Last Update 2017/12/12 14:54:14
I am working in the area of geometry and topology in mathematics. My interests cover 3-dimensional manifolds, braid groups, knot theory, and the geometry of configuration spaces and moduli spaces. The fundamental group reflects the geometric structure of the space. A starting point of my research is to understand this non-commutative group in a geometric manner by means of differential forms on the space.
In attempting to construct representations of braid groups based on iterated integral of logarithmic forms, I found a relation between the monodromy of the KZ equation in conformal field theory and quantum groups. My recent research achievements include integral representation of the space of conformal blocks by multi-variable hypergeometric functions, geometry of infinite dimensional spaces such as the space of knots and the loop spaces of configuration spaces and the algebraic structure of their homology. In particular, the latter is closely related to string theory.
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