# Welcome to my Website !!

**Masato Wakayama**

NTT Institute for Fundamental Mathematics

3-9-11, Midori-cho, Musashino, Tokyo 180-8585

e-mail: masato.wakayama (at) ntt.com

wakayama (at) imi.kyushu-u.ac.jp

**Current post**

· Fundamental Mathematics Research Principal,

NTT Institute for Fundamental Mathematics, Nippon Telegraph and Telephone Corporation

· Principal Fellow, Center for Research and Development Strategy,

Japan Science and Technology Agency

· Professor Emeritus, Kyushu University

**Visiting Professor**

· Specially Appointed Professor, Tokyo Institute of Technology

· Guest Professor, Center for Data Science, Tokyo University of Science

· Guest Professor, Institute of Mathematics for Industry, Kyushu University

# Recent lectures

“Arithmetic study behind quantum interactions”

Mathematics Colloquium: Department of mathematics, University Illinois Urbana-Champaign,

March 5, 2024,

“Arithmetic Study Behind Spectra of Quantum Interactions”

Analysis and Mathematical Physics: Institute for Advanced Study, Princeton

March 1, 2024,

“Number Theory behind quantum interactions”

Algebraic geometry and Number theory Seminar, Department of Mathematics, University of Patova,

September 25, 2023,

“Representation and number theoretical aspects of the heat kernel for the quantum Rabi model”

More Anomalies in Partial Differential Equations - in honour of the 60th anniversary of Daniele Del Santo (Trieste) and

Alberto Parmeggiani (Bologna),

Castle of Bertinoro, Italy, (September 18 - 22, 2023),

September 22, 2023,

“The Mathematics behind Quantum Models with Fermion-Boson Interaction”

Seminar on Theoretical Physics, Institute of Physics, Augsburg University,

September 15, 2023,

“Consecutive eigenvalues distribution of asymmetric quantum Rabi models”

ICIAM 2023 Minisymposium, Quantification of Business Uncertainties through Industrial Mathematics:

Waseda University, Tokyo,

August 23, 2023,

“Quantum computation and its viewpoint from spectral zeta functions”

ICIAM 2023 Minisymposium, The mathematics of quantum interaction models:

Waseda University, Tokyo,

August 21, 2023,

“Number theory for certain quantum interaction models”

Tel Aviv Number Theory seminar, School of Mathematical Sciences, Tel Aviv University:

May 18, 2023,

“Algebraic/geometric problems for certain quantum interaction models”

PDE and Applied Mathematics Seminar, Faculty of Mathematics, Technion:

May 17, 2023,

“Geometric and algebraic problems on quantum interaction models”

Geometry Seminar, Department of Mathematics, Radboud University Nijmegen

March 6, 2023,

“Heat Kernels of Quantum Interaction Models for Quantum Computers”

SIAM Computational Science and Engineering 2023,

Part of MS302 Mathematics for Industry in the Asia Pacific Area - Part I of II

March 2, 2023,

“Algebra and geometry for quantum interaction models”

Colloquium, Department of Mathematics, University of Tübingen,

February 24, 2023,

“Covering of asymmetric quantum Rabi models and possible zeta problems.”

Symposium “Rabi and Spin Boson models” Kyushu University, Fukuoka

January 26, 2023,

“Geometric and algebraic problems on quantum interaction models”

RIMS Kyoto University (Workshop on “Fields theory and related Topics”), 16-18 January 2023

January 18, 2023,

“Quantum Interaction and Number Theory, Representation Theory – modular forms a bit beyond, infinite symmetric group, Fuchsian ODE”

French-Japan Web-Seminar on Painlevé equations and related topics

October 19, 2022,

“Quantum Interaction Models and Number Theory, Representation Theory”

Colloquium, Department of Mathematics, University of Bologna

October 5, 2022,

“Number Theory and Quantum Physics Based on Symmetry−Themes from Quantum Optics”

