# 数理理論物理学ユニット （氷上 忍）

## 数理理論物理学ユニット

#### 氷上 忍 教授

## 出版物

E. Brezin and S. Hikami,

Random Matrix Theory with an External Source,

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

## 概要

物理現象には普遍的な振る舞いが見られます。磁性体での相転移現象では臨界指数と呼ばれる量が対称性や次元数で決まり、どのような原子から出来ているのかには依りません。

また金属・絶縁体転移も普遍的な現象であることが分かっています。このユニットではランダムな不純物散乱やポテンシャルがある無秩序系での普遍的現象を研究しています。

ブラウン運動でのランダムウオークは良く知られていますが、これを多体問題にしたランダム行列模型を研究して、さまざまな普遍現象に応用しています。量子ドットのエネルギー準位や弦理論・ゲージ理論にも応用出来ます。ＤＮＡやたんぱく質の分子配列はランダムな配列に見えますが、その配列には統計的な普遍的性がありランダム行列理論で説明出来るものがあります。生物系は複雑系ですが、それに数理理論物理学からランダム行列理論を使ってアプローチすることを目指しています。

## 今後のイベント

**Special Lecture: Modularity of Calabi-Yau Manifolds**

- Date: Friday, February 22, 2019
- Time: 10:00 am - 4:00 pm
- Venue: Lecture room B715 (Lab3), OIST.
- Speaker: Noriko Yui (Queen’s University)
- Abstract :

Let X be a Calabi-Yaumanifold of dimension d. In this talk, I would like to address the modularity questions around Calabi-Yau manifolds. We will confine ourselves to Calabi-Yau manifolds of small dimensions, e.g., d ≤ 3. There are two types of modularity:

(A) Arithmetic modularity/automorphy. This is concerned with Calabi-Yau varieties defined over Q (ornumberfields). The main questions are the modularity/automorphy of the cohomological L-seriesofthel-adic Galois representations associated to these varieties in the framework of Langlands Philosophy.

(G) Geometric modularity. This is concerned with families of Calabi-Yau manifolds. The main questions are the modular/automorphic properties of various invariants associated to these varieties, e.g., mirror maps, Gromov-Witten invariants, Donaldson-Thomas invariants, holomorphic anomaly equations, etc. arising in string theory. Quasi-modular forms, Jacobi forms, Siegel modular forms, and more general modular-like forms show their appearances in this land scpae.

**Seminar: Towards a theory of classification: general setting**

- Speaker: George Elliott (University of Toronto)
- Date: Feb.27, 2019, 14:00-16:00
- Venue: C210, OIST Center building

An abstract classifying invariant—a functor!—for a certain kind of given category is constructed by passing to equivalence classes of morphisms, which themselves form a category. Thus, the objects are the same, but the classifying category—so named because isomorphism of objects downstairs implies isomorphism upstairs—is typically much simpler than the given one, as many morphisms are identified by the classification functor, and many automorphisms killed. (Note that one cannot just replace objects by isomorphism classes, as one doesn’t get a category this way.) The classifying category is a priori an abstract one, but, perhaps surprisingly, in interesting cases, its Yoneda concretization becomes spectacularly simple.

**Silver Workshop: Complex Geometry and Non-Cummutative Geometry**

- Organizers: Noriko Yui (Queen's University), Kyoji Saito (IPMU) and Shinobu Hikami (OIST)
- Date: Feb 28-Mar1, 2019
- Time: Feb 28 10:30 am - 6:00 pm, Mar 1 10:30 am - 4:50 pm
- Venue: C210, Center Building, OIST Campus
- Talkers:
- George Elliott (Toronto Univ) Abstract
- Shinobu Hikami (OIST) Abstract
- Tomoyuki Mano (Ryukyu Univ.) Abstract
- Yasuyuki Kawahigashi (Univ. Tokyo) Abstract
- Kyoji Saito (IPMU) Abstract
- Noriko Yui (Queen's Univ.) Abstract
- Konstantin Aleshkin (Landau Institute) Abstract
- Motoko Kato (Univ. Tokyo) Abstract
- Shigeru Iitaka (Gakushuin University) Abstract
- Mutsuo Oka (Tokyo Univ. of Science) Abstract

- Program
- Accommodation: Hotel Moon Beach
- Transportation
- Contact: shiho.saito@oist.jp

**Workshop “Quantum Math”**

- Organizers: Y. Kawahigashi (Univ. Tokyo) and S. Hikami (OIST)
- Description:

Collaboration between mathematics and physics becomes more important and essential for recent development in quantum mathematical physics. We discuss new issues such as entropy of black hole, integrable system, conformal field theory and bootstrap in higher dimensions, algorithm in resolution of singularities, super moduli space, non-commutative geometry and operator algebra, and their application to quantum information and quantum computation.

