Today seminar reminder

[Boris Dubrovin]

Dear All,

This is a gentle reminder about the seminar by

Dr. V.Shevchishin (University of Warmia and Mazury in Olsztyn, Poland)

who will give a talk on

Strong Moser theorem for Kähler symplectic forms on K3-surfaces

on Wednesday, August 9 at 14:30 - 16:00 in room 136 of SISSA Main Building

Abstract: A classical theorem due to Moser (called Moser's trick)
states that a family of symplectic forms \omega_t on a compact
manifold X with a constant cohomology class [\omega_t] is obtained by
an isotopy: There exists an isotopy F:X -> X such that
\omega_1 =F_*(\omega_0).
   Dusa McDuff proved the following generalisation of this theorem
("strong Moser theorem"):  If X is a rational or ruled 4-manifold,
and \omega_t is a family of symplectic forms on X, such that
[\omega_0]=[\omega_1] (equality of cohomology classes  only for
the  endpoints  of the family), then the forms \omega_0 and \omega_1
are isotopic: There exists an isotopy F:X -> X such that
\omega_1 =F_*(\omega_0).
   Also McDuff found a counterexample which shows that the strong
Moser theorem does not hold for general symplectic manifolds.

   In my talk I give a proof of the strong Moser theorem for the case
when \omega_t is a family of Kähler symplectic forms on a K3-surface X.
The Kählerness means that every \omega_t is a Kähler form for some
complex structure J_t on X. The proof exploits the Kähler and
Calabi-Yau geometries of K3-surfaces.
 I also explains the meaning of this theorem for the action of
the diffeomorphism group Diff(X) of a K3-surface X on the spaces
of symplectic and Kähler forms.

Everybody is welcome.

Prof. B. Dubrovin
Dept. of Mathematics
SISSA, Trieste, Italy
http://people.sissa.it/~dubrovin/ <http://people.sissa.it/~dubrovin/>