The displaced disks problem via symplectic topology

We prove that a $C^0$--small area preserving homeomorphism of a closed surface with vanishing mass flow can not displace a topological disk of large area. This resolves the displaced disks problem posed by F. B\'eguin, S. Crovisier, and F. Le Roux.Comment: 3 page

A note on C^0 rigidity of Hamiltonian isotopies

We show that a symplectic isotopy that is a $C^0$ limit of Hamiltonian isotopies is itself Hamiltonian, if the corresponding sequence of generating Hamiltonians converge in $L^{(1, \infty)}$ topology.Comment: 7 pages, to appear in Journal of Symplectic Geometr

Spectral killers and Poisson bracket invariants

We find optimal upper bounds for spectral invariants of a Hamiltonian whose support is contained in a union of mutually disjoint displaceable balls. This gives a partial answer to a question posed by Leonid Polterovich in connection with his recent work on Poisson bracket invariants of coverings.Comment: 16 pages, 2 figures. V2: to appear in Journal of Modern Dynamic

A Macro Policy for Poverty Eradication through Structural Change

Bangladesh, cooperatives, institutions, land, micro-credit, women