- Date: Mar 2-3, 2019
- Time: 13:00-18:00 (Mar 2), 9:30-13:00 (Mar3)
- Venue: B700, Lab3, OIST Campus
- Confirmed Speakers:
- Program
- Accommodation: Hotel Moon Beach
- Transportation
- Correspondence: shiho.saito@oist.jp

*This workshop is supported by KAKENHI KIBAN(C)16K05491

**Seminar:**

- Date: Tue, Mar 5- 2019
- Time: 10:30-11:30
- Venue: C016, Lab1
- Speaker: Prof. Chushun Tian (Institute of Theoretical Physics, Chinese Academy of Sciences)

Title: "Topology from chaos: quantum Hall physics, Haldane conjecture and beyond"

Abstract: Chaotic and topological phenomena have totally opposite characteristics: the former/latter are extremely sensitive to/robust against the change in system's details (e.g., the parameters of the Hamiltonian, the initial conditions, etc.). Thus they are commonly considered not to be compatible. In this talk, I will show how, by introducing a spin degree of freedom to the canonical model of chaotic dynamics, the so-called quantum kicked rotor (QKR), which is simply a particle moving on a ring and subjected to pulsed external force, rich dynamical behaviors of topological origin arise. These include, notably, the realization of quantum Hall physics and Haldane conjecture, which occur originally to totally different systems, namely, many-electron systems and quantum antiferromagnetic chains, respectively. I will show how a supersymmetry structure arises from the time-driving nature of QKR, and serves as a seed for a wealth of topological phenomena in this chaotic system as simple as being single-particle.

## 過去のイベント

**Workshop on "Hyperbolic Geomerty of the Moduli Space and Related Topics."**

- Dates: January 24-26, 2019
- Venue

Jan 24-25: Room #123, Jan 26: #056

Graduate School of Mathematical Sciences, The Univ. of Tokyo

(Komaba Campus) -
Description:

The moduli space of compact Riemann surfaces, the space of all biholomorphism classes of compact Riemann surfaces, is one of the most attractive subjects in mathematics. Nowadays it firmly combines

mathematical physics and integrable systems with low-dimensional topology including hyperbolic geometry of surfaces, which induces the Weil-Petersson symplectic structure on the space. In particular, the topological recursion by Eynard and Orantin generalizing Mirzakhani's recursive formula for the Weil-Petersson volume has some strong influence in various research areas.

In this workshop, we will intensively discuss some specific topics on the hyperbolic structure of the moduli space, and will have some talks on original researches. - Program

**Seminar:**

- Date: Wednesday, January 30, 2019
- Time: 11:00 - 12:00
- Venue: C016, Lab1
- Speaker: Prof. Anton Zabrodin (National Research University Higher School of Economics, Moscow)

Title: "Elliptic solutions to BKP equation and many-body systems"

Abstract: We derive equations of motion for poles of double-periodic (elliptic) solutions to the B-version of the KP equation. The motivation is the well-known story about elliptic solutions of the usual KP equation, where the dynamics of poles is given by the Calogero-Moser many-body system with elliptic potential. The basic tool is the auxiliary linear problem for the wave function.The result is a new many-body dynamical system with three-body interaction expressed through the Weierstrass elliptic function. This system does not admit Lax representation but, instead, it is equivalent to a sort of Manakov's triple equation with a spectral parameter. We also discuss integrals of motion which follow from the equation of the spectral curve and analyze analytic properties of the wave function on the spectral curve.

