mathematical physics, field theory, Clifford algebras
Biography
Graduated from Lomonosov Moscow State University with high honors in 2009 (Faculty of mechanics and mathematics, Department of gas and wave dynamics). Post-graduate education in Steklov Mathematical Institute of Russian Academy of Sciences (Department of mathematical physics, supervisor: N. G. Marchuk). Ph.D. (Candidate Phys.-Math. Sci.), 2013, Speciality 01.01.03 Mathematical physics. D.S. (Doctor of Sciences), 2023, Speciality 1.1.2 Differential equations and mathematical physics.
Professor of HSE University (Department of Mathematics, Faculty of Economic Sciences, Moscow). Head of Laboratory for Geometric Algebra and Applications (laboratory website, HSE University, Moscow). Senior scientific researcher of Kharkevich Institute for Information Transmission Problems of Russian Academy of Sciences (Moscow).
Head of Research and study group ''Clifford algebra and applications'' (group website) and Organizer of scientific seminar (seminar website) at the HSE University. Head of Research working group ''Algebro-geometric methods in applied sciences'' (group website).
Best teacher at the HSE University (2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024).
Winner of the "Competition of the best Russian-language scientific and popular scientific works of HSE employees" in the scientific category Mathematics (2022, 2023).
Head of projects of RSF (18-71-00010, 21-71-00043, 23-71-10028), RFBR (16-31-00374, 20-11-0009), President of RF (MK-404.2020.1), HSE Academic Fund Programme (17-01-0009, 20-01-003, 22-00-001, 24-00-001).
More than 50 publications (including 3 books), 50 reports at international conferences. Lecturer of 3 courses at Steklov Mathematical Institute (2011, 2014, 2021).
D. S. Shirokov, “Clifford algebras and their applications to Lie groups and spinors”, Lectures, Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June 2 - 7, 2017), eds. Ivaïlo Mladenov and Akira Yoshioka, Avangard Prima, Sofia, Bulgaria, 2018, 11–53 , arXiv: 1709.06608
D. S. Shirokov, Lectures on Clifford algebras and spinors, Lekts. Kursy NOC, 19, Steklov Math. Inst., RAS, Moscow, 2012 , 180 pp.
N. G. Marchuk, D. S. Shirokov, Vvedenie v teoriyu algebr Klifforda, Fazis, Moskva, 2012 , 590 pp.
E. R. Filimoshina, D. S. Shirokov, “On generalization of Lipschitz groups and spin groups”, Mathematical Methods in the Applied Sciences, 47:3 (2024), 1375–1400 , arXiv: 2205.06045
E. R. Filimoshina, D. S. Shirokov, “On some Lie groups in degenerate geometric algebras”, Advanced Computational Applications of Geometric Algebra. ICACGA 2022. Lecture Notes in Computer Science (Denver, CO, USA, October 2-5, 2022), 13771, eds. Silva, D.W., Hitzer, E., Hildenbrand, D., Springer, Cham, 2024, 186–198
D. S. Shirokov, “On Singular Value Decomposition and Polar Decomposition in Geometric Algebras”, Advances in Computer Graphics. CGI 2023. Lecture Notes in Computer Science (Shanghai, August 28 – September 1, 2023), 14498, eds. Sheng, B., Bi, L., Kim, J., Magnenat-Thalmann, N., Thalmann, D., Springer, Cham, 2024, 391–401
D. S. Shirokov, “On SVD and Polar Decomposition in Real and Complexified Clifford Algebras”, Advances in Applied Clifford Algebras, 34 (2024), 23 , 20 pp., arXiv: 2404.11920
5.
E. R. Filimoshina, D. S. Shirokov, “A Note on Centralizers and Twisted Centralizers in Clifford Algebras”, Advances in Applied Clifford Algebras, 34 (2024), 50 , 22 pp., arXiv: 2404.15169
6.
D. S. Shirokov, “Noncommutative Vieta theorem in Clifford geometric algebras”, Mathematical Methods in the Applied Sciences, 47:14 (2024), 11305–11320 , arXiv: 2301.06848
S. V. Rumyantseva, D. S. Shirokov, “Introducing Multidimensional Dirac-Hestenes Equation”, 2024, 20 pp., arXiv: 2411.04214
2023
8.
D. S. Shirokov, On constant solutions of $SU(2)$ Yang–Mills–Dirac equations, 2023 , 19 pp., arXiv: 2207.12313
9.
