# 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

RIMS x OIST Jointly-funded Workshop:

"Interactions of New Trends in Algebraic Geometry and Singularities"

- Date: October 11- 15, 2021
- Remote: Zoom
- Organizers:
- Shihoko Ishii (Univ. of Tokyo)
- Hiraku Kawanoue (Chubu Univ.)
- Tohru Ohmoto (Hokkaido Univ.)
- Shinobu Hikami (OIST)

- Description :

Algebraic Geometry has 400 years history after René Descartes introduced coordinates to geometry. Recently this area is remarkably developing under cooperation with Number Theory, Commutative Algebra, Combinatorics, Representation Theory and so on.

In Algebraic Geometry, Japan is in one of the central position. Three Fields Medalists from Japan; Kunihiko Kodaira, Heisuke Hironaka and Shigefumi Mori contributed the big development of Algebraic Geometry. Nowadays a new generation; like Takehiko Yasuda, Yoshinori Gongyo and Masahiko Yoshinaga made remarkable progress in Algebraic Geometry. Because of this broad and quick progress, it became difficult for an algebraic geometer to cover all ideas. On the other hand, it is very important and useful for an algebraic geometer to know many ideas in topics different from ones own.

The aim of the workshop is to bring together experts of various fields of algebraic geometry who would like to learn different fields from their own and let them have a chance to learn other fields. We try to make the atmosphere very friendly and easy to ask any questions. To this end, it is very nice for all participants stay in a one accommodation and spend time together whole a week.

The topics we take in the workshop are (1) Minimal Model Problem, (2) Hyperplane arrangement and (3) Stacks.

Three main speakers - Yoshinori Gongyo (University of Tokyo), Masahiko Yoshinaga (Hokkaido University) and Takehiko Yasuda (Tohoku University) - will give five courses each. These are all quite new fields and developed very quickly. In the workshop the participants will learn these topics and try to find ways to make use of them for their own researches.

- Titles & Abstracts

- Schedule (each lecture50 min. discussion 5 min.)

- Lecturers:

MMP

- Yoshinori Gongyo (Expository, Univ. Tokyo)
- Anne-Sophie Kaloghiros (Brunel Univ.)
- Chen Jiang (Fudan Univ.)

Stack

- Takehiko Yasuda (Expository, Osaka Univ.)
- Yusuke Nakamura (Univ. of. Tokyo)
- Victoria Hoskins (Freie Univ. Berlin)

Arrangement

- Masahiko Yoshinaga (Expository, Hokkaido Univ.))
- Takuro Abe (Kyushu Univ.)
- Elisa Palezzato (Hokkaido Univ.)

- List of participants
- Kohsuke Shibata (Nihon Univ.)
- Shoji Yokura (Kagoshima Univ.)
- Kei-ichi Watanabe (Nihon Univ.)
- Takahiro Yamamoto (Tokyo Gakugei Univ.)
- Mahito Tanno (Osaka Univ.)
- Herwig Hauser (Univ. Wien)

- This workshop will be held on zoom. Registration for the general public is also accepted. Please register using this webform. Registration will be completed after approval by the organizers.

- Contact: miwako.tokuda@oist.jp, workshop@oist.jp

*This workshop is supported by RIMS, OIST, and JSPS KAKENHI

● Code of Conduct for OIST Workshops and Mini-symposia

https://groups.oist.jp/cws/code-conduct