We study geometric constructions such as Floer homology in relation to combinatorial quantities associated to knots and graphs.
Low dimensional topology
Knot theory
Algebraic combinatorics
Isobe Laboratory
Calculus in infinite dimensional spaces
We study nonlinear problems on manifolds and have an interest in infinite dimensional Morse theory arising from geometry and physics.
Nonlinear analysis on manifolds
Variational methods
Functional analysis
Ma Laboratory
Global structure of moduli spaces
Moduli spaces
Modular forms
Rationality problem
Naito Laboratory
Understanding identities through representations
Our aim is to understand identities through representations of quantum groups, by means of crystal bases; one of the main tools for the study of representations of quantum groups.
Representation theory of infinite-dimensional Lie algebras
We study lifestyle changes occurring in the 21st century and the use of information and communication technology for the realization of a knowledge-based society.