Course by N. A. Tyurin "Introduction to lagrangian geometry of symplectic manifolds" February 13–June 6, 2023, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
Symplectic geometry was built up under classical mechanics. Indeed, the phase space is the total space of the cotangent bundle to the configuration space, while any cotangent bundle always admits canonical symplectic structure. Another example class - of compact symplectic manifolds - comes from the considerations of complex submanifolds of complex projective spaces. These submanifolds are the central objects of algebraic geometry; at the same time they could be studied from the point of view of symplectic geometry. The main topic of the present lecture course is the properties of lagrangian submanifolds, related to the classification problem of lagrangian submanifolds. This subject appears in the case of integrable classical mechanical systems: the classical Liouville theorem says that the common level set for first integrals of a completely integrable system is a lagrangian submanifold (in the compact case - lagrangian torus).
We discuss examples of lagrangian submanifolds, present the theory of local deformation of these submanifolds and introduce certain invariants of these submanifolds.
The course is intended for the students with primary knowledge of differential geometry. Since the course itself is short we will be focused mostly on geometric interpretation while omitting some particular details of the proofs.
Lecturer
Tyurin Nikolai Andreevich
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. 075-15-2022-265).
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center |
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Course by N. A. Tyurin "Introduction to lagrangian geometry of symplectic manifolds", February 13–June 6, 2023 |
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June 6, 2023 (Tue) |
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Ëåêöèÿ 10. Ââåäåíèå â ëàãðàíæåâó ãåîìåòðèþ ñèìïëåêòè÷åñêèõ ìíîãîîáðàçèé N. A. Tyurin June 6, 2023 13:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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April 17, 2023 (Mon) |
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Lecture 9. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin April 17, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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April 3, 2023 (Mon) |
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Lecture 8. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin April 3, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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March 27, 2023 (Mon) |
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Lecture 7. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin March 27, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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March 20, 2023 (Mon) |
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Lecture 6. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin March 20, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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March 13, 2023 (Mon) |
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Lecture 5. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin March 13, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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March 6, 2023 (Mon) |
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Lecture 4. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin March 6, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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February 27, 2023 (Mon) |
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Lecture 3. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin February 27, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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February 20, 2023 (Mon) |
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Lecture 2. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin February 20, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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February 13, 2023 (Mon) |
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Lecture 1. Introduction to lagrangian geometry of symplectic manifolds N. A. Tyurin February 13, 2023 18:00, Steklov Mathematical Institute, Room 313 (8 Gubkina) + online
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