Dmitrii Shirokov
- Associate Professor, Senior Research Fellow:Faculty of Economic Sciences / Department of Mathematics
- Dmitrii Shirokov has been at HSE University since 2015.
Education and Degrees
- 2013
Candidate of Sciences* (PhD) in Mathematical physics, Steklov Mathematical Institute of Russian Academy of Sciences
- 2009
Degree
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
Continuing education / Professional retraining / Internships / Study abroad experience
Scientific visits:
- University College London (London, UK), April 1 – May 15, 2018;
- Chinese Academy of Sciences, Academy of Mathematics and Systems Science (Beijing, China), April 9 – May 23, 2019.
Participated with talks and lectures at international conferences, symposia, summer schools, and scientific seminars: in Russia, Azerbaijan, Belgium, Brazil, Bulgaria, Czech Republic, Chile, China, Estonia, France, Germany, India, Morocco, Romania, Switzerland, UK (see file with CV).

Young Faculty Support Program (Group of Young Academic Professionals)
Category "Future Professoriate" (2018-2019)
Category "New Lecturers under 30" (2016-2017)
Courses (2022/2023)
- Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 1, 2 module)Rus
- Linear Algebra (Bachelor’s programme; Graduate School of Business; 1 year, 1, 2 module)Rus
- Past Courses
Courses (2021/2022)
- Foundations of the Theory of Clifford Algebras (Mago-Lego; 3 module)Rus
- Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 1, 2 module)Rus
- Linear Algebra (Bachelor’s programme; Graduate School of Business; 1 year, 1, 2 module)Rus
Courses (2020/2021)
- Foundations of the theory of Clifford algebras and spinors (Optional course; 1, 2 module)Rus
- Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 1, 2 module)Rus
- Linear Algebra (Bachelor’s programme; Graduate School of Business; 1 year, 1-3 module)Rus
Courses (2019/2020)
- Algebra and Geometry (Bachelor’s programme; Graduate School of Business; 1 year, 1, 2 module)Rus
- Foundations of the Theory of Clifford Algebras (Mago-Lego; 3, 4 module)Rus
- Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 1, 2 module)Rus
Courses (2018/2019)
- Algebra and Geometry (Bachelor’s programme; Graduate School of Business; 1 year, 1, 2 module)Rus
- Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 1, 2 module)Rus
Courses (2017/2018)
- Algebra and Geometry (Bachelor’s programme; Graduate School of Business; 1 year, 1, 2 module)Rus
Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; field of study "38.03.01. Экономика", field of study "38.03.01. Экономика"; 1 year, 1, 2 module)Rus
Editorial board membership
2022: Member of the Editorial Board (Review Editor), Frontiers in Physics.
2021: Member of the Editorial Board (Associate Editor), Journal of Geometry and Symmetry in Physics.
2019: Guest Editor, Advances in Applied Clifford Algebras.
Grants
Head of the projects:
- grant 22-00-001 "Clifford algebras and applications'" (Research and Study Group) of the HSE Academic Fund Programme, 2022,
- grant 21-71-00043 of the Russian Science Foundation "Algebraic and geometric methods in theory of Yang–Mills equations", 2021 – 2023,
- grant MK-404.2020.1 "Some problems of the theory of Clifford algebras arising in mathematical physics" of the President of the Russian Federation, 2020 – 2021,
- grant 20-01-003 "Computational problems in Clifford algebra theory" of the Academic Fund Program at the HSE University, 2020 – 2021,
- grant 20-11-00009 of the Russian Foundation for Basic Research for publishing the book "Theory of Clifford algebras and spinors", 2020,
- grant 18-71-00010 "Algebraic and geometric methods in the theory of nonlinear equations of mathematical physics" of the Russian Science Foundation, 2018 – 2020,
- grant 17-01-0009 "Lie groups and Lie algebras in Clifford algebras" of the Academic Fund Program at the HSE University, 2017 – 2018,
- grant 16-31-00347 "Algebraic and geometric methods in field theory" of the Russian Foundation for Basic Research, 2016 – 2017.
Scientific consultant of the projects:
- initiative collective research project of HSE students "Clifford algebras: computational problems and applications", 2021.
Performer of the projects:
- grant 14-11-00687 of the Russian Science Foundation, 2014 – 2016,
- grant 11-01-00828-a of the Russian Foundation for Basic Research, 2011 – 2013,
- grant NSh-2928.2012.1 of the President of RF for the Leading Scientific Schools, 2012 – 2013,
- grant 8215 of the Ministry of Education and Science of the Russian Federation, 2012 – 2013.
