## Staff -IRIE, Kei-

Name

**IRIE, Kei**
Position
Assistant Professor

E-Mail
iriek (email address: add @kurims.kyoto-u.ac.jp)

URL

Research

Kei Irie is working on symplectic geometry. In particular, he is
interested in symplectic homology and symplectic capacities.

Symplectic capacities are quantitative invariants of symplectic manifolds, which measure "2-dimensional width" of symplectic manifolds. In 80-90's, Hofer et al. discovered several capacities which are closely related with studies of periodic orbits of Hamiltonian systems. Combined with Floer theory, these discoveries developed into theory of symplectic homology.

Irie's current interests are developments and applications of these works.

For example, he used symplectic capacity to prove a geometric inequality concerning shortest length of periodic billiard trajectories.

Symplectic capacities are quantitative invariants of symplectic manifolds, which measure "2-dimensional width" of symplectic manifolds. In 80-90's, Hofer et al. discovered several capacities which are closely related with studies of periodic orbits of Hamiltonian systems. Combined with Floer theory, these discoveries developed into theory of symplectic homology.

Irie's current interests are developments and applications of these works.

For example, he used symplectic capacity to prove a geometric inequality concerning shortest length of periodic billiard trajectories.