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Geometric Analysis Seminar
Seminar information archive ～02/24｜Next seminar｜Future seminars 02/25～
| Organizer(s) | Shouhei Honda, Hokuto Konno, Asuka Takatsu |
|---|---|
| URL | https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/ |
2026/04/10
16:00-17:00 Room # (Graduate School of Math. Sci. Bldg.)
Shinichiroh Matsuo (Nagoya University)
Discretization of Dirac operators and lattice gauge theory (日本語)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Shinichiroh Matsuo (Nagoya University)
Discretization of Dirac operators and lattice gauge theory (日本語)
[ Abstract ]
Our ultimate goal is to discretize Seiberg-Witten theory.
Considering PL = DIFF in dimension four, we would like to construct something like PL Seiberg-Witten theory.
As a first step towards this goal, we study the discretization of the analytic index of Dirac operators.
However, the analytic index of Fredholm operators is an essentially infinite-dimensional phenomenon, while the index theory of finite-dimensional self-adjoint operators is trivial.
Thus, a naive discretization of Dirac operators does not work.
In this talk, I will explain how the “Wilson-Dirac operator” from lattice gauge theory provides a correct discretization, at least from the viewpoint of the analytic index.
This talk is based on a joint work with Shoto Aoki, Hidenori Fukaya, Mikio Furuta, Tetsuya Oonogi, and Satoshi Yamaguchi.
https://arxiv.org/abs/2602.12576
https://arxiv.org/abs/2407.17708
[ Reference URL ]Our ultimate goal is to discretize Seiberg-Witten theory.
Considering PL = DIFF in dimension four, we would like to construct something like PL Seiberg-Witten theory.
As a first step towards this goal, we study the discretization of the analytic index of Dirac operators.
However, the analytic index of Fredholm operators is an essentially infinite-dimensional phenomenon, while the index theory of finite-dimensional self-adjoint operators is trivial.
Thus, a naive discretization of Dirac operators does not work.
In this talk, I will explain how the “Wilson-Dirac operator” from lattice gauge theory provides a correct discretization, at least from the viewpoint of the analytic index.
This talk is based on a joint work with Shoto Aoki, Hidenori Fukaya, Mikio Furuta, Tetsuya Oonogi, and Satoshi Yamaguchi.
https://arxiv.org/abs/2602.12576
https://arxiv.org/abs/2407.17708
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
