantum Flag Manifolds Day, Radboud University, Nijmegen, The Netherlands. (invited speaker) (19 January)
- "Schubert Calculus for Quantum Grassmannians", Colloquium Mathematics, University of Groningen, The Netherlands. (16 January)
- Conference "Algebraic Groups, Lie Algebras and their Representations on the occasion of Jens Carsten Jantzen's 70th birthday", MPIM Bonn, Germany. (attended)
- Conference "Enveloping Algebras and Geometric Representation Theory", Oberwolfach, Germany. (attended)
- 2017
- "The Structure of Quantum Flag Manifolds" (3 joined posters with Réamonn Ó Buachalla and and Karen R. Strung.) International Festival in Schubert Calculus, Sun Yat-sen University, Guangzhou, China. (November 6-10, 2017)
- "On integrability of new fifth order \(N{=}1\) supersymmetric evolution equation" (joined poster with Arthemy V. Kiselev). XXXVI Workshop on Geometric Methods in Physics, Białowieża, Poland. (July 2-8, 2017)
- "On integrability of new fifth order \(N{=}1\) supersymmetric evolution equation'' (joined poster with Arthemy V. Kiselev). Int. Conference ``Geometry and Algebra of PDEs'', Tromsø, Norway. (June 6-10, 2017)
- "Introduction to the geometry of PDEs". Young Researchers Colloquium, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland. (2 June)
- "On gradings module 2 of simple Lie algebra in characteristic 2". Seminar Geometrical Methods in Physics, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland. (24 May)
- "Lie algebroids over infinite jet spaces". Mathematical Seminar, New York University Abu Dhabi, The United Arab Emirates. (16 April)
- "Lie algebroids over infinite jet spaces", "Gardner's deformations of integrable systems", "On gradings modulo 2 of simple Lie algebras in characteristic 2". Ostrava Seminar on Mathematical Physics, Ostrava University, Czech Republic. (April)
- 2016
- "Deformations of nonlocal structures over partial differential equations". Seminar Geometry and Differential Equations, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland. (30 November)
- "Gradings modulo 2 of simple Lie algebra in characteristic 2". Symposium "Groningen Deformation Day", University of Groningen, The Netherlands. (invited speaker) (7 October)
- "Geometry of jets spaces and PDE I-II", "Lie algebroids over infinite jet spaces". Seminar Geometrical Methods in Physics, Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland.
- 2015
- International Geometry Conference in memory of Mark Losik, Pereslavl-Zalessky, Russia. (attended)
- 2014
- "Gardner's deformation of Krasil'shchik-Kersten system". 7th Int. Workshop "Group analysis of differential equations and integrable systems", Larnaca, Cyprus.
- "Gardner's deformations and zero-curvature representations for KdV-like systems". Mathematical Colloquium, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, The Netherlands. (June)
- "Gardner's deformation problem for \(N{=}2\) supersymmetric \(a{=}4\) Korteweg-de Vries eqaution". Utrecht Dynamical Systems Seminar, Mathematical Institute, Utrecht University, The Netherlands. (June)
- 2013
- "Application of zero-curvature representations for solving Gardner's deformation problem for \(N{=}2\), \(a{=}4\)-SKdV equation". Int. Workshop "Supersymmetries & Quantum Symmetries - SQS'2013", JINR, Dubna, Russia.
- "On the (non)removability of spectral parameters in \(\mathbb{Z}_2\)-graded zero-curvature representations and its applications". 3rd Int. Conference "Nonlinear Waves --- Theory and Applications", Beijing, China.
- "Non-Abelian Lie algebroids over infinite jet spaces". Conference "Computer-analytical methods in control theory and mathematical physics", Sochi, Russia.
- "Non-Abelian Lie algebroids over infinite jet spaces" (poster). Jubilee Workshop "Nonlinear Mathematical Physics: 20 Years of JNMP", Sophus Lie Centre, Nordfj\o rdeid, Norway. (June 4-14)
- "Non-Abelian Lie algebroids over infinite jet spaces". Int. Conference "Lomonosov 2013", Faculty of Mathematics and Mechanics, Lomonovos MSU, Moscow, Russia. (seminar "Algebraic topology and its Applications" by prof. V. M. Buchstaber)
- "Gardner's deformation as generators of new integrable systems". Seminar at 2nd Summer School on Geometry of PDE, Kouty nad Desnou, Czech Republic.
