Abstract: In a recent paper, McDuff proves the connectedness of the symplectomorphism group of a resolution of a weighted projective space. Her argument is likely to adapt to some other orbifolds. As a stepping stone, we will explain the proof of the connectedness of Symp($CP^2$), a result originally proved by Gromov.

Abstract: We begin with the sub-Laplacian on the Heisenberg group. The twisted Laplacian is then introduced by taking the inverse Fourier transform of the sub-Laplacian with respect to the center of the Heisenberg group. After a recapitulation of the spectral theory of the twisted Laplacian in terms of the Wigner transform, the spectral theory and number theory of the twisted bi-Laplacian obtained by Gramchev, Pilipović, Rodino and me are reported. We end the talk with a glimpse into a connection of the twisted bi-Laplacian with the Riemann zeta-function.