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Курс Е. В. Щепина "Геометрия фракталов"
(September 17–December 24, 2025, Steklov Mathematical Institute, Room 530 (8 Gubkina))
We kindly ask all participants, including remote ones and those
watching recorded videos, to register at this link.
The special course is intended for a wide audience and is available to first-year students. It will present the main results of the lecturer on the theory of multidimensional Peano curves, including the solution of Arnold's problem on the Hölder mapping of a square onto a cube.
Program.
- Fractals and fractal curves.
- Hausdorff and asymptotic dimension and measure.
- Dimension-raising Hölder mappings.
- The theorems of stabilization of Hölder ratio.
- Arnold's problem of the Hölder mapping of a square onto a cube.
- Variations and hypervariations of curves and compacts.
- The Kakutani-Gomori problem about the «length of a square».
- Continuous-discrete duality.
- The digital plane.
- Computer applications of fractals.
 Lecturer
Shchepin Evgeny Vital'evich
Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, agreement no. 075-15-2025-303).
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
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December 3, 2025 (Wed) |
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| 1. |
Лекция 12. Геометрия фракталов
E. V. Shchepin
December 3, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 26, 2025 (Wed) |
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Лекция 11. Геометрия фракталов
E. V. Shchepin
November 26, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 19, 2025 (Wed) |
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Лекция 10. Геометрия фракталов
E. V. Shchepin
November 19, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 12, 2025 (Wed) |
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Лекция 9. Геометрия фракталов
E. V. Shchepin
November 12, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 5, 2025 (Wed) |
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Лекция 8. Геометрия фракталов
E. V. Shchepin
November 5, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 29, 2025 (Wed) |
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Лекция 7. Геометрия фракталов
E. V. Shchepin
October 29, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 22, 2025 (Wed) |
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Лекция 6. Геометрия фракталов
E. V. Shchepin
October 22, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 15, 2025 (Wed) |
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Лекция 5. Геометрия фракталов
E. V. Shchepin
October 15, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 8, 2025 (Wed) |
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Лекция 4. Геометрия фракталов
E. V. Shchepin
October 8, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 1, 2025 (Wed) |
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Лекция 3. Геометрия фракталов
E. V. Shchepin
October 1, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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September 24, 2025 (Wed) |
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Лекция 2. Геометрия фракталов
E. V. Shchepin
September 24, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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September 17, 2025 (Wed) |
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Лекция 1. Геометрия фракталов
E. V. Shchepin
September 17, 2025 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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