- "Gardner's deformation of integrable systems". Seminar at Department of Mathematical Analysis, Ivanovo State University, Ivanovo, Russia. (Mar)
- 2012
- "Removability of the spectral parameter in zero-curvature representations: \(\mathbb{Z}_2\)-graded case" (poster). "Geometric Structures in Integrable Systems", Dubrovin lab, Lomonosov MSU, Moscow, Russia.
- "Gardner's deformation of the \(N{=}2\), \(a{=}4\)-SKdV equation". Seminar "Nonlinear analysis and its applications", Vladimir State University, Vladimir, Russia. (Nov)
Selected seminars in Prague
Here is a list of selected mathematical seminar that I often attend in Prague- Seminars on Harmonic Analysis, on Fridays, 10:40 at the Mathematical Institute of Charles University.
- Prague Mathematical Physics Seminar, on Thursdays, 14:00 at the Mathematical Institute of Charles University.
- NCG&T Prague, on Tuesdays,16:00 at IMCAS.
- Seminar Cohomology in algebra, geometry, physics and statistics, on Wednesdays, 13:30 at IMCAS.
- Set Theory and Analysis on Tuesdays, 10:00 at IMCAS.
Other academic activity
Research visits (selected)
- Oct 2024. University of Zagreb, Croatia.
- Jun 2024. SISSA, Italy.
- May 2024. University of Zagreb, Croatia.
- Apr 2023. Université de Genève, Switzerland.
- Feb 2024. University of Zagreb, Croatia.
- Dec 2023. Université de Genève, Switzerland.
- Nov 2023. University of Zagreb, Croatia.
- Apr 2023. Université de Genève, Switzerland.
- Feb 2023. University of Zagreb, Croatia.
- May 2022. University of Zagreb, Croatia.
- Nov 2021. University of Zagreb, Croatia.
- Jul 2020. Mathematical Institute, Czech Academy of Sciences, Czechia.
- Nov 2019. Université Libre de Bruxelles, Belgium.
- Jul 2019. Université Libre de Bruxelles, Belgium.
- Jun 2019. University of Zagreb, Croatia.
- Apr 2019. Université Libre de Bruxelles, Belgium.
- Jun 2018. New York University Abu Dhabi, The United Arab Emirates.
- Apr-May 2018. National Institute of Science Education and Research, Bhubaneswar, India.
- Feb 2018. New York University Abu Dhabi, The United Arab Emirates.
- Jan 2018. Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands
- Sep 2017. New York University Abu Dhabi, The United Arab Emirates.
- Apr 2017. New York University Abu Dhabi, The United Arab Emirates.
- May 2009. Mathematical Institute, Utrecht University, The Netherlands.
Visitors (selected)
- Apr 2023. K. Grizelj (University of Zagreb) at Institute of Mathematics, Czech Academy of Sciences.
- Nov 2022. K. Calvert (University of Manchester), K. Grizelj, and P. Pandžić (University of Zagreb) at Institute of Mathematics, Czech Academy of Sciences.
- Aug 2019. S. Bouarroudj (NYU Abu Dhabi) at University of Zagreb.
- Jul 2019. R. Ó Buachalla (Université Libre de Bruxelles) and K. R. Strung (Radboud Universiteit) at University of Zagreb.
- Nov-Dec 2018. D. Leites (NYU Abu Dhabi, Stocholm University) at Oberwolfach Research Institute for Mathematics.
- Dec 2018. R. Ó Buachalla (Université Libre de Bruxelles) and K. R. Strung (Radboud Universiteit) at Oberwolfach Research Institute for Mathematics.
Graduate Schools
I attended five graduate schools in geometry of partial differential equations (Kostroma, 2008, 2009, Gdynia 2012 (Diffiety schools); Kouty nad Desnou, 2013; Pereslavl-Zalessky, 2015), the graduate school and the conference in Geometry & Quantum Theory of the GQT-cluster (Zeist, 2014), Advanced School on Integrability (Warsaw, 2017), Mini School on Schubert Calculus (Guangzhou, 2017).
Other Service
- Co-organiser of the conference "Quantum groups and Lie groups" (Zagreb, 25.09-26.09; WG3 meetings of the COST action CaLISTA).
- Co-organiser of the seminar "The geometry of Flag Manifolds" (IMPAN, Warsaw, 2017).