# 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

### Workshop “Super-Riemann surfaces and related topics”

--- This is a joint project between OIST and University of Tokyo.

- Date: 2019.12.2-4
- Venue: University of Tokyo,Graduate school of mathematical sciences
- Organizers: Nariya Kawazumi (Univ. of Tokyo), Takuya Sakasai(University of Tokyo),

Shinobu Hikami(OIST) - Schedule

#### December 2 (Mon)

10:30 - 11:30 Yusuke Kuno (Tsuda University)

On spin structures associated with a trivalent fatgraph spine

13:00 - 15:00 Anton Zeitlin (Louisiana State University)

Introduction to the theory of super Riemann surfaces.

#### December 3 (Tue)

10:30 - 11:30 Casey Blacker(EastChinaNormalUniversity)

Polysymplectic Reduction and the Moduli Space of Flat Connections

13:00 - 15:00 Anton Zeitlin (Louisiana State University)

*N *= 1 and *N *= 2 super-Teichmueller theory

15:30 - 16:30 Shinobu Hikami(OIST)

Ramond punctures and p-spin curves in a random matrix theory

17:00 - 18:30 Tuesday Seminar on Topology

Anton Zeitlin (Louisiana State University)

Homotopy Gerstenhaber algebras, Courant algebroids, and Field Equa- tions

#### December 4 (Wed)

10:30 - 11:30 Motoko Kato (EhimeUniversity)

Thompson’s groups and their actions on non-positively curved spaces

13:00 - 15:00 Anton Zeitlin (Louisiana State University)

Super-Teichmueller theory: some recent results

2020 OIST Workshop “Quantum Math, Singularities and Applications”

- Dates: 7/20-7/24, 2020
- Venue: Lecture Room in Lab. 4, OIST
- Dead line of application: Dec. 31. 2019.
- Contact: workshop@oist.jp
- 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.

- Detail: PDF

## Past Events

## News