20223
- Article Kamron Abdulkhaev, Shirokov D. Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras // Advances in Applied Clifford Algebras. 2022. Vol. 32. No. 5. Article 57. doi
- Article D. S. Shirokov. Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations // Computational Mathematics and Mathematical Physics. 2022. Vol. 62. No. 6. P. 1007-1019. doi
- Article Ekaterina Filimoshina, Dmitry Shirokov. On generalization of Lipschitz groups and spin groups // Mathematical Methods in the Applied Sciences. 2022. P. 1-26. doi
20217
- Chapter Shirokov D. A note on subspaces of fixed grades in Clifford algebras, in: AIP Conference Proceedings Vol. 2328: ICMM-2020. AIP Publishing LLC, 2021. Ch. 060001. P. 060001-1-060001-4. doi
- Article Shirokov D. A note on the hyperbolic singular value decomposition without hyperexchange matrices // Journal of Computational and Applied Mathematics. 2021. Vol. 391. Article 113450. doi
- Article Shirokov D. Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension // Advances in Applied Clifford Algebras. 2021. Vol. 31. P. 1-19. doi
- Article Shirokov D. On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension // Computational and Applied Mathematics. 2021. Vol. 40. P. 1-29. doi
- Chapter Abdulkhaev K., Shirokov D. On explicit formulas for characteristic polynomial coefficients in geometric algebras, in: Advances in Computer Graphics: 38th Computer Graphics International Conference, CGI 2021, Virtual Event, September 6–10, 2021, Proceedings. Springer, 2021. P. 670-681. doi
- Article Shirokov D. On inner automorphisms preserving fixed subspaces of Clifford algebras // Advances in Applied Clifford Algebras. 2021. Vol. 31. Article 30. doi
- Chapter Shirokov D. On solutions of the Yang-Mills equations in the algebra of h-forms, in: Journal of Physics: Conference Series, Volume 2099 Vol. 2099: International Conference «Marchuk Scientific Readings 2021» (MSR-2021) 4-8 October 2021, Novosibirsk, Russian Federation. IOP Publishing, 2021. Ch. 012015. P. 1-7. doi
20205
- Article Marchuk N., Shirokov D. Local Generalization of Pauli's Theorem // Azerbaijan Journal of Mathematics. 2020. Vol. 10. No. 1. P. 38-56.
- Chapter Shirokov D. On Basis-Free Solution to Sylvester Equation in Geometric Algebra, in: Advances in Computer Graphics. CGI 2020. Springer, 2020. P. 541-548. doi
- Article Marchuk N., Shirokov D. On Some Equations Modeling the Yang–Mills Equations // Physics of Particles and Nuclei. 2020. Vol. 51. No. 4. P. 589-594. doi
- Article Shirokov D. On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space R^n // Journal of Nonlinear Mathematical Physics. 2020. Vol. 27. No. 2. P. 199-218. doi
20191
20183
- Article Shirokov D. Classification of Lie algebras of specific type in complexified Clifford algebras // Linear and Multilinear Algebra. 2018. Vol. 66. No. 9. P. 1870-1887. doi
- Chapter Shirokov D. Clifford algebras and their applications to Lie groups and spinors, in: Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization Vol. 19. Sofia : Avangard Prima, 2018. Ch. 1. P. 11-53. doi
- Article Shirokov D. Covariantly constant solutions of the Yang-Mills equations // Advances in Applied Clifford Algebras. 2018. Vol. 28. No. 3. P. 1-16. doi
20171
20164
- Article Shirokov D., Marchuk N. Constant solutions of Yang-Mills equations and generalized Proca equations // Journal of Geometry and Symmetry in Physics. 2016. Vol. 42. P. 53-72. doi
- Article Shirokov D., Marchuk N. General solutions of one class of field equations // Reports on Mathematical Physics. 2016. Vol. 78. No. 3. P. 305-326. doi
- Preprint Shirokov D. Method of generalized Reynolds operators and Pauli's theorem in Clifford algebras / Cornell University. Series math "arxiv.org". 2016.
- Article Shirokov D. On Some Lie Groups Containing Spin Group in Clifford Algebra // Journal of Geometry and Symmetry in Physics. 2016. Vol. 42. P. 73-94. doi
20153
- Article Shirokov D. Calculations of elements of spin groups using generalized Pauli's theorem // Advances in Applied Clifford Algebras. 2015. Vol. 25. No. 1. P. 227-244.