2022nd - NTT Communication Science basic Research Lab. Open House Lecture

June 2, 2022,

“Study on quantum interactions and number theory”

iTHEMS Coffee Meeting, RIKEN

March 4, 2022,

“Spectral Degeneracy and Hidden Symmetries – Asymmetric quantum Rabi model as an example”

Colloquium, College of Science and Engineering, Kanazawa University

January 14, 2021,

“Interaction models in quantum opticus, representation theory and Number theory”

iTHEMS Colloquium, RIKEN

April 10, 2020,

# Article publication information

M. Wakayama and I. Fesenko: Increasing investment in mathematics in changing times,

EMS Magazine No. 126 pp. 51-54, 2022. DOI: 10.4171/MAG/10

M. Wakayama, Number Theory and Quantum Physics Based on Symmetry-Themes from Quantum Optics,

NTT Technical Review, Vol. 20, No. 10, pp. 67-76, Oct. 2022. https://doi.org/10.53829/ntr202210fa10

# Forum "Math-for-Industry"2023

**Forum "Math-for-Industry"2023 in Fukuoka**

-MfI2.0-

Date: 29 August - 1 September 2023

Venue: Kyushu University Nishijin Plaza

-MfI2.0-

Date: 29 August - 1 September 2023

Venue: Kyushu University Nishijin Plaza

(2-16-23 Nishijin, Sawara-ku, Fukuoka 814-0002, JAPAN)

Website

# Forum "Math-for-Industry"2022

**Forum "Math-for-Industry"2022 in Australia**

-Mathematics of Public Health and Sustainability-

Date: 21 - 24 November 2022

Venue: La Trobe University City Campus

-Mathematics of Public Health and Sustainability-

Date: 21 - 24 November 2022

Venue: La Trobe University City Campus

(Level 2, 360 Collins Street, Melbourne, Australia)

Website

# Forum "Math-for-Industry"2021

**Forum "Math-for-Industry"2021 in Vietnam**

-Mathematics for Digital Economy-

Date: December 13-16, 2021

Venue: Vietnam Institute for Advanced Study in Mathematics

-Mathematics for Digital Economy-

Date: December 13-16, 2021

Venue: Vietnam Institute for Advanced Study in Mathematics

Website

# Forum "Math-for-Industry"2019

**Forum "Math-for-Industry"2019 in New Zealand**

-Mathematics for the Primary Industries and the Environment-

Date: November 18-21, 2019

Venue: Massey University, Albany campus North Shore, Auckland New Zealand

-Mathematics for the Primary Industries and the Environment-

Date: November 18-21, 2019

Venue: Massey University, Albany campus North Shore, Auckland New Zealand

Website

# International Symposium on Mathematics, Quantum Theory, and Cryptography

**International Symposium on Mathematics, Quantum Theory, and Cryptography**

Date: September 25(Wed)- 27(Fri),2019

Venue: Kyushu University Ito campus, IMI auditorium, W1-D413

Organizer: CryptoMathCREST

Date: September 25(Wed)- 27(Fri),2019

Venue: Kyushu University Ito campus, IMI auditorium, W1-D413

Organizer: CryptoMathCREST

Website

# ANDE2019 (APPLICATIONS OF NONLINEAR DIFFUSION EQUATIONS 2019)

**【Invited talk】“Heat kernel of the quantum Rabi mode”**

Date: June 22(Sat), 2019

Venue: La Trobe University、Melbourne

Date: June 22(Sat), 2019

Venue: La Trobe University、Melbourne

# Forum "Math-for-Industry"2018

**Forum "Math-for-Industry"2018 in Shanghai**

-Big Data Analysis, AI, Fintech, Math in Finances and Economics-

Date: November 17 to 21, 2018

Venue: Fudan University, Shanghai, ChinaS

-Big Data Analysis, AI, Fintech, Math in Finances and Economics-

Date: November 17 to 21, 2018

Venue: Fudan University, Shanghai, ChinaS

Website

# Forum "Math-for-Industry"2015

Forum "Math-for-Industry" 2015

The role and importance of mathematics in innovation

Date : October 26 to 30, 2015

Venue : Kyushu University Ito campus, IMI auditorium

Website

# Proceedings of Forum "Math-for-Industry" 2014

Applications + Practical Conceptualization + Mathematics = fruitful Innovation

Editors: Anderssen, B., Broadbridge, P., Fukumoto, Y., Kajiwara, K., Takagi, T., Verbitskiy, E., Wakayama, M.

