## 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, several symplectic capacities, which are closely related with studies of periodic orbits of Hamiltonian systems, were discoverd (Hofer-Zehnder, Ekeland-Hofer, etc). Combined with Floer theory, these discoveries developed into the 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 the 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, several symplectic capacities, which are closely related with studies of periodic orbits of Hamiltonian systems, were discoverd (Hofer-Zehnder, Ekeland-Hofer, etc). Combined with Floer theory, these discoveries developed into the 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 the shortest length of periodic billiard trajectories.