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
* Candidate of Sciences
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.
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
Article Shirokov D. Calculation of elements of spin groups using method of averaging in Clifford`s geometric algebra // Advances in Applied Clifford Algebras. 2019. Vol. 29. No. 50. P. 1-12. doi
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
Article Shirokov D. Method of averaging in Clifford algebras // Advances in Applied Clifford Algebras. 2017. Vol. 27. No. 1. P. 149-163. doi
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
Article Shirokov D. A classification of Lie algebras of pseudo-unitary groups in the techniques of Clifford algebras // Advances in Applied Clifford Algebras. 2010. Vol. 20. No. 2. P. 411-425.
20091
Article Широков Д. С. Классификация элементов алгебр Клиффорда по кватернионным типам // Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2009. Т. 427. № 6. С. 758-760.
20081
Article Shirokov D., Marchuk N. Unitary spaces on Clifford algebras // Advances in Applied Clifford Algebras. 2008. Vol. 18. No. 2. P. 237-254. doi
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);