- Article Shirokov D. Symplectic, orthogonal and linear Lie groups in Clifford algebra // Advances in Applied Clifford Algebras. 2015. Vol. 25. No. 3. P. 707-718.
- Article Широков Д. С. Свертки по рангам и кватернионным типам в алгебрах Клиффорда // Вестник Самарского государственного технического университета. Серия: Физико-математические науки. 2015. Т. 19. № 1. С. 117-135.
20133
- Article Shirokov D. Pauli theorem in the description of n-dimensional spinors in the Clifford algebra formalism / Пер. с рус. // Theoretical and Mathematical Physics. 2013. Vol. 175. No. 1. P. 454-474.
- Article Широков Д. С. Использование обобщëнной теоремы Паули для нечëтных элементов алгебры Клиффорда для анализа связей между спинорными и ортогональными группами произвольных размерностей // Вестник Самарского государственного технического университета. Серия: Физико-математические науки. 2013. Т. 30. № 1. С. 279-287.
- Article Широков Д. С. Обобщение теоремы Паули на случай алгебр Клиффорда // Наноструктуры. Математическая физика и моделирование. 2013. Т. 9. № 1. С. 93-104.
20124
- Article Shirokov D. Development of the method of quaternion typification of Clifford algebra elements // Advances in Applied Clifford Algebras. 2012. Vol. 22. No. 2. P. 483-497.
- Article Shirokov D. Quaternion typification of Clifford algebra elements // Advances in Applied Clifford Algebras. 2012. Vol. 22. No. 1. P. 243-256.
- Book Широков Д. С. Лекции по алгебрам Клиффорда и спинорам Вып. 19. М. : Математический институт им. В. А. Стеклова РАН, 2012.
20113
- Article Shirokov D. On some relations between spinor and orthogonal groups // P-Adic Numbers, Ultrametric Analysis, and Applications. 2011. Vol. 3. No. 3. P. 212-218.
- Article Широков Д. С. Обобщение теоремы Паули на случай алгебр Клиффорда // Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2011. Т. 440. № 5. С. 1-4.
- Article Широков Д. С. Теорема о норме элементов спинорных групп // Вестник Самарского государственного технического университета. Серия: Физико-математические науки. 2011. Т. 22. № 1. С. 165-171.
20101
20091
20081
Conferences
- 2022Computer Graphics International 2022 (Женева). Presentation: On Noncommutative Vieta Theorem in Geometric Algebras
- International Conference of Advanced Computational Applications of Geometric Algebra (Денвер). Presentation: On some Lie groups in degenerate geometric algebras,
- 2021Математическая физика, динамические системы и бесконечномерный анализ 2021 (Долгопрудный). Presentation: On constant solutions of the Yang--Mills--Dirac equations
- Computer Graphics International 2021 (Женева). Presentation: On explicit formulas for characteristic polynomial coefficients in geometric algebras
- The 8th Conference on Applied Geometric Algebras in Computer Science and Engineering (Брно). Presentation: On Lie groups defining inner automorphisms that leave invariant fundamental subspaces of geometric algebra
- International Conference ''Marchuk Scientific Readings 2021'' (Новосибирск). Presentation: Hyperbolic SVD for obtaining solutions of SU(2) Yang--Mills equations
- 20209th International Conference on Mathematical Modeling (Якутск). Presentation: On determinant and inverses in Clifford algebras
- The 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12) (Хэфэй). Presentation: On determinant, other characteristic polynomial coefficients, and inverses in Clifford algebras
- Computer Graphics International (CGI) 2020 (Женева). Presentation: On basis-free solution to Sylvester equation in geometric algebra
- International Conference on Mathematical Physics in Memory of Academic V. S. Vladimirov (Москва). Presentation: On some equations modeling the Yang-Mills equations
- 2019International Conference on Mathematical Methods in Physics (Марракеш). Presentation: Method of averaging in Clifford algebras and applications
- International Symposium on Wen-Tsun Wu's Academic Thought and Mathematics Mechanization (Пекин). Presentation: SVD and hyperbolic SVD for obtaining solutions of SU(2) Yang-Mills equations
- The 2nd JNMP Conference on Nonlinear Mathematical Physics (Сантьяго). Presentation: On constant solutions of SU(2) Yang-Mills equations
- International Conference "Mathematical Physics, Dynamical Systems and Infinite-Dimensional Analysis" (Долгопрудный). Presentation: On constant solutions of SU(2) Yang-Mills equations
- 4th Alterman Conference on Computational and Geometric Algebra-cum-Workshop on Kahler Calculus (Манипал). Presentation: Method of averaging in Clifford algebras and applications