**OIST Mini Symposium "Holographic Tensors"**

- Organizers: Reiko Toriumi (OIST) , Vincent Rivasseau (Univ. Paris Sud) and Shinobu Hikami (OIST)
- Date: Oct 31-Nov 2
- Venue: OIST Conference Center & Seaside House
- URL: https://groups.oist.jp/cws/event/oist-mini-symposium-holographic-tensors

**Silver Workshop : Complex geometry and related topics**

- Organizers: Noriko Yui (Queen’s Univ.), Kyoji Saito (IPMU) and Shinobu Hikami(OIST)
- Date: July 27th (Friday)
- Time: 10:30 am – 6:00 p.m. (6:00p.m. – 8:00pm, dinner for Prof. Sasakura)
- Venue: University of Tokyo, Math. Department, Room 123

- Tentative Program:
- 10:30-10:40 Opening Kyoji Saito (IPMU)
- 10:40-11:10 Shinobu Hikami (OIST), Brieskorn singularity and intersection theory (Abstract)
- 11:10-11:30 Coffee break
- 11:30-12:30 Kei-ichi Watanabe (Nihon Univ.), Homogeneous prime elements of 2 dimensional normal graded rings (Abstract)
- 12:30-13:40 Lunch
- 13:40-14:10 Shigeru Iitaka (Gakushuin), Super perfect numbers and super twin primes
- 14:10-14:15 Break
- 14:15-15:15 Shihoko Ishii (Tokyo Woman’s Christian Univ.) Singularities in positive characteristic (Abstract)
- 15:15-15:35 Coffee break
- 15:35-16:35 Noriko Yui (Queen’s Univ.), Supercongruences for rigid hypergeometric Calabi–Yau threefolds (Abstratct)
- 16:35-16:45 Break
- 16:45-17:15 Kyoji Saito (IPMU), Elliptic Artin group (Abstract)
- 17:15-17:25 Break
- 17:25-17:55 Mutsuo Oka (Tokyo University of Science), Remarks on the roots of generalized Lens equation
- 18:00-20:00 Dinner at Lever son Verre (inside Campus)

**Symposium: Bootstrap Approach to Conformal Field Theories and Applications**

Scale invariant theories, i.e. theories which look the same at all distance and energy scales, play an important role in physics. Through Wilson’s renormalization group, scale invariant theories arise naturally in phase transitions. They are also the bread and butter of current thinking about particle physics beyond the Standard Model. These theories usually possess an emergent symmetry, conformal invariance, and are hence referred to as `Conformal Field Theories’ (CFTs). The quest to classify and solve CFTs is a major goal of theoretical physics. Recently, this quest has received a strong boost with the development of the ‘conformal bootstrap’ technique. This workshop will bring together two groups of researchers: theorists working on the conformal bootstrap and on formal aspects of CFTs, and condensed-matter and statistical theoretical physicists working on the concrete examples of systems exhibiting phase transitions described by CFTs. The goal will be to inform about the most important theoretical and practical developments in the conformal bootstrap, and about the most urgent questions relevant for condensed matter and statistical physics which can be addressed using conformal bootstrap.

- Organizers: Slava Rychkov and Shinobu Hikami
- Date: March 19-23, 2018
- Venue: Conference Center, OIST
- Invited Speakers:
- Luis Fernando Alday (Oxford)
- Nando Gliozzi (Torino)
- Rajesh Gopakumar (ICTS-TIFR)
- Sean Hartnoll (Stanford)
- Shinobu Hikami (OIST)(organizer)
- Yu Nakayama (Rikkyo)
- Silviu Pufu (Princeton)
- Leonard Rastelli (SUNY)
- Slava Rychkov (ENS, CERN)(organizer)
- Aninda Sinha (IIS, Bangalore)
- Satoshi Yamaguchi (Osaka)
- Masahito Yamazaki (IPMU,Tokyo)

**RIKEN-Osaka-OIST Joint Workshop 2018**

- Organizers: :Koji Hashimoto (Osaka), Yoshimasa Hidaka (RIKEN), Hirohiko Shimada (OIST), Sotaro Sugishita (Main) (Osaka)
- Date: March 12-14, 2018
- Venue: B250 (Mar 12 & 13), C209 (Mar 14), OIST

**研究集会「モジュライ空間のシンプレクティック幾何」**

期日: 2018年1月26日(金)～1月28日(日)

会場: 東京大学大学院数理科学研究科 123教室 東京大学駒場キャンパス

内容: モジュライ空間の射影的接続に絡むシンプレクティック幾何に関する2つ の論文の精読とオリジナルの講演

講演者: 池田 暁志(東大 Kavli IPMU) 石橋 典(東大数理) 小櫃 邦夫(鹿児島大理) 河井 真吾(東工大理学院) 信田 萌伽(東大数理) 宮地 秀樹(阪大理) 逆井 卓也(東大数理) 田所 勇樹(木更津高専)