D. S. Shirokov, “On Noncommutative Vieta Theorem in Geometric Algebras”, Empowering Novel Geometric Algebra for Graphics and Engineering. ENGAGE 2022. Lecture Notes in Computer Science, 13862, eds. Hitzer, E., Papagiannakis, G., Vasik, P., Springer, Cham, 2023, 28–37
E. R. Filimoshina, D. S. Shirokov, “On Some Lie Groups in Degenerate Clifford Geometric Algebras”, Advances in Applied Clifford Algebras, 33 (2023), 44 , 29 pp., arXiv: 2301.06842
D. S. Shirokov, “Development of the method of averaging in Clifford geometric algebras”, Mathematics, 11:16 (2023), 3607 , 18 pp., arXiv: 1409.8163
12.
D. S. Shirokov, “Classification of all constant solutions of $\,{\rm SU}(2)$ Yang–Mills equations with arbitrary current in pseudo-Euclidean space ${\mathbb R}^{p,q}$”, Modern Physics Letters A, 38:20n21 (2023), 2350096 , 54 pp., arXiv: 1912.04996
D. S. Shirokov, “Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations”, Computational Mathematics and Mathematical Physics, 62:6 (2022), 1007–1019
14.
K. S. Abdulkhaev, D. S. Shirokov, “Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras”, Advances in Applied Clifford Algebras, 32 (2022), 57 , 27 pp., arXiv: 2205.13449
D. S. Shirokov, “A note on the hyperbolic singular value decomposition without hyperexchange matrices”, Journal of Computational and Applied Mathematics, 391 (2021), 113450 , arXiv: 1812.02460
D. S. Shirokov, “A note on subspaces of fixed grades in Clifford algebras”, AIP Conference Proceedings, ISBN: 978-0-7354-4072-2 (Yakutsk, Russia, July 27 - August 1, ICMM-2020), 2328, AIP Publishing, 2021, 060001
18.
D. S. Shirokov, “On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension”, Computational and Applied Mathematics, 40 (2021), 173 , 29 pp., arXiv: 2005.04015
D. S. Shirokov, “Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension”, Advances in Applied Clifford Algebras, 31 (2021), 70 , 19 pp., arXiv: 2109.01816
K. S. Abdulkhaev, D. S. Shirokov, “On Explicit Formulas for Characteristic Polynomial Coefficients in Geometric Algebras”, Advances in Computer Graphics. CGI 2021. Lecture Notes in Computer Science, 13002, eds. N. Magnenat-Thalmann et al., Springer, Cham, 2021, 670–681
D. S. Shirokov, “On solutions of the Yang-Mills equations in the algebra of h-forms”, Journal of Physics: Conference Series (International Conference «Marchuk Scientific Readings 2021» (MSR-2021) 4-8 October 2021, Novosibirsk, Russian Federation), 2099, IOP Publishing, 2021, 012015
D. S. Shirokov, “On constant solutions of $\,{\rm SU}(2)$ Yang-Mills equations with arbitrary current in Euclidean space ${\mathbb R}^n$”, Journal of Nonlinear Mathematical Physics, 27:2 (2020), 199–218 , arXiv: 1804.04620
D. S. Shirokov, “On Basis-Free Solution to Sylvester Equation in Geometric Algebra”, Advances in Computer Graphics. CGI 2020. Lecture Notes in Computer Science, 12221, eds. Magnenat-Thalmann N. et al., Springer, Cham, 2020, 541–548
D. S. Shirokov, “Calculation of elements of spin groups using method of averaging in Clifford`s geometric algebra”, Advances in Applied Clifford Algebras, 29 (2019), 50 , 12 pp., arXiv: 1901.09405
D. S. Shirokov, “Classification of Lie algebras of specific type in complexified Clifford algebras”, Linear and Multilinear Algebra, 66:9 (2018), 1870–1887 , arXiv: 1704.03713
D. S. Shirokov, “Clifford algebras and their applications to Lie groups and spinors”, Lectures, Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June 2 - 7, 2017), eds. Ivaïlo Mladenov and Akira Yoshioka, Avangard Prima, Sofia, Bulgaria, 2018, 11–53 , arXiv: 1709.06608
D. S. Shirokov, “Covariantly constant solutions of the Yang-Mills equations”, Advances in Applied Clifford Algebras, 28 (2018), 53 , 16 pp., arXiv: 1709.07836
N. G. Marchuk, D. S. Shirokov, “Constant Solutions of Yang-Mills Equations and Generalized Proca Equations”, Journal of Geometry and Symmetry in Physics, 42 (2016), 53–72 , arXiv: 1611.03070
D. S. Shirokov, “On Some Lie Groups Containing Spin Group in Clifford Algebra”, Journal of Geometry and Symmetry in Physics, 42 (2016), 73–94 , arXiv: 1607.07363
D. S. Shirokov, “Calculation of elements of spin groups using generalized Pauli's theorem”, Advances in Applied Clifford Algebras, 25:1 (2015), 227–244 , arXiv: 1409.2449
D. S. Shirokov, “Contractions on ranks and quaternion types in Clifford algebras”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 19:1 (2015), 117–135
37.
D. S. Shirokov, “Symplectic, Orthogonal and Linear Lie Groups in Clifford Algebra”, Advances in Applied Clifford Algebras, 25:3 (2015), 707-718 , arXiv: 1409.2452
D. S. Shirokov, “Pauli theorem in the description of $n$-dimensional spinors in the Clifford algebra formalism”, Theoret. and Math. Phys., 175:1 (2013), 454–474
39.
D. S. Shirokov, “The use of the generalized Pauli's theorem for odd elements of Clifford algebra to analyze relations between spin and orthogonal groups of arbitrary dimensions”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(30) (2013), 279-287
40.
D. S. Shirokov, “Obobschenie teoremy Pauli na sluchai algebr Klifforda”, Shkola-seminar "Vzaimodeistvie matematiki i fiziki: novye perspektivy dlya studentov, aspirantov i molodykh issledovatelei (Moskva, Matematicheskii institut im. V.A.Steklova RAN, 22–30 avgusta 2012), Nanostruktury. Matematicheskaya fizika i modelirovanie, 9, no. 1, 2013, 93–104www.nano-journal.ru/images/8/8e/94_pdfsam_Nano15.pdf
2012
41.
D. S. Shirokov, “Quaternion typification of Clifford algebra elements”, Adv. Appl. Clifford Algebr., 22:1 (2012), 243–256 , arXiv: 0806.4299
D. S. Shirokov, “Development of the method of quaternion typification of Clifford algebra elements”, Adv. Appl. Clifford Algebr., 22:2 (2012), 483–497 , arXiv: 0903.3494
D. S. Shirokov, Lectures on Clifford algebras and spinors, Lekts. Kursy NOC, 19, Steklov Math. Inst., RAS, Moscow, 2012 , 180 pp.
44.
N. G. Marchuk, D. S. Shirokov, Vvedenie v teoriyu algebr Klifforda, Fazis, Moskva, 2012 , 590 pp.
45.
D. S. Shirokov, “Concepts of trace, determinant and inverse of Clifford algebra elements”, Progress in analysis. Proceedings of the 8th congress of the International Society for Analysis, its Applications, and Computation (ISAAC), Moscow, Russia, August 22–27, 2011. Volume 1., v. 1, eds. Burenkov, V. I. (ed.); Goldman, M. L. (ed.); Laneev, E. B. (ed.); Stepanov, V. D. (ed.), Moscow: Peoples’ Friendship University of Russia (ISBN 978-5-209-04582-3/hbk), 2012, 187-194 , 8 pp., arXiv: 1108.5447
46.
D. S. Shirokov, Nekotorye voprosy teorii algebr Klifforda, voznikayuschie v teorii polya, Diss. kand. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova Rossiiskoi akademii nauk, Moskva, 2012 , 151 pp.
47.
D. S. Shirokov, Nekotorye voprosy teorii algebr Klifforda, voznikayuschie v teorii polya, Avtoreferat diss. kand. fiz.-matem. nauk, Matematicheskii institut im. V.A. Steklova Rossiiskoi akademii nauk, Moskva, 2012 , 17 pp.
2011
48.
D. S. Shirokov, “On some relations between spinor and orthogonal groups”, p-Adic Numbers Ultrametric Anal. Appl., 3:3 (2011), 212–218
D. S. Shirokov, “Quaternion types of Clifford algebra elements, basis-free approach”, Proceedings of 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (Weimar, Germany, 15–20 July), Bauhaus-University Weimar, 2011, 9 pp. , arXiv: 1109.2322
50.
D. S. Shirokov, “Extension of Pauli's theorem to Clifford algebras”, Dokl. Math., 84:2 (2011), 699–701
51.
D. S. Shirokov, “Theorem on the norm of elements of spinor groups”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 165-171
2010
52.
D. S. Shirokov, “A classification of Lie algebras of pseudo-unitary groups in the techniques of Clifford algebras”, Adv. Appl. Clifford Algebr., 20:2 (2010), 411–425 , arXiv: 0705.3368
Classification of all constant solutions of SU(2) Yang-Mills equations D. S. Shirokov III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 11, 2023 16:10
2024
Contact us: