谷口 正樹の写真
研究分野
数学、トポロジー
着任履歴
2020-04-01 - 基礎科学特別研究員
関連ウェブサイト
谷口 正樹の個人ウェブサイト

自己紹介

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.

関連イベント

iTHEMS × academist オンラインイベント「数理で読み解く科学の世界 2022」

2022年4月24日(日)10:00 - 16:30 特別講演会

Knotted 2-spheres in the 4-space and Yang-Mills gauge theory

2020年5月27日(水)16:00 - 18:10 セミナー iTHEMS数学セミナー

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