世話人: 逆井卓也(東京数理)，河澄響矢(東大数理)，田所勇樹(木更津高専)

**MINI SYMPOSIUM: New development in Teichmuller space theory ; MCM2017**

Theory of Teichmuller space has a long history for the moduli space of Riemann surface. Recently beyond classical Teichmuller space research, new extended concept and technique are developed and they are important for various areas of mathematical physics. Particularly higher Teichmuller space attracts interest, which concerns SL(n,R) geometry and its boundary. In this mini symposium, we concentrate on the new concept and technique and discuss from wide point of view of topology, physics and integrable systems. For examples, the cluster algebra and open intersection numbers are discussed closely. We intend to develop a theory for new structure of Teichmuller space in a new direction of mathematical physics.

- Date:
- Venue: C210, Center Building, OIST
- Organizers: Nariya Kawazumi (Univ. of Tokyo), Takuya Sakasai (Univ. of Tokyo), Shinobu Hikami (OIST)
- Invited talkers:
- A. Alekseev, Geneve Univ.
- R. Inoue, Chiba Univ.
- R. Kashaev, Geneve Univ.
- T. Kitayama, Univ. of Tokyo
- A. Kuniba, Univ. of Tokyo
- A. Tsvietkova, OIST

- Program: PDF

**Seminar:**

- Date: Thursday, November 9, 2017
- Time: 13:30 - 14:30
- Venue: Room 056, Graduate School of Mathematical Sciences Bldg., University of Tokyo (Komaba Campus). The seminar will be also aired parallel via TV conference system in Room B611 (Lab2) , OIST.
- Speaker: Prof. Edouard Brezin (lpt ens, Paris)

Title: "Various applications of supersymmetry in statistical physics".

Abstract: Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.

**Workshop: MSRI Summer Graduate School – Commutative Algebra and Related Topics**

The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research. The lecturers will give topics courses and then the graduate students will meet in small groups and challenge problems and have discussion sessions related to each topic.

- Date:
- Venue: OIST Seaside House (May 23 at Conference Center, OIST Campus)
- Organizers: Shihoko Ishii (TWCU), Kazuhiko Kurano (Meiji), Ken-ichi Yoshida (Nihon), Shinobu Hikami (OIST)
- Lecturers:
- David Eisenbud (MSRI / University of California)
- Claudia Polini (University of Notre Dame)
- Claudiu Raicu (University of Notre Dame)
- Shunsuke Takagi (University of Tokyo)
- Ryo Takahashi (Nagoya University)

- Program:
- Photo: jpg

**Symposium: Geometry of Quadratic Differentials and Related Topics**

Quadratic differentials, meromorphic tensor fields on Riemann surfaces of some special type, have been studied classically in hyperbolic geometry and complex analysis. Recently it has been clarified that low-dimensional topology including hyperbolic geometry of surfaces is closely related to mathematical physics and integrable systems. This can be illustrated by the topological recursion by Eynard and Orantin generalizing computation of the Weil-Petersson volume of the moduli space of Riemann surfaces, whose influence one can find in various research areas. Accordingly quadratic differentials are playing some important roles also in mathematical physics and integrable systems. In this workshop, we will read intensively some research papers on the geometry of quadratic differentials and related topics, and will have some talks on original researches. This workshop is supported by a joint project between the OIST and the University of Tokyo.

- Organizers: Y. Tadokoro (Kisarazu), T. Sakasai (Univ. Tokyo) and N. Kawasumi (Univ. Tokyo)
- Date: January 11-13, 2017
- Venue: University of Tokyo, Komaba, Mathematical Science Building #002 Info (in Japanese)

**Pre-Conference MCM2016 at Tokyo**

- Date: October 20-22, 2016
- Venue: University of Tokyo, Komaba, Mathematical Science Building
- Organizers: Nariya Kawazumi(Univ. Tokyo), Shinobu Hikami(OIST)
- Program & Abstracts

**Workshop: Moduli space, conformal field theory and matrix models; MCM2016**

- Date: October 24-27, 2016
- Venue: C209, OIST
- Organizers: Nariya Kawazumi(Univ. Tokyo), Shinobu Hikami(OIST)
- Program & Abstracts
- Group Photo

