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.

Keywords	Topology, Algebraic Topology, Combinatorial Algebraic Topology
Faculty , Department	Faculty of Mathematics , Department of Mathematics
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