Website

# MEIS2014

Symposium MEIS2014:

Mathematical Progress in Expressive Image Synthesis

Date: 12-14 November 2014

Venue: Nishijin Plaza Kyushu University, Fukuoka, Japan

Website

# Forum "Math-for-Industry" 2014

Forum "Math-for-Industry" 2014"

Applications + Practical Conceptualization + Mathematics = fruitful Innovation

October 27 to 31, 2014

Venue: Nishijin Plaza, Fukuoka

2-16-23 Nishijin, Sawara-ku, Fukuoka City, JAPAN

Website

# "Mathematics and Physics of Interacting Quantum Systems (MPIQS)"

"Mathematics and Physics of Interacting Quantum Systems (MPIQS)"

Date: October 23-24, 2014

Venue: Kyushu University

Website

Organizer:

Fumio Hiroshima(Kyushu University)

Enrique Solano(University of the Basque Country UPV/EHU)

Masato Wakayama(Kyushu University)

# Past Lectures

"Analysis of quantum interaction models"

"Analysis of the quantum harmonic oscillator - oscillator representation of sl(2),

Heat kernel, Riemann zeta function, Apery numbers,"

「Colloquium & Pre-colloquium lectures (for post graduate students」

Date: February 25,27 , 2019

Venu: Department of Mathematics, University of Tübingen

"Mathematical problems around the quantum Rabi model"

「 Workshop on Mathematical Developments Related to the Quantum Rabi Model 」

Date: January 29, 2019

Venue: Mathematical Sciences Institute, The Australian National University

【Invited talk】“Heat kernel of the quantum Rabi mode”

「Applications of Nonlinear Diffusion Equations 2019」

Date: June 22(Sat), 2019

Venue: La Trobe University, Melbourne

“A sign of the beginning for connecting photons and lattices - symmetry in quantum interactions”

「Symposium on representation theory 2018 」

Date: November 17 to 21, 2018

“Non-commutative harmonic oscillator and quantum rabi model - A sign of the beginning for connecting photons and lattices”

「Zeta Functions in OKINAWA 2018 」

Date: October 24 to 26, 2018

Venue: Okinawa Convention Center (Ginowan, Okinawa)

“Activities on mathematics for industry in Japan and Asia-Pacific region”

「Future and Emerging Mathematical Technologies in Europe 」

Date: December 11 to 15, 2017

Venue: Lorentz Center, Netherlands

“Spectral determinants of the asymmetric quantum Rabi models”

Zeta Functions in Okinawa 2017

Date: 18/November/2017,

Venue: Okinawa Convention Center (Ginowan, Okinawa)

“Spectrum of the asymmetric quantum Rabi models and zeta regularized product”

Zeta functions and trace formulas in Fukuoka

Date: October 12 to 14, 2017,

Venue: Lecture Room M W1-C-513 , West Zone 1, Ito campus, Kyushu University

“Mathematics for Industry in Japan”

International Seminar on Mathematics in Industry 2017

Date: 1/August/2017,

Venue: Pulai Springs Resort, Malaysia

“Spectral degeneracies in asymmetric quantum Rabi models and representations”

Integrability in Low-Dimensional Quantum Systems

AMSI (Australian Mathematical Sciences Institute) Conference

Date: 12/July/2017,

Venue: University of Melbourne

“Symmetry and spectral degeneracies in asymmetric quantum Rabi models”

Spectral analysis of Quantum Rabi models

Date: 10/March/2017,

Venue: Lecture Room M W1-C-616 , West Zone 1, Ito campus, Kyushu University

“Symmetry of asymmetric quantum Rabi models”

