# dr. Andrey Krutov

Žitná 25
115 67 Praha 1
Czech Republic

Emails: a.o.krutov at gmail dot com GPG key, krutov at math dot cas dot cz GPG key.

MR author ID: 912066, Google Scholar ID: UIOivHUAAAAJ, arXiv ID: krutov_a_1

I am a postdoctoral researcher at Institute of Mathematics of Czech Academy of Sciences (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

1. 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.
2. 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, arXiv:2005.09652 [math.QA] link
3. 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
4. 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, arXiv:1711.00638 [math.RT] link (Open access)
5. 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].
6. 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]
7. 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
8. A. V. Kiselev, A. O. Krutov, Gardner's deformation of the Krasil'shchik–Kersten system, J. Phys.: Conf. Ser. 621 (2015), no. 1, 19, Group Analysis of Differential Equations and Integrable Systems (GADEISVII) (June 15–19, 2014; Larnaca, Cyprus). arXiv:1409.6688 [nlin.SI], link (Open access)
9. 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)
10. A. V. Kiselev, A. O. Krutov, Gardner's deformations as generators of new integrable systems, J. Phys.: Conf. Ser. 482 (2014), no. 1, 6, Physics and Mathematics of Nonlinear Phenomena 2013, (June 22–29, 2013; Gallipoli, Italy). arXiv:1312.6941 [nlin.SI] link (Open access)
11. 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, arXiv:1108.2211 [nlin.SI] link
12. 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, arXiv:0911.2681 [nlin.SI] link

## Preprints

1. A. Krutov, P. Pandžić, Cubic Dirac operator for $$U_q(\mathfrak{sl}_2)$$, 14 p. arXiv:2209.09591, [math.RT]
2. A. O. Krutov, R. Ó Buachalla, K. R. Strung, Nichols algebras and quantum principal bundles, 31 p. arXiv:1701.04394 [math.QA]
3. F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Positive line bundles over the irreducible quantum flag manifolds, 30 p. arXiv:1912.08802 [math.QA] OWP-2020-01
4. A. Krutov, D. Leites, J. Shang, Duflo-Serganova homology for exceptional modular Lie superalgebras with Cartan matrix, 20 p. arXiv:2008.12033 [math.RT]

## Talks at conferences, workshops and research seminars

• 2022
• 2021
• 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
• 2018
• 2017
• 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)

### Research visits

• May 2009. Mathematical Institute, Utrecht University, The Netherlands.
• Apr 2017. New York University Abu Dhabi, The United Arab Emirates.
• Sep 2017. New York University Abu Dhabi, The United Arab Emirates.
• Jan 2018. Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands
• Feb 2018. New York University Abu Dhabi, The United Arab Emirates.
• Apr-May 2018. National Institute of Science Education and Research, Bhubaneswar, India.
• Jun 2018. New York University Abu Dhabi, The United Arab Emirates.
• Apr 2019. Université Libre de Bruxelles, Belgium.
• Jun 2019. University of Zagreb, Croatia.
• Jul 2019. Université Libre de Bruxelles, Belgium.
• Nov 2019. Université Libre de Bruxelles, Belgium.
• Jul 2020. Mathematical Institute, Czech Academy of Sciences, Czechia.
• Nov 2021. University of Zagreb, Croatia.
• May 2022. University of Zagreb, Croatia.

### Visitors

• 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.
• Jul 2019. R. Ó Buachalla (Université Libre de Bruxelles) and K. R. Strung (Radboud Universiteit) at University of Zagreb.
• Aug 2019. S. Bouarroudj (NYU Abu Dhabi) at University of Zagreb.