# Mathematical and Theoretical Physics Unit (Shinobu Hikami)

## Mathematical and Theoretical Physics Unit

#### Professor Shinobu Hikami

## Book

E. Brezin and S. Hikami,

Random Matrix Theory with an External Source,

SpringerBriefs in Mathematical Physics 19, (2016), Springer Singapore.

## Abstract

Universal behaviors can be observed in various physical phenomena. For instance, a magnet shows a phase transition with critical indices, which are determined by the symmetry and the space dimensions. They do not depend on the details of the materials. In our unit, we study the universal phenomena of the disordered systems which are typically described by random scatterings and random potentials. The random walk in Brown motion is one of the well-known problems in this field. The aim of our study is to generalize these approaches through the random matrix model and to discuss the universal phenomena.

The random matrix model can be applied to low dimensional electronic system such as a quantum dot, and also to the string theory and gauge theory. The molecular-sequence of DNA or protein seems randomly distributed, but some of these sequences can be explained by random matrix theory. The biological system is an extremely complex system. Our research project is an approach to the biological system from the mathematical and theoretical physics by the use of the random matrix theory.

## Upcoming Events

### New schedule

2020 OIST Workshop “Quantum Math, Singularities and Applications”

- Dates: 2/8-2/12, 2021
- Remote: Zoom
- Application was closed
- Organizers:
- Shihoko Ishii (Tsinghua University/Univ. Tokyo)
- Yasuyuki Kawahigashi (The University of Tokyo)
- Shinobu Hikami ( OIST)

- Contact: workshop@oist.jp

- Tentative list of invited talkers
- Shihoko Ishii (Tsinghua Univ. /Univ. Tokyo, Organizer)
- Lawrence Ein (University of Illinois at Chicago)
- Kei-ichi Watanabe (Nihon University)
- Yasuyuki Kawahigashi (The University of Tokyo, Organizer)
- Vladimir Dotsenko (Univ. Strasbourg)
- Benoit Collins (Kyoto University)
- Shunsuke Takagi (The University of Tokyo)
- Kohsuke Shibata (Nihon University)
- Takehiko Yasuda (Osaka University)
- Zhenghan Wang (Microsoft Station Q)
- Kyoji Saito (Kyoto Univ. RIMS)
- Shinobu Hikami (OIST, Organizer)
- Masahiko Yoshinaga (Hokkaido University)
- Terry Gannon(University of Alberta)
- Motoko Kato (Ehime University)
- Makiko Mase (Mannheim University)
- Mayuko Yamashita (Kyoto Univ. RIMS)

- Conference description:

This conference of quantum mathematics and singularity includes subjects in new developments of the singularity theories and the conformal field theory. The followings are key words: two and three dimensional normal singularities, arc space and jet scheme, moduli space and operad, noncommutative geometry, conformal bootstrap and super conformal field theory. The topological materials of condensed matter physics need rigorous mathematical classifications, which will be one of applications.

- Program: PDF
- Titles and Abstracts: PDF
- Zoom recording FILE
- 20210208 10:00-12:00 (JST) Prof. S. Ishii, Prof. S. Takagi
- 20210208 18:00-20:00 (JST) Dr. K. Shibata, Prof. M. Kato
- 20210209 10:00-12:00 (JST) Prof. L. Ein, Prof. K. Watanabe
- 20210209 18:00-20:00 (JST) Prof. M. Mase, Prof. V. Dotsenko
- 20210210 10:00-12:00 (JST) Prof. T. Gannon, Prof. Y. Kawahigashi
- 20210210 18:00-20:00 (JST) Prof. M. Yamashita, Prof. B. Collins
- 20210211 10:00-12:00 (JST) Prof. Z. Wang, Prof. M. Yoshinaga
- 20210211 18:00-19:00 (JST) Prof. K. Saito
- 20210212 10:00-12:00 (JST) Prof. T. Yasuda, Prof. S. Hiakmi