Dmitrii Shirokov

Associate Professor: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.

Continuing education / Professional retraining / Internships / Study abroad experience

Scientific visits:

University College London (London, UK), April - May 2018;
Chinese Academy of Sciences, Academy of Mathematics and Systems Science (Beijing, China), April - May 2019.

Participated with talks and lectures at international conferences / symposia / summer schools / scientific seminars in Russia, Azerbaijan, Belgium, Brazil, Bulgaria, Chile, China, Estonia, France, Germany, India, Morocco, Romania, UK (see file with CV).

Professional Interests

mathematical physics field theory linear algebra Clifford algebra

I am always looking to supervise motivated students for Term papers, Thesis papers, Postgradute Study. Please write in advance to discuss the topic of your research.

Awards and Accomplishments

Best Teacher – 2019, 2018, 2017, 2016

Young Faculty Support Program (Group of Young Academic Professionals)
Category "Future Professoriate" (2018-2019)
Category "New Lecturers under 30" (2016-2017)

Courses (2019/2020)

Algebra and Geometry (Bachelor’s programme; Faculty of Business and Management; 1 year, 1, 2 module)Rus
Foundations of the Theory of Clifford Algebras (Mago-Lego; 3 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
Past Courses

Courses (2018/2019)

Algebra and Geometry (Bachelor’s programme; Faculty of Business and Management; 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

Courses (2017/2018)

Algebra and Geometry (Bachelor’s programme; Faculty of Business and Management; 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

Courses (2016/2017)

Algebra and Geometry (Bachelor’s programme; Faculty of Business and Management; 1 year, 1, 2 module)Rus
Linear Algebra (Bachelor’s programme; Faculty of Economic Sciences; 1 year, 1, 2 module)Rus

Courses (2015/2016)

Algebra and Geometry (Bachelor’s programme; Faculty of Business and Management; 1 year, 1-3 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

Grants

Head of projects:

grant 18-71-00010 of Russian Science Foundation "Algebraic and geometric methods in the theory of nonlinear equations of mathematical physics", 2018-2019,
grant 17-01-0009 of the Academic Fund Program at the National Research University Higher School of Economics (HSE) "Lie groups and Lie algebras in Clifford algebras", 2017-2018,
grant 16-31-00347 of Russian Foundation for Basic Research "Algebraic and geometric methods in field theory'', 2016-2017.

Performer of projects:

grant 14-11-00687 of Russian Science Foundation, 2014-2016,
grant NSh-2928.2012.1 of the President of RF for the Leading Scientific Schools, 2012-2013,
grant 8215 of Ministry of Education and Science of the Russian Federation, 2012-2013.

Editorial board membership

2019: Guest Editor, Advances in Applied Clifford Algebras.

Publications

2020¹

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 (in press)

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., Марчук Н. Г. Введение в теорию алгебр Клиффорда. М. : ФАЗИС, 2012.
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 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 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

2019
International 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
2018
Operators, 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
2017
International 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
2016
Alterman 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
2014
International 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
2012
The 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
2011
8th 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
2010
The Second International Conference on Mathematical Physics and Its Applications (Самара). Presentation: Structure of Euclidean and unitary space on hypercomplex number systems
2008
Ломоносовские чтения (Москва). Presentation: Method of quaternion typification of Clifford algebra elements

Employment history

2015 - present: National Research University Higher School of Economics, Faculty of Economic Sciences, Department of Mathematics, Moscow, Senior Lecturer (2015-2016), Associate Professor (2016 - present). Lecturer and seminarist of course "Algebra and geometry" (Faculty of Business and Management), seminarist of courses "Mathematical analysis-2", "Linear algebra and geometry" (Faculty of Computer Science), "Linear algebra" (Faculty of Economic Sciences);

2014 - present: Kharkevich Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, M.S.Pinsker Laboratory 1, Senior Researcher;

2014 - 2016: Bauman Moscow State Technical University, Faculty of Fundamental Sciences, Department of Higher Mathematics, Moscow, Associate Professor. Lectuter and seminarist of courses "Analytic geometry", "Mathematical analysis", "Integrals and differential equations", seminarist of courses "Linear algebra and multivariable functions", "Theory of probability and mathematical statistics", "Theory of functions of a complex variable and operational calculus";

2011, 2014: Lecturer of special courses in Research and Education Center of Steklov Mathematical Institute of Russian Academy of Sciences ("Clifford algebra and spinors" (lectures), "Clifford algebras and field theory equations");

2017: Lecturer of course "Clifford algebras and their applications to Lie groups and spinors" at the International Summer School "Hypercomplex numbers, Lie groups, and Applications" (lectures).

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