C^0-closedness of the set of symplectomorphisms, spherical symplectic nonsqueezing, and holomorphic maps]]>

Symplectic geometry originated from classical mechanics, where the canonical symplectic form on phase space appears in Hamilton's equation. A (smooth) diffeomorphism on a symplectic manifold is called a symplectomorphism iff it preserves the symplectic form. This happens iff the diffeomorphism solves a certain inhomogeneous quadratic first order system of PDE's. In classical mechanics symplectomorphisms play the role of canonical transformations.

A famous result by Eliashberg and Gromov states that the set of symplectomorphisms is $C^0$-closed in the set of all diffeomorphisms. This is remarkable, since in general, the $C^0$-limit of a sequence of solutions of a first order system of PDE's need not solve the system. A well-known proof of the Eliashberg-Gromov theorem is based on Gromov's symplectic nonsqueezing theorem for balls.

In my talk I will sketch this proof. Furthermore, I will present a symplectic nonsqueezing result for spheres that sharpens Gromov's theorem. The proof of this result is based on the existence of a holomorphic map from the (real) two-dimensional unit disk to a certain symplectic manifold, satisfying some Lagrangian boundary condition. Such a map solves the Cauchy-Riemann equation for a certain almost complex structure. ]]>

Graded Rings and Birational Geometry]]>

The main purpose of the talk is to give a short introduction to the theory and describe some of its applications.

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For further information about the seminar, please visit this webpage.

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Algebraic torus actions]]>

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For further information about the seminar, please visit this webpage.

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For further information about the seminar, please visit this webpage.

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Leonhard Euler's methods of celestial mechanics (start: 15:15) ]]>

Further details can be found on the website of the Department of Physics.

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For further information about the seminar, please visit this webpage.

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For further information about the seminar, please visit this webpage.

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For further information about the seminar, please visit this webpage.

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