Date: 28/February/2017,

Venue: Department of Mathematics, University of Bologna

"Endeavors for Mathematics for Industry in Japan"

9th Ludwig Boltzmann Symposium Tokyo 2017

Date: 16/February/2017

Venue: Austrian Embassy Tokyo

International Workshop on Ultra-Strong Light-Matter Interactions: theory and applications to quantum information

Date: 19/September/2016 - 21/ September/2016,

Venue: University of the Basque Country, Bilbao, Spain

"Representation theoretic approach to the spectrum of quantum Rabi or its generalized models",

Kyushu IMI joint research center for advanced and fundamental math-for-industry

Mathematical quantum field theory and related topics

IMI Kyushu University West 1 building D-413 Auditrium，6 /June/2016 - 8/June/2016,

Japan-Australia University Symposium 2015

Towards Successful Partnerships:Learning from Experiences

Date: 24 November 2015, Venue: The University of Sydney

"Endeavors for Mathematics for/in Industry in Japan", Industrial Mathematics Awareness Week,

COEX Hall, Seoul, Korea 22 October, 2015

Website (in Korean only)

"Can representation theory contribute quantum optics?"

Zeta functions in Okinawa 2015,

10-12 October 2015

Website

"Mathematics-for-Industry and Industry-for-Mathematics"ICIAM2015,

China National Convention Centre, 8-14 August, 2015

Website

"Quantum Rabi's model and Non commutative Harmonic Oscillators, and Number Theory and Representation Theory",

RIMS Workshop, RIMS, Kyoto University, June23-26,2015

"Spectrum of the quantum Rabi model and representation theory", Workshop on Probabilistic models with determinantal structure, Kyushu University, April 30-May 1, 2015

Website

"Quantum Rabi's model and representation theory" Department of Methematics, University of Bologna, Wednesday 25 February, 2015

"Activities of Mathematics for Industry" University of Bologna, Tuesday 24 February 2015

"Quantum Rabi's model and non-commutative harmonic oscillators", Kyoto University, October 7,2014

"Quantum Rabi's model and non-commutative harmonic oscillators",

Mathematical Quantum Field Theory and Related Topics, RIMS, Kyoto University,

October 6 to 8, 2014 (Wakayama's lecture is scheduled on Oct. 7, 2014).

"Lie Algebra Representations and the Quantum Rabi Model - A View from Non-Commutative Harmonic Oscillators and Heun ODEs.", Mathematical and Physical Aspects of Interacting Quantum Systems and Models

Seminar Room 7, Institute of Mathematics for Industry, Kyushu University, October 23 to 24, 2014

(Wakayama's talk is scheduled on Oct. 24).

"Quantum Rabi's model and non-commutative harmonic oscillators-between number theory and physics",

Colloquium, Department of Mathematics , University of Hawaii at Manoa, September 5, 2014.

"An introduction and application of Lie theory-a theme from spherical harmonics",

Seminar for undergraduates, Department of Mathematics,

University of Hawaii at Manoa, September 3, 2014.

"Non-commutative harmonic oscillators and the Rabi model", RIMS Workshop, RIMS, Kyoto University, June 24-28, 2014.

"Activities of Mathematics for Industry", University Montpellier 2, Feb. 26, 2014.

"An application of Lie theory to computer graphics via spherical harmonics", Berliner Colloquium fur wissenschaftliche Visualisierung, Zuse-Institut Berlin (ZIB), Germany, Feb. 28, 2014.

"Activities of Mathematics for Industry", Zuse-Institut Berlin (ZIB), Germany, Mar. 1, 2014.