**TSUDA COLLEGE AND OIST JOINT WORKSHOP ONCALABI–YAU VARIETIES:ARITHMETIC, GEOMETRY AND PHYSICS **

- Date: August 1–3, 2016
- Venue: August 1–2 at Tsuda College Room 7309, August 3 at Tokyo University Komaba Campus Room 117
- Organizers: Noriko Yui (Queen’s University) and Takayuki Oda (OIST)
- Program (PDF) & Abstracts (PDF)

**"OIST-iTHES-CTSR 2016" International Workshop**

- Date: Friday 8 - Monday 11 July, 2016
- Venue: Fri 8th (B250), Sat 9th (C209), Mon 11th (B250)
- Organizers: RIKEN iTHES, OSAKA CTSR, and OIST (Theoretical Units)
- Program (PDF)

**Seminar:**

- Date: Thursday, July 7, 2016
- Time: 15:00 - 16:00
- Venue: C209, Center Building, OIST
- Speaker: Prof. Jean Zinn-Justin (CEA Saclay)

**Title**: 3D field theories with Chern-Simons term for large N in the Weyl gauge

**Abstract:** ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.

We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.

We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.

Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.

**Seminar: **

- Date: Wednesday, March 30, 2016
- Time: 11:00 - 12:00
- Venue: C209, OIST
- Speaker: Prof. Katsuya Shimizu（Osaka University）

**Title**: 200-K superconductivity in compressed hydrogen sulfide systems

**Abstract: **After finding superconductivity in 100 years ago, "room-temperature"superconductor has been long-fascinated target for physicists. Superconductivity above 200K was recently reported in the highly compressed hydrogen sulfide (H2S) by Drozdov et al1. The crystal structure of the superconducting sulfur hydride systems was studied by using the synchrotron x-ray diffraction at room temperature and the superconducting temperature. H2S and D2S were compressed to 150 GPa in DAC with same process with Drozdov et al1, and cooled down to 10 K in the cryostat in the x-ray diffractometer in SPring-8. The resistivity was onitored at all cooling process. The critical temperature and zero resistivity were observed around 180 K, and the collected x-ray diffraction data showed good agreement with the theoretically predicted structures of R3m and Im-3m2. No structural difference was observed between at 10 K and room temperature. The creation of the high-temperature superconductor was experimentally also confirmed by our Osaka group. H2S gas was cooled down to around 200 K and liquefied then compressed up to 150 GPa in a diamond-anvil cell (DAC). The resistance decreased with increasing pressure and showed metallic behavior in cooling process. The superconducting transition was observed at 60-70 K with zero resistance. At the second cooling after warmed up to room temperature, the resistance dropped to zero from 180 K.

This work was supported by JSPS KAKENHI Grant Number 26000006 and the European Research Council 2010-Advanced Grant 267777.

References:

[1] A. Drozdov et al., Nature 525 73 (2015).

[2] D. Duan et al., Scientific Reports 4, 6968 (2014).

**Seminar: **

- Date: Friday, December 25, 2015
- Time: 11:00 - 12:00
- Venue: C015, Lab1, OIST
- Speaker: Prof. Yasutomo J. Uemura （Columbia University）

**Title**: BEC to BCS crossover picture for high-Tc cuprate and unconventional superconductors, and pairing due to comparable spin-charge energy scales: message from muons and neutrons

**Abstract:** Soon after the discovery of high-Tc superconductors in 1986, we started muon spin relaxation (MuSR) measurements of the magnetic field penetration depth, and demonstrated nearly linear correlations between Tc and the superfluid density n_{s}/m^{*}, which are manifest not only in cuprates but also in many other unconventional superconductors including Alkali doped C60, FeAs and some of the heavy-fermion systems . The strong dependence of Tc on carrier density is not expected in the BCS condensation, but is a main characteristic of Bose Einstein Condensation. Another important scaling of Tc is seen with the energy of the magnetic resonance mode measured by neutron scattering, which can be viewed as a spin–charge soft mode related to competing antiferromagnetic state, analogous to rotons in superfluid He related to competing solid HCP phase. This roton-like scaling is expected when condensed bosons are excited with phase fluctuations to another bosonic state, without pair breaking. This again is different from pair-breaking excitations across the energy gap in BCS condensation. We discuss these features and adopting BEC-BCS crossover picture for the cuprates, which I proposed in 1994 . Further analyses of the Tc-superfluid density (charge energy) scaling and Tc-spin wave energy (mediating boson energy) correlations lead to a possible pairing mechanism based on comparable spin and charge energy scales and dynamic synchronized charge motion in “traffic-light resonance”

References:

[1] Y.J. Uemura et al., Universal Correlations between Tc and ns/m∗ (Carrier Density over Effective Mass) in High-Tc Cuprate Superconductors, Phys. Rev. Lett. 62 (1989) 2317-2320.

