# 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

**OIST Symposium: Quantum and Gravity**

- Date: July 23-27, 2019
- Venue: OIST, Seaside house
- Organizers:
- Reiko Toriumi(OIST) and Shinobu Hikami(OIST)

- Description:

Quantizing gravity has been one of the most difficult problems in physics. There have been many approaches to quantizing gravity, which have given us mathematically and physically interesting ideas, such as the unification of forces, the emergence of spacetime, the problem of time, information paradox, spacetime foam, non-commutativity of spacetime, extra dimensions like Calabi-Yau manifold, duality, holography, etc. Geometry, which initially found a link to gravity by Einstein has been playing a major role in the studies of quantum gravity such as matrix models, tensor models, lattice methods like causal dynamical triangulations and Regge calculus, etc. Quantum field theory (QFT), which gave us a tremendous success in describing the Standard Model including the weak, the strong and the electromagnetic forces, is also a central solid modern tool in describing physical systems with many degrees of freedom. QFT lets us explore critical phenomena and the scale dependence of the physics through the renormalization group. In this symposium, we focus on such pillars of modern physics which are tied together in the research of quantum gravity. We aim at creating an open versatile atmosphere in order to advance further in the better understanding of each approaches in order to understand the grand problems of quantum description of gravitation. - Website
- Correspondence: quantumandgravity@oist.jp, workshop@oist.jp

**Workshop: Singularities and related topics**

- Date: July 30-August 2, 2019
- Venue: The University of Tokyo (Komaba),Room 002.
- Organizers:
- Shihoko Ishii (The university of Tokyo/Tsinghua University)
- Kei-ichi Watanabe (Nihon University)
- Masataka Tomari (Nihon University)
- Shinobu Hikami (OIST)

- Invited Speakers:
- Anna Pratoussevitch (Liverpool )
- Anne Moreau(Lille)
- Claus Hertling(Mannheim)
- Shihoko Ishii(The University of Tokyo/Tsinghua University)
- Masataka Tomari(Nihon University)
- Kei-ichi Watanabe(Nihon University)
- Makiko Mase (Mannheim)
- Kazuhiko Kurano (Meiji University)

(others)

**Description;**Brieskorn type quasi homogeneous singularities are related to the theory of the moduli space of spin curves, as discussed by Natanzon and Pratoussevitch. In this workshop, we discuss related topics of the singularities, jet schemes and arc spaces, mirror symmetry and conformal field theory.- Program
- Correspondence: shiho.saito@oist.jp

## Past Events

## News