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Universität Augsburg
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Universität Augsburg
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Oliver Fabert
Amsterdam
spricht am
Montag, 28. November 2016
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| For complex projective spaces a version of the Arnold conjecture states that the number of fixed points of every Hamiltonian flow with Hofer norm less than one is greater than the complex dimension. In my talk I will discuss how this result generalizes to the projectivization of the Hilbert space of complex-valued square-integrable functions on the circle. While there exist smooth time-periodic Hamiltonians with Hofer norm less than one without any fixed points, I will show why the corresponding nonlinear Schrödinger equation (obtained by adding the Laplacian term) indeed has infinitely many time-periodic solutions. In order to prove the existence of the relevant holomorphic curves from Floer theory in infinite dimensions, I employ the following bizarre fact from nonstandard model theory: Every infinite-dimensional symplectic Hilbert space is contained in a symplectic vector space which behaves as if it were finite-dimensional. |
| Hierzu ergeht herzliche Einladung. |
| Kai Cieliebak |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).