[2] Y.J. Uemura et al., Basic Similarities among Cuprate, Bismuthate, Organic, Chevrel Phase, and Heavy-Fermion Superconductors Shown by Penetration Depth Measurements, Phys. Rev. Lett. 66 (1991) 2665-2668.

[3] Y.J. Uemura, Superconductivity: Exotic Commonalities in Phase and Mode, Nature Materials 8 (2009) 253-255.

[4] Y.J. Uemura, Energy Scales of Exotic Superconductors, an invited talk presented at the International Workshop on Polarons and Bipolarons in High-Tc Superconductors and Related Materials,Cambridge, UK, April, 1994, in Polarons and Bipolarons in High-Tc Superconductors and Related Materials, ed. by E. Salje, A.S. Alexandrov and Y. Liang, Cambridge University Press (1995), p.p.453-460.

[5] Y.J. Uemura, Energy-scale phenomenology and pairing via resonant spin-charge motion in FeAs, CuO, heavy-fermion and other exotic superconductors (Plenary Talk at SCES2008, Buzios, Brazil, Aug., 2008), Physica B404 (2009) 3195-3201.

#### Workshop on "Moduli spaces of abelian varieties and curves, and related analysis"

- Dates: December 15-18, 2015
- Venue : Graduate School of Mathematical Sciences, The Univ. of Tokyo (@Komaba Campus)
- Program: PDF

#### RMT2015: Random matrix theory from fundamental mathematics to biological applications

- Date: Monday, November 2- Friday, November 6, 2015
- Venue: C209, OIST
- Schedule, Title and Abstract: PDF
- Slides

**Seminar: **

- Date: Friday, November 20, 2015
- Time: 11:00-12:00
- Venue: C016, Lab1, OIST
- Speaker: Tsunehide Kuroki (Kagawa Kosen)

**Title**: Spontaneous supersymmetry breaking in matrix model and superstring theory

**Abstract:** We show that a supersymmetric matrix model is a promising candidate for the first example of nonperturbative definition of superstring theory. We prove that in this model, the supersymmetry is preserved in all orders in perturbation theory in the 1/N expansion, but that it gets broken nonperturbatively and spontaneously. We observe that this breaking is triggered by an instanton in the matrix model. We also present quite recent results of correlation functions in the matrix model in all orders of the 1/N expansion by using the random matrix theory. These results convince us that the matrix model is a string theory.

**MCM2015Autumn: **

- Date: Thursday, October 29 and Friday, October 30, 2015
- Venue: Komaba, University of Tokyo, Math. Dep. Room 002.
- Schedule:
- October 29th (Thursday)
- 10:00-11:00 Hikami
- 11:30-12:30 Andersen
- 14:30-15:30 Sakasai
- 16:00-17:00 Hayata
- 18:00- Dinner at Komaba

- October 30th (Friday)
- 10:00-11:00 Murakami
- 11:30-12:30 Zinn-Justin
- 14:30-15:30 Kuno
- 16:00-17:00 Shimada

- October 29th (Thursday)

- Title and Abstract: PDF

**Seminar: **

- Date: Wednesday, May 27th, 2015
- Time: 13:00-14:00
- Venue: C016, Lab1, OIST
- Speaker: Dr. Serguei Brazovskii from CNRS & University Paris-Sud, Orsay, France