# Forum "Math-for-Industry" 2013

Forum "Math-for-Industry" 2013 "

The Impact of Applications on Mathematics"

Venue: Nishijin Plaza, Fukuoka

2-16-23 Nishijin, Sawara-ku, Fukuoka City, JAPAN

FMI2013 Website

# Forum "Math-for-Industry" 2012

Forum "Math-for-Industry" 2012 "Information Recovery and Discovery"

Date: October 22 to October 26, 2012

Place: Fukuoka International Congress Center

Organiging Committee

Yasuhide Fukumoto (IMI, Kyushu University)

Osamu Saeki (IMI, Kyushu University)

Ryuei Nishii (IMI, Kyushu University)

Tsuyoshi Takagi (IMI, Kyushu University)

Tim Hoffmann (TU Berlin)

Masato Wakayama (IMI, Kyushu Univesrity)

# Mathematics for Industry:

Biological and climatic aspects - a Joint Workshop of IMS and
IMI -

Mathematics for Industry: Biological and climatic aspects - a Joint Workshop of IMS and IMI-

Program date: September 3 to 7, 2012.

Organized by:

Robert S.Anderssen (CSIRO)

Kim Chuan Toh (Department of Mathematics, NUS)

Tomoyuki Shirai (Institute of Mathematics for Industry, Kyushu University)

Kenji Kajiwara (Institute of Mathematics for Industry, Kyushu University)

Masato Wakayama (Institute of Mathematics for Industry, Kyushu University)

Website

# Workshop on "Avoided ? Crossing of Eigenvalue Curves"

-- Non-commutative Harmonic Oscillator, Special Functions and Number Theory--

"Avoided ? Crossing of Eigenvalue Curves"

-- Non-commutative Harmonic Oscillator, Special Functions and Number Theory--

Website

Program Date: March 7 to 9, 2012.

Program Place: IMI, Kyushu University

Organized by:

Masato WAKAYAMA(Institute of Mathematics for Industry, Kyushu University)

Fumio HIROSHIMA (Institute of Mathematics for Industry, Kyushu University)

# Study Group Workshop 2011

August 1-3, Faculty of Mathematics, Kyushu University

August 8, 9 (tentative schedule), Graduate School of Mathematical Sciences, the University of Tokyo

Study Group Workshop 2011

August 1-3, Faculty of Mathematics, Kyushu University

August 8, 9 (tentative schedule), Graduate School of Mathematical Sciences, the University of Tokyo

SGW2011 Website

# Forum "Math-for-Industry" 2011

"TSUNAMI - Mathematical Modelling"

Using Mathematics for Natural Disaster Prediction, Recovery and Provision for the Future,

October 24-28, 2011, East-West Center, University of Hawaii

**Forum "Math-for-Industry" 2011**

"TSUNAMI - Mathematical Modelling" Using Mathematics for Natural Disaster Prediction, Recovery and Provision for the Future, October 24-28, 2011, East-West center, University of Hawaii

FMI2011 Website

"TSUNAMI - Mathematical Modelling" Using Mathematics for Natural Disaster Prediction, Recovery and Provision for the Future, October 24-28, 2011, East-West center, University of Hawaii

FMI2011 Website

We would like to express our deepest sympathy to those affected by the terrible earthquake and tsunami that hit the Tohoku region in Japan in March, 2011, and by the succeeding Fukushima nuclear power plant accident.

The main topic of our forum is motivated by this catastrophic disaster: we sincerely feel that it is our responsibility to make use of mathematics for predicting natural disasters, recovering from catastrophic events, and making provision for the future. Thus, we have thought that the Forum "Math-for-Industry" in this year should be fully devoted to discussing a large variety of possibilities for using mathematics to these purposes. There are additional reasons for this choice. First, this year we expected participants (including speakers) to come from New Zealand (where there was a big earthquake in February) and Chile (also the location of a big earthquake last year, whose related tsunamis reached Japan, on the opposite side of the Pacific Ocean). Second, the word "tsunami" ("津波" =harbor wave (in Japanese)) made its way into the English language through Hawai'i. After the Hawai'i islands suffered from the big tidal waves caused by the 1946 earthquake near Alaska, the first-generation Japanese immigrants in Hawai'i introduced the spoken word into the English language.

