Doctor (Science)

No

Algebraic Topology

00years00months

I am an algebraic topologist. Topological spaces have various algebraic and combinatorial structures inside of them. For instance, every loop space has the A-infinity structure which is like a group structure incorporating a combinatorial structure of a polytope, and the base topological space can be recovered from its loop space by the A-infinity structure. Then it is of particular importance to understand algebraic and combinatorial structures in spaces. The following are most important in my study.

(1) Multiplicative structures of Lie groups and the topology of mapping spaces.
(2) The topology and combinatorial structures of subspace arrangements.
(3) Applications of algebraic topology to combinatorics.

Research Interests

• I am an algebraic topologist. In algebraic topology, we study properties of spaces which are invariant under bending, stretching, and sometimes more hard deformations, by representing them algebraically. Iam studying algebraic and combinatorial structures inherent in spaces such as the A_\infty structure. I am also studying spaces constructed combinatorially such as a subspace arrangement from a view of algebraic topology.
  keyword : Topology, Algebraic Topology, Combinatorial Algebraic Topology
  2001.04～2032.12.

Academic Activities Membership in Academic Society

• The Mathematical Society of Japan

Educational Activities