**Title**: Solitons in low dimensional electronic systems of synthetic conductors.

**Abstract:** A vast variety and whole families of “synthetic conductors” have been designed by motivation and for the purpose of obtaining desired electronic and optical properties. A firework of new physical effects of electronic correlations feeds fundamental experimental and theoretical researches. Diverse phase transitions are commonly observed towards various electronic phases: superconductivity, anti-ferromagnetism, ferroelectricity, charge order, charge- and spin density waves, Mott and Peierls insulators, phases induced by high magnetic and electric fields and by optical pumping. Vulnerability of the broken symmetries gives rise to topological defects like electronic vortices, walls, stripes. The typical low-dimensional architecture of these compounds brings these objects to a microscopic scale giving rise to “solitons” which description will be the major content of this talk. The solitons are self-localized configurations which shapes explore the ground state degeneracy. The mathematics of exact solutions for many-body models relates these trajectories to profiles of waves’ arrays and of superwaves in the ocean and to pulses in optical fibers. The solitons can be the lowest energy optical excitations or the carriers of charge or/and spins, taking these functions from conventional electrons. The “instantons” appear as processes of dynamic conversion of normal electrons into solitons. In a broad class of strongly correlated systems, beyond the low-dimensionality, the solitons can persist acquiring forms of more complicated topological excitations which give incarnations to long time searched “spinons” and "holons"

**Host:** Prof. Shinobu Hikami

**Seminar: **

- Date: Wednesday, June 3, 2015
- Time: 13:00-14:00
- Venue: C016, Lab1, OIST
- Speaker: Dr. Natasha Kirova from CNRS & University Paris-Sud, Orsay, France

**Title**: Electronic ferroelectricity in carbon-based systems: from reality of organic conductors to promises of polymers

**Abstract:** All families of carbon based materials – graphite, graphene, nanotubes, fullerenes and a vast multitude of conjugated polymers and organic crystals – are promising electronically and optically active substances. Recently a new perspective has been added to their researches: an electronic ferroelectricity. Ferroelectrics are exploited as active gate materials, in capacitors, electro-optical-acoustic modulators, in WiFi devices, in perspective RAM. Flexible lightweight carbon ferroelectrics are desired as ultrasound sensors in medical imaging. The super-polarisable state of “the ferroelectric Mott semiconductor” was discovered (Grenoble-Orsay-Moscow) in conducting organic stacks. Less conducting ferroelectrics complexes with neutral-ionic transitions (Tokyo-Tsukuba) became the objects of studies by advanced femto-second and tera-Hz optics (Tokyo). The principle novelty of organic ferroelectrics is that the polarization comes from electronic ordering rather than from ionic displacements. The microscopic design of all new materials is based on coexisting symmetry lowering effects: the dimerization of bonds and the dimerization of sites. With this forecast we could indicate the class of conducting polymers where the ferroelectricity should be present. The theory predicted an existence of solitons (which might have been already observed in Utah experiments on Kyoto materials) with non-integer variable charges, which are the walls separating domains with opposite electric polarisations. Their physics will serve to relate transient ferroelectric processes and the visible range optics. The same symmetry principle applies also to zigzag edges of graphene nano-ribbons which can be tested for the ferroelectricity.

**Host:** Prof. Shinobu Hikami

#### RIKEN-Osaka-OIST-Taiwan mathphys workshop 2015

- Date: March 2-4, 2015
- Venue: OIST Main Campus, B503, Lab.1

**Seminar: **

- Date: March 5, 2015 at 10:00 -11:00
- Venue: C016, Lab1, OIST
- Speaker: Dr. Tatsuo Azeyanagi (LPTENS, Paris)

**Title**: Anomalies, Chern-Simons Terms and Black Hole Entropy

**Abstract: ** Quantum anomalies enable us to access to some important information about quantum field theories in a robust way. Recently, the hydrodynamic limit of the systems with the anomalies has been actively investigated, together with its dual holographic description by gravitational theories with Chern-Simons terms. In this presentation, I will start with a review on the effect of the anomalies in the hydrodynamic limit of conformal field theories. Then I would like to explain how the beautiful property of Chern-Simons terms helps us to compute in detail various quantities relevant to the anomalies through the dual gravitational description. I will also discuss the implication of our analysis to microscopic counting of black hole entropy in higher dimensions.

**Topotronics2015**: The 1st International Workshop on the Topological Electronics, OIST B250, March 9-11, 2015

**MCM2015**: Moduli Space, Conformal Field Theory and Matrix Model, OIST C209, March 16-18, 2015 Program & Talks (PDF)

**RMT2013** - Fluctuations of Complex Systerms , OIST Seaside House & C209, October 27 - November 1 , 2013

**JIBW** : 3rd Japan-Israel Binational Workshop on Quantum Phenomena, OIST Seaside House, March 10 - March 13, 2013

**RMT2012** : OIST Spring Course on Random Matrix Theory for Complex Systems OIST Seaside House, April 15 - April 21, 2012