Our objective is to consider what help can mathematics provide against natural disasters: to understand their fundamental mechanisms; to increase the accuracy of predictions, to minimize damages and risks; to establish more robust and efficient social systems for recovery; and so on.

Thus, the lecture theme includes the following research topics: tsunami, earthquake, environmental pollutions, logistics, optimization, control theory, statistics and data analysis, information security, CG visualization, PDE, inverse problems, numerical analysis, fluid dynamics, integrable systems (solitons), geometry and topology, etc.

On this occasion, we will inaugurate the Asian Consortium of Mathematics for Industry (ACMI) in the East Asian and Pacific areas, an idea planned since the fall of 2009. ACMI aims to create a strong international platform for development of worldwide activities involving mathematics for the industry.

# Lectures

"From the Euler operator to multivariate Meixner-Pollaczek polynomials",

National University of Singapore (June 24, 2011, Singapore)

# Forum "Math-for-Industry" 2010

Information security, visualization, and inverse problems, on the basis of optimization techniques,

October 21-23, 2010, Fukuoka

**Forum "Math-for-Industry" 2010**

Information security, visualization, and inverse problems, on the basis of optimization techniques, October 21-23, 2010, Hilton Fukuoka, Sea Hawk

Study Group Workshop

October 25-29, 2010,

Graduate School of Mathematical Sciences, The University of Tokyo

Information security, visualization, and inverse problems, on the basis of optimization techniques, October 21-23, 2010, Hilton Fukuoka, Sea Hawk

Study Group Workshop

October 25-29, 2010,

Graduate School of Mathematical Sciences, The University of Tokyo

**▼“FMI2010”**

At the 3-day workshop, we will mutually relate and discuss the three topics: the information security, visualization, inverse problems, on the basis of optimization techniques, and at the succeeding 5-day study group, after proposals of concrete real problems from companies and public institutes, we will work towards solutions by divided groups of participants.

# “Ever-Expanding Mathematics--- Expectations from the Society”

▼“Report”**“Ever-Expanding Mathematics--- Expectations from the Society”**

DATE: 22th (afternoon)-23th February 2010

PLACE: The University of Tokyo, Komaba Campus, Graduate School of Mathematical Sciences, The Main Auditorium

Implementing Organizations:

Kyushu University (Main), The University of Tokyo, The Mathematical Society of Japan, Nippon Steel Corporation

Support Organizations:

The Japan Society for Industrial and Applied Mathematics, Japan Federation Statistical Science Associations

DATE: 22th (afternoon)-23th February 2010

PLACE: The University of Tokyo, Komaba Campus, Graduate School of Mathematical Sciences, The Main Auditorium

Implementing Organizations:

Kyushu University (Main), The University of Tokyo, The Mathematical Society of Japan, Nippon Steel Corporation

Support Organizations:

The Japan Society for Industrial and Applied Mathematics, Japan Federation Statistical Science Associations

▼“Website”

# CCRH2009

**Casimir Force, Casimir Operators and the Riemann Hypothesis**

9-13 November, 2009

@ Nishijin Plaza, Kyushu University, Fukuoka, Japan

9-13 November, 2009

@ Nishijin Plaza, Kyushu University, Fukuoka, Japan

The year 2009 marks the 100

^{th}birthday of Casimir and the 150

^{th}birthday of the Riemann hypothesis. Actually the paper in which Riemann proposed the hypothesis was published in November 1859. It was also the year when he was appointed as full-professor at Göttingen. Casimir, known for the Casimir force in physics and Casimir operators in mathematics, was director of Philips research for a long time in his career.

Casimir got his PhD in November 1931 at Leiden University and the named operators appeared in his thesis. He is remembered for his outspoken opinion on the importance of fundamental science for industry. There is a nice connection between Casimir and Riemann.

The Casimir force was first proven to exist theoretically, using the analytic continuation of the Riemann zeta function. Recently the force was measured experimentally.

▼ccrh2009 Website

▼ccrh2009Program