## 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 and related topics.
In particular, he is interested in symplectic capacities, periodic orbits of Hamiltonian systems, and symplectic homology.

Symplectic homology is a version of Floer homology for periodic Hamiltonian systems, introduced by Floer-Hofer and Viterbo. It has many applications in symplectic and contact geometry, including partial solutions to the Weinstein conjecture, obstructions to Lagrangian embeddings, and definition of symplectic capacities.

Irie is interested in developments and applications of these works. For example, he used symplectic homology to study short periodic billiard trajectories. He also gave a new estimate of the Hofer-Zehnder capacity, using product structure on symplectic homology. He is also working on chain-level string topology, motivated by potential applications to symplectic geometry.

Symplectic homology is a version of Floer homology for periodic Hamiltonian systems, introduced by Floer-Hofer and Viterbo. It has many applications in symplectic and contact geometry, including partial solutions to the Weinstein conjecture, obstructions to Lagrangian embeddings, and definition of symplectic capacities.

Irie is interested in developments and applications of these works. For example, he used symplectic homology to study short periodic billiard trajectories. He also gave a new estimate of the Hofer-Zehnder capacity, using product structure on symplectic homology. He is also working on chain-level string topology, motivated by potential applications to symplectic geometry.