Professor Yuli B. Rudyak, University
of Florida, Gainesville

Let $(M^{2n}, \omega)$ be a closed symplectic manifold,
and let f: M --> M be a symplectomorphism, i.e. a diffeomorphism with $f^*(\omega)=\omega$.

In mid of 1960-th Arnold conjectured that the number
of fixed points of a so-called Hamiltonian symplectomorphism is at least
the minimal number of

critical points of a smooth function on $M$. We prove
that the conjecture holds for so-called symplectically aspherical manifolds,
i.e. for manifolds $(M^{2n}, \omega)$

such that the cohomology class $[\omega]$ vanishes on
$\pi_2(M)$.

No preliminary special knowledge is required to understand
the talk, all the necessary concepts will be defined. It is expected
that any graduate student

will be able to understand the talk.