Tsujii Masato | Last modified date：2018.05.18 |

Graduate School

Undergraduate School

Homepage

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English version .

Academic Degree

Doctoral degree of Science

Country of degree conferring institution (Overseas)

No

Field of Specialization

Mathematics

ORCID(Open Researcher and Contributor ID)

https://orcid.org/0000-0002-2332-0870

Total Priod of education and research career in the foreign country

01years00months

Outline Activities

My research area is dynamical system theory(the qualitative theory of ordinary differential equations). I study transfer operators associated to dynamical systems by using methods of functional analysis such as Fourier analysis and semi-classical analysis. My main target of research now is the geodesic flows on negatively curved manifold, which is a type of chaotic hyperbolic flow, and the corresponding transfer operators and semi-calsscial zeta funtions.

For education, I gave lectures on basic calculus and linear algebra for freshmen, on comlex function theory for senior students in the technology depatrment and also for students in mathematics department. In the lectures, I tried to let the student understand that mathematics is available in many aspects of real life and also in many braches of science. I also tried to present mathematics as a type of exact science.

For contribution to the society, I am convinced that my main contribution should be to educate the student and develop their talents. I am organizing the ESSP program for talented high school student in science.

For education, I gave lectures on basic calculus and linear algebra for freshmen, on comlex function theory for senior students in the technology depatrment and also for students in mathematics department. In the lectures, I tried to let the student understand that mathematics is available in many aspects of real life and also in many braches of science. I also tried to present mathematics as a type of exact science.

For contribution to the society, I am convinced that my main contribution should be to educate the student and develop their talents. I am organizing the ESSP program for talented high school student in science.

Research

**Research Interests**

- Transfer operators for geodesic flows and the semi-classical zeta function

keyword : geodesic flow, transfer operators, the semi-classical zeta functions

2010.04～2015.03. - Functional analytic methods in dynamical systems theory

keyword : hypebolic dynamical systems, transfer operators, dynamical zeta functions

2006.04～2010.03.

**Academic Activities**

**Papers**

**Presentations**

1. | 辻井 正人, Gutzwiller-Voros zeta functions for geodesic flows on negatively curved manifolds, The third international conference on the dynamics of differential equations, 2017.12. |

2. | 辻井 正人, On cohomological theory of dynamical zeta functions, Spectral geometry, graphs and semiclassical analysis, 2017.12. |

3. | 辻井 正人, Exponential decay of correlations for Anosov flows, Analytical aspects of hyperbolic flows, 2017.07. |

4. | 辻井 正人, The spectrum of semi-classical transfer operator for expanding-semi flows, Tokyo–Berkeley Mathematics Workshop Partial Differential Equations and Mathematical Physics, 2017.01. |

5. | 辻井 正人, Exponential mixing for generic volume-preserving Anosov flows in dimension three, Analytical Methods in Classical and Quantum Dynamical Systems, 2016.07. |

6. | 辻井 正人, Exponential mixing for generic volume-preserving Anosov flows in dimension three, Mixing flows and averaging method, 2016.04, [URL]. |

7. | 辻井 正人, The spectrum of semi-classical transfer operator for expanding semi-flows with holes, Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism, 2016.03, [URL]. |

8. | Tsujii Masato, The error term of The prime Orbit Theorem for expanding semi-flows, School and Conference on Dynamical Systems, 2015.08, [URL]. |

9. | Tsujii Masato, Spectrum of transfer operators for expanding semi-flows., 国際数学者会議（ICM2014）サテライト会議 Dynamical systems and related topics, 2014.08. |

10. | Tsujii Masato, Resonances for geodesic flows on negatively curved manifolds, 国際数学者会議（ICM2014）, 2014.08, We report some recent progress in the study of geodesic flows on negatively curved manifolds (or more generally contact Anosov flows). We consider one-parameter groups of transfer operators associated to the flows and investigate the spectra of their generators. The main ingredients are the recent results about a band structure of the discete spectrum, which are obtained in the authors’ joint works.. |

11. | 辻井 正人, Geodesic flows on negatively curved manifolds and the semi-classical zeta function, Measurable and Topological Dynamical Systems, Keio 2013, 2013.12, [URL], We consider the semi-classical (or Gutzwiller-Voros) zeta functions for $C^\infty$ contact Anosov flows. Analyzing the spectra of the generators for some transfer operators associated to the flow, we prove, for any $\tau>0$, that its zeros are contained in the union of the $\tau$-neighborhood of the imaginary axis, $|\Re(s)|<\tau$, and the region $\Re(s)<-\chi_0+\tau$, up to finitely many exceptions, where $\chi_0>0$ is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law. . |

12. | Tsujii Masato, Spectrum of geodesic flow on negatively curved manifold, Hyperbolicity and Dimension, 2013.12, [URL], We consider the one-parameter families of transfer operators for geodesic flows on negatively curved manifolds. We show that the spectra of the generators have some "band structure" parallel to the imaginary axis. As a special case of "semi-classical" transfer operator, we see that the eigenvalues concentrate around the imaginary axis with some gap on the both sides. Those eigenvalues appear as the zeros of the so-called semi-classical (or Gutzwiller-Voros) zeta functions. These results are obtained as application of some ideas in the semi-classical analysis.. |

13. | Tsujii Masato, The semi-classical zeta function, ICTP-ESF School and Conference in Dynamical Systems, 2012.06, We discuss about analytic properties of the so-called semi-classical zