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Staff Introduction
I am an algebraic topologist. Topological spaces have various algebraic and combinatorial structures inside of them. For instance, every loop space has the Ainfinity 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 Ainfinity 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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