I am Masaki Taniguchi, a mathematician, who has been working at iTHEMS/RIKEN since April 2020. My interests cover gauge theory, Floer theory and its applications to 3- and 4-dimensional topology. In a mathematical study of gauge theory, we obtain information of 4-manifolds by observing the moduli space of solutions to a certain non-linear partial differential equation for a given 4-manifold. This method enables us to find interesting phenomena of 3- and 4-dimensional topology which are different from that of other dimensions.
Currently, I am studying the following topics:
1. gauge theory for a class of non-compact 4-manifolds called 4-manifolds with periodic ends and their applications to existence of codimension-1 embedding of 3-manifolds and positive scalar curvature on spin 4-manifolds,
2. a quantitative formulation of instanton Floer homology and its applications to a study of the homology cobordism group which is related to existence of triangulations of topological manifolds, and
3. a study of 2-dimensional knots in the 4-space using gauge theory.
I'm also interested in physical aspects of gauge theory. I'm looking forward to discussing with researchers in various fields at RIKEN.