# Profile

**Masato Wakayama**

**Personal Data**

Dr. Sc. Masato WAKAYAMA

November, 1955 (Date of Birth)

**Institutional Data**

Executive Vice President

Kyushu University

Professor

Institute of Mathematics for Industry, Kyushu University

Professor

Graduate School of Mathematics, Kyushu University

Distinguished Professor,

Kyushu University

**Research & Education Projects**

2006-2011.3 | Program Leader, Challenge to Open Problems in Mathematics and Mathematical Sciences, "The Kyushu University Research Superstar Program (SSP), 2006, Special Coordination Funds for Promoting Science and Technology, MEXT". |

2007-2010.3(Expiration) | Program Leader, GP Program "Training Program of Ph.D. and new Master's in Mathematics as Required by Industry", MEXT. |

2008-2013.3 | Program Leader, Global COE Program "Education and Research Hub for Mathematics-for-Industry", MEXT. |

2009 | Program Leader, Investigation project commissioned by MEXT in 2009:“Investigation and estimation of promotion of cooperation of mathematics and mathematical science with other fields --- For examination of the fourth governmental science & technology master plan” |

2010-2015 | Program Leader, Graduate School of Mathematics “Special Project Fund of Graduate Education for Mathematics” |

2014-2019 | Member of a research project JST CREST, Mathematical Modelling for Next-Generation Cyptography |

# Grant-in-Aid for Scientific Research (Supported by MEXT & JSPS) and JST/CREST

2016-2018.3 Grant-in-Aid for Scientific Research(C), MEXT, Japan | Development and Deepening of Number Theory and Representation Theory through Mathematical Analysis of Quantum Interaction Models |

2014.10-2020.3 CREST(Core Research of Evolutional Science & Technology), JST, Japan | Mathematical Modelling for Next-Generation Cryptography |

2013.4-2017.3, Challenging Exploratory Research, MEXT, Japann | A new development of studies on stochastic process, statistical distributions and representation theory |

2010.10-2016.3, CREST(Core Research of Evolutional Science & Technology), JST, Japan | Mathematics for Expressive Image Synthesis |

2009-2014.3,Grant-in-Aid for Scientific Research(B), MEXT, Japan | Mathematics for Non-commutative Harmonic Oscillators and Representation Theory of α-determinants |

2006-2009.3, Grant-in-Aid for Exploratory Research, MEXT, Japan | Invariant Theory of α-determinants and Zeta Functions for Matrix Variable |

2003-2007.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan | Study of Zeta Functions and Duality --- “Infinite Sum = Infinite Product” Based on the Trace Formulas Viewpoint |

2001-2004.3, Grant-in-Aid for Exploratory Research, MEXT, Japan | Study of Casimir Effects --- from Casimir Elements and Prime Geodesic Theorems |

1999-2003.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan | Duality Based on Trace Formulas --- Applications of "Infinite Product=Infinite Sum" Type Formulas and Representation Theory |

1997-1999.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan | Duality Based on Trace Formulas --- Study on "Infinite Product=Infinite Sum" Type Formulas |

1996-1997.3, Grant-in-Aid for Scientific Research(B), MEXT, Japan | Study on "Infinite Product=Infinite Sum" Type Formulas, Based on Evaluation of Determinants |

**Academic Degree**

Doctor of Science (Hiroshima University, 1985)

**Research Interests**

Representation theory

Automorphic forms and zeta functions

Harmonic analysis

**Research Interests**

・ Casimir effects, Prime Geodesic Theorems

・ Invariant theory of classical and quantum groups

・ Minor summation formula of Paffians and its aplications to combinatrics and representation theory

・ Spectrum of Non-commutative harmonic oscillators and related arithmetic study (elliptic curves and automorphic forms)

・ Zeta regularized determinants and their applications to number theory

・ Representation and Invariant theory of α-determinants

・ Harmonic analysis on symmetric spaces and orthogonal polynomials

**Lectures in the past**

"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.

"Spectrum of non-commutative harmonic oscillators - Modular forms, representation theory and the Rabi model", Mathematical Institute, Leiden University, November 29, 2013.

"Plans for cooperation in the Pacific region - Activities of Mathematics for Industry ", EU-MATHS-IN, the Centre for Mathematics and Computer Science (CWI), Science Park 123, Amsterdam, November 27, 2013.

"Residual modular forms and curves, the quantum Rabi model, and discrete series representations from the study of spectral zeta functions of the NcHO.", Masato Wakayama, Geometric zeta functions and related topics, Saga University, October 30 to 31, 2013. (my talk is scheduled on October 31, 2013)

"A Lie theoretic proposal on algorithms for spherical harmonic lighting.", Masato Wakayama, Symposium: Mathematical Progress in Expressive Image Synthesis, Centennial Hall Kyushu University School of Medicine, October 21 to 23, 2013. (my talk is scheduled on October 22, 2013)

"Quantum Interaction Models and Number Theory.", Masato Wakayama, Zeta Functions in OKINAWA 2013, 沖縄コンベンションセンター, October 19 to 22, 2013. (my talk is scheduled on October 19, 2013)

"Aiming at New Industrial Mathematics", Masato Wakayama, The Japan Society for Industrial and Applied Mathematics 2013, ACROS Fukuoka, September 9 to 11, 2013. (my talk is scheduled on September 10, 2013)

"Hankel actions, holomorphic discrete series and Meixner-Pollaczek polynomials.", Masato Wakayama, JSPS-NWO Seminar "Analysis, Geometry and Group Representations for Homogeneous Spaces", Graduate School of Mathematics, Nagoya University, August 26 to 30, 2013. (my talk is scheduled on August 28, 2013)

April 22-26, 2013

"Analysis and Number Theory for Non-commutative Harmonic Oscillators"

i) Spectral problem of non-commutative harmonic oscillators

ii) The spectral zeta function of NcHO and modular forms

iii) Residual modular forms and related cohomology groups

Distinguished Lecture Series, Department of Mathematics, Indiana University, Bloomington

March 01, 2013

"Introduction to Mathematics for Industry" Seminar in Grenoble, Univ. Joseph Fourier

March 01, 2013

Basque Center of Applied Mathematics BCAM Seminar, "Analysis and arithmetic of non-commutative harmonic oscillators", Speaker:Masato WAKAYAMA, Director of Institute of Mathematics for Industry, Kyushu University, Japan

November 27, 2012

Masato Wakayama, Kyushu IMI, "Eichler cohomology groups for spectrum of NcHO's", Spectral analysis of non-commutative harmonic oscillators and quantum devices, Kyushu University

"Remarks on parity of eigenfunctions of NcHO via Heun DE", Zetas and Limit Laws in OKINAWA 2012, Festone, Ginowan, OKINAWA, November 18, 2012

"Multivariate Meixner-Pollaczek polynomials and an application"(Jun 22, 2012, Research Institute for Mathematical Sciences, Kyoto University)

"Multivariate Meixner-Pollaczek Polynomials", Sala de Seminarios (Jun 6, 2012, Centro de Modelamiento Matematico, Chile)

"Long-term-internship for PhD students in Mathematics in Japan -status and procedure in the course-curriculum, joint research activities " (Jun 6, 2012, Centro de Modelamiento Matematico, Chile)

"Higher regularizations for zeros of cuspidal automorphic L-functions of GL(d)", Mathematical Society of Japan 2012 (March 29, 2012, Tokyo University of Science) (M. Wakayama, Y. Yamasaki)

"Γ(2)-modularity appealing at the special values of spectral zeta function for the NcHO", Mathematical Society of Japan 2012 (March 28, 2012, Tokyo University of Science (K. Kimoto, M. Wakayama)

"Remarks on geodesics for multivariate normal models", Mathematical Society of Japan 2012 (March 28, 2012, Tokyo University of Science)(T. Imai, A.Takaesu, M.Wakayama)

"Hermitian symmetric spaces of tube type and multivariate Meixner Pollaczek polynomials", Mathematical Society of Japan 2012 (March 28, 2012, Tokyo University of Science)(J. Faraut, M. Wakayama)

"Number theoretical approach to spectrum for non-commutative harmonic oscillators"( March 7-9, 2012, Workshop on "Avoided ? Crossing of Eigenvalue Curves" -- Non-commutative Harmonic Oscillator, Special Functions and Number Theory- , Inamori Center, Ito Campus, Kyushu University)

"Residual modular forms, Eichler cohomology and spectrum of non-commutative harmonic oscillators(February 27-28, 2012, "New Zealand Institute for Advanced Study + NZIAS.)

"Educational & Research with Mathematics-for-Industry in Japan", Mathematics and Statistics-in-Industry Study Group 2012 (February 6, 2012, RMIT University, Australia)

"Long-term-internship for PhD students in Mathematics in Japan ?status and procedure in the course-curriculum, joint research activities ", IDTC Research Methodology Workshop (February 3, 2012, RMIT University, Australia)

"Remarks on geodesics for multivariate normal models" , WIAS+MATHON joint seminar(January 9, 2012, WIAS+MATHON, Berlin)

"Non Commutative Harmonic Oscillators and Modular Forms" (January 6, 2012, Bologna University)

"Spectrum of Non-commutative Harmonic Oscillators and Modular Forms", Spectral and Scatteing Theory and Related Topics, (December 15, 2011, RIMS, Kyoto University)

"Negative Weight Modular Forms", Zetas and Limit Laws in OKINAWA 2011, (November 27, 2011, Festone, Okinawa)

"Non-commutative harmonic oscillators and Number theory.", Industrial mathematics Institute Johannes Kepler University Linz (February 18-19, 2011, Linz)

"On Mathematics-for-Industry", mathematics in the real world 2(December 17-18, 2010, TMU)

"Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials", Analysis, Geometry and Group Representations for Homogeneous Spaces (November 22-26, 2010, Lorentz Center, Leiden University)

"Non commutative Harmonic Oscillators and Number Theory", Non Commutative Geometry and Number Theory RIMS Special Year on Non Commutative Geometry (November 25-26, 2010, Department of Mathematics, Kyoto University)

"Number theory for Non commutative harmonic oscillators", 2010 Annual Symposium of Representation Theory (November 9-12, 2010, Izu, Shizuoka)

"Ramanujan's Delta and zeta regularizations",Zeta conference in Okinawa (November 6-9, 2010, Okinawa Convention Center)

"A Trial for PhD Education & Research in Mathematics for Industrial Technology ","Educational Interfaces between Mathematics and Industry (EIMI-study)"Lisbon, October 11-15, 2010

"Over the zeta regularized numeration", RIMS, Kyoto University, October 4-8, 2010

"A study on zeta regularized products", Representation theory; a link of Number theory-Analysis-Combinatorics, Ehime University, August 23-26

“Prime numbers can produce (elusive) Vacuum energy” The 5th Seminar on Algebra・Analysis・Geometry, Department of Mathematics, Kagoshima University, February 16, 2010

”Wreath type Group Determinants” Various problems and their perspectives in mathematical analysis−in memory of Professor Tetsuro Miyakawa −, Kanzawa University, February 20, 2010

"Representation Theory of α-determinants" Department of Mathematics, National University of Singapore,January 29, 2010

"Representation theory for α-determinants" Mathematical Sciences Colloquium, RIKEN, 6 July 2009

"Geodesics on a multivariate normal distribution- from Representation theoretic points of view", Workshop on Deeping and Expansion of Statisical Mechanical Informatics, Informatics on log P, Nishijin Plaza, Kyushu University, 16 June 2009.

Arithmetics on Non-commutative harmonic oscillators, International workshop on verified computations and related topics, University of Karlsruhe (TH), Germany, March 7-10, 2009.

Harmonic analysis on Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials, Zetas and Limit Laws in OKINAWA 2008, Okinawa Convention Center, November 22-25, 2008.

Special values of the spectral zeta functions for the non-commutative harmonic oscillator and elliptic curves, “International Conference on Arithmetic Geometry" Euler International Mathematical Institute, Saint Petersburg, June 2007.

Zeta Functions for the Spectrum of the Non-Commutative Harmonic Oscillators, "Conference on L-function" Nishijin Plaza, Kyushu University, February 2006.

**Professional Career**

1986.9 - 1989.3 | Full-Time Lecturer, Faculty of Engineering, Fukuyama University |

1989.4 - 1994.3 | Associate Professor, General Education, Tottori University |

1994.4 - 1997.6 | Associate Professor, Faculty of Science, Kyusyu University (1994.6- Graduate School of Mathematics) |

1997.9 - | Professor, Graduate School of Mathematics, Kyusyu University (2000.4- Facuty of Mathematics) |

2006.7 - 2010.7 | Dean, Faculty of Mathematics, Graduate School of Mathematics, Kyushu Univetsity |

2009.5- | Distinguished Professor, Faculty of Mathematics, Graduate School of Mathematics, Kyushu Univetsity |

2010.4- 2011.3 | Director, Mathematical Research Center for Industrial Technology, Kyushu Univetsity |

2010.10- 2014.9 | Vice-President, Kyushu Univetsity |

2010.10- 2011.9 | Director, Center for Research and Advancement in Higher Education, Kyushu University |

2011.4- 2014.9 | Director, Institute of Mathematics for Industry, Kyushu University |

2011.10- 2014.9 | Executive Vice Dean, Faculty of Arts and Science, Kyushu University |

2014.10- | Executive Vice President, Kyushu University |

1995.9 - 1996.8 | Visiting Fellow, Department of Mathematics, Princeton Univeisity |

1999.3 - 4, 2000.3 - 5, 2006.4 - 5 |
Guest Professor, University of Bologna |

2007.12 | Nice-Step-Researcher Award 2007（by MEXT) |