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Department of Geometrical Structure Analysis

Department chair: Professor Takashi Shioya

Our department conducts applied research from a geometrical standpoint, using modern advances in geometry (differential geometry and topology) as a base.
As for the relationship between topology and physics, we intend to explain how supersymmetric gauge theory has a structure in common with three-dimensional manifold theory and knot theory. In our study of quantum walks, we will develop our research from the standpoint of discrete geometric analysis and aim to provide feedback to computer science.

Common Structures Between Topology and Physics

We are working on a new theory about a hidden structure that is common to three-dimensional topology and supersymmetric gauge theory, and we will expand upon the mathematical consequences of this theory.

Common Structures Between Topology and Physics

Quantum Walk Research

We conduct research aimed at clarifying and developing the theory of quantum walks,
which is originated in computer sciences, through various methods in discrete geometric analysis.

Quantum Walk Research