Professor Dr Paul Biran

Research Priorities: Symplectic geometry and topology, algebraic geometry, Lagrangian topology, Lagrangian submanifolds
Paul Biran is an Israeli mathematician. His work covers a broad range of mathematical topics, with a particular interest in symplectic geometry and topology, as well as algebraic geometry. Symplectic geometry is a branch of differential geometry with close links to theoretical physics.
In his dissertation Paul Biran managed to find a remarkable solution to the symplectic packing problem in four dimensions. He proved that a symplectic 4-manifold can be fully packed with balls of equal diameter provided that the number of balls is sufficiently large. His proof introduced original new techniques into symplectic topology: in particular the decomposition of symplectic manifolds. This provided the basis for, among other things, his discovery of the “Lagrangian barrier” phenomenon.
Paul Biran was also able to use symplectic techniques to obtain new results in algebraic geometry, thus providing new connections between symplectic and algebraic geometry, including his contributions to the Nagata conjecture. Additionally, Paul Biran has made important contributions to the theory of periodic orbits of Hamiltonian systems.
In other research, Paul Biran has studied symplectic crossings, the decomposition of sympleptic manifolds, and Lagrangian submanifolds. He has also studied Lagrangian topology and its application in geometry dynamics.