- IX-th International Conference "Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives" (SCT-19) in honor of Vladimir Zakharov's 80th birthday (Ярославль). Presentation: Classiffcation of all constant solutions of SU(2) Yang-Mills equations with arbitrary current
- International Bogolyubov Conference "Problems of theoretical and mathematical physics" (Москва - Дубна). Presentation: On constant solutions of SU(2) Yang-Mills equations
- 2018Operators, Functions, and Systems of Mathematical Physics Conference (Баку). Presentation: On some solutions of Yang-Mills equations with SU(2) gauge symmetry
- The 7th Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE) (Кампинас). Presentation: Calculation of elements of spin groups using method of averaging in Clifford’s geometric algebra
- International conference ``Modern Mathematical Physics. Vladimirov-95'' (Москва). Presentation: On some solutions of Yang-Mills equations with SU(2) gauge symmetry
- 2017International Summer School “Hypercomplex Numbers, Lie Groups, and Applications” (Варна). Presentation: Introduction to the theory of Clifford algebras (5 лекций)
- International Conference on Mathematical Modeling (Якутск). Presentation: Local generalized Pauli’s theorem and one field equation
- The 11th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA11) (Гент). Presentation: Yang-Mills equations and Clifford algebras
- 2016Alterman Conference on Geometric Algebra and Summer School on Kahler Calculus (Брашов). Presentation: On some Lie groups containing Spin groups in Clifford algebra
- VI Russian-Armenian Conference on Mathematical Analysis, Mathematical Physics and Analytical Mechanics (Ростов-на-Дону). Presentation: Covariantly constant solutions of the Yang-Mills equations
- New trends in Mathematical and Theoretical Physics (Москва). Presentation: Covariantly constant solutions of the Yang-Mills equations
- The 2nd French-Russian Conference ``Random Geometry and Physics'' (Париж). Presentation: On connection between two sets of higher-dimensional gamma matrices and a primitive field equation
- 2014International Scientific Conference PHYSICAL AND MATHEMATICAL PROBLEMS OF ADVANCED TECHNOLOGY DEVELOPMENT (PhysMathTech-2014) (Москва). Presentation: New class of gauge invariant solutions of Yang-Mills equations
- The Fourth International Conference on Mathematical Physics and Its Applications (Самара). Presentation: Method of contractions in Clifford algebras with applications to the field theory equations
- The 10th International Conference on Clifford Algebras and their Applications (ICCA10) (Тарту). Presentation: The method of contractions in Clifford algebras
- International conference “Representations, Dynamics, Combinatorics: in the Limit and Beyond” in honor of Anatoly Vershik’s 80th birthday (Санкт-Петербург). Presentation: Vershik’s combinatorial approach and phase transitions in the classical thermodynamics
- 2012The Third International Conference on Mathematical Physics and Its Applications (Самара). Presentation: Generalization of Pauli’s theorem on the case of Clifford algebras
- Взаимодействие математики и физики: новые перспективы (Москва). Presentation: Generalization of Pauli’s theorem on the case of Clifford algebra
- The 5th conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE), (La Rochelle). Presentation: Calculation of elements of spin groups using Generalized Pauli’s theorem
- 20118th International ISAAC Congress (Москва). Presentation: Pauli’s fundamental theorem for Clifford algebras
- The 9th International Conference on Clifford Algebras and their Applications (ICCA9) (Weimar). Presentation: Quaternion types of Clifford algebra elements, basis-free approach
- 2010The Second International Conference on Mathematical Physics and Its Applications (Самара). Presentation: Structure of Euclidean and unitary space on hypercomplex number systems
- 2008Ломоносовские чтения (Москва). Presentation: Method of quaternion typification of Clifford algebra elements
Employment history
2015 – present: HSE University, Faculty of Economic Sciences, Department of Mathematics, Moscow, Senior Lecturer (2015 – 2016), Associate Professor (2016 – present) and Senior Research Fellow (2021 - present);
2014 – present: Kharkevich Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Researcher in Laboratory 7 (2014 – 2015), Senior Researcher in M.S.Pinsker Laboratory 1 (2015 – present);
2014 – 2016: Bauman Moscow State Technical University, Faculty of Fundamental Sciences, Department of Higher Mathematics, Moscow, Assistant (2014), Associate Professor (2014 – 2016);