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.