Projects supported by grants from the Russian Science Foundation, the Russian Foundation for Basic Research, the President of the Russian Federation, and the HSE Academic Fund Programme

• D. S. Shirokov, “Development of the method of averaging in Clifford geometric algebras”, Mathematics, 11:16 (2023), 3607, 18 pp. (Q1)
• N. G. Marchuk, “A class of field equations for neutrinos with nonzero masses”, Theoret. and Math. Phys., 219:3 (2024), 897–912
• D. S. Shirokov, “On SVD and Polar Decomposition in Real and Complexified Clifford Algebras”, Advances in Applied Clifford Algebras, 34 (2024), 23, 20 pp.
• 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 Grade Automorphism in Ternary Clifford Algebras”, Hypercomplex Analysis and Its Applications. Trends in Mathematics (Aveiro, Portugal, March 18-22, 2024), eds. Ferreira, M., Faustino, N., Kähler, U., Vieira, N., Birkhäuser, Cham, 2025
• D. S. Shirokov, “On SU(3) in Ternary Clifford Algebra”, Advances in Computer Graphics. CGI 2024. Lecture Notes in Computer Science (Geneva, Switzerland, July 1–5, 2024), 15340, eds. Magnenat-Thalmann, N., Kim, J., Sheng, B., Deng, Z., Thalmann, D., Li, P., Springer, Cham, 2025, 336–348
• E. R. Filimoshina, D. S. Shirokov, “Generalized Degenerate Clifford and Lipschitz Groups”, Advances in Computer Graphics. CGI 2024. Lecture Notes in Computer Science (Geneva, Switzerland, July 1–5, 2024), 15340, eds. Magnenat-Thalmann, N., Kim, J., Sheng, B., Deng, Z., Thalmann, D., Li, P., Springer, Cham, 2025, 364–376
• S. V. Rumyantseva, D. S. Shirokov, “On Multidimensional Dirac-Hestenes Equation in Geometric Algebra”, Advances in Computer Graphics. CGI 2024. Lecture Notes in Computer Science (Geneva, Switzerland, July 1–5, 2024), 15340, eds. Magnenat-Thalmann, N., Kim, J., Sheng, B., Deng, Z., Thalmann, D., Li, P., Springer, Cham, 2025, 323–335
• N. G. Marchuk, “Classification of Field Equations for Weyl and Elko Spinors”, Differential Equations, 61, 338–345 (2025) (Q2 rus)
• N. G. Marchuk, “Conservative Equations in Field Theory: Conservation and Symmetry Laws”, Differential Equations, 61, 872–892 (2025) (Q2 rus)

• 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.
• S. V. Rumyantseva, D. S. Shirokov, “Introducing Multidimensional Dirac-Hestenes Equation”, Advances in Applied Clifford Algebras, 35 (2025), 24, 20 pp.
• E. R. Filimoshina, D. S. Shirokov, “Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras”, Advances in Applied Clifford Algebras, 35 (2025), 29, 35 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
• 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.
• D. S. Shirokov, “Noncommutative Vieta theorem in Clifford geometric algebras”, Mathematical Methods in the Applied Sciences, 47:14 (2024), 11305–11320
• 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.

• 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
• D. S. Shirokov, “Classification of all constant solutions of SU(2) Yang–Mills equations with arbitrary current in pseudo-Euclidean space R^{p,q}”, Modern Physics Letters A, 38:20n21 (2023), 2350096 , 54 pp.
• 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 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 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 inner automorphisms preserving fixed subspaces of Clifford algebras”, Advances in Applied Clifford Algebras, 31 (2021), 30, 23 pp.
• 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.
• 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, “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
• 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
• N. G. Marchuk, D. S. Shirokov, Theory of Clifford Algebras and Spinors [in Russian]. KRASAND (URSS), 2020, 560 pp.

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 computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension”, Computational and Applied Mathematics, 40 (2021), 173, 29 pp. (Q1)
• D. S. Shirokov, “A note on the hyperbolic singular value decomposition without hyperexchange matrices”, Journal of Computational and Applied Mathematics, 391 (2021), 113450 (Q1)

N. G. Marchuk, D. S. Shirokov, Theory of Clifford Algebras and Spinors [in Russian]. KRASAND (URSS), 2020, 560 pp.

• 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.
• N. G. Marchuk, D. S. Shirokov, “Local Generalization of Pauli`s Theorem”, Azerb. J. Math., 10:1 (2020), 38–56
• D. S. Shirokov, “On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space R^n”, Journal of Nonlinear Mathematical Physics, 27:2 (2020), 199–218
• N. G. Marchuk, D. S. Shirokov, “On some equations modeling the Yang-Mills equations”, Physics of Particles and Nuclei, 51:4 (2020), 589–594
• N. G. Marchuk, D. S. Shirokov, Theory of Clifford Algebras and Spinors [in Russian]. KRASAND (URSS), 2020, 560 pp.

D. S. Shirokov, “Classification of Lie algebras of specific type in complexified Clifford algebras”, Linear and Multilinear Algebra, 66:9 (2018), 1870–1887 (Q1)

• D. S. Shirokov, “On Some Lie Groups Containing Spin Group in Clifford Algebra”, Journal of Geometry and Symmetry in Physics, 42 (2016), 73–94
• 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
• D. S. Shirokov, “Covariantly constant solutions of the Yang-Mills equations”, Advances in Applied Clifford Algebras, 28 (2018), 53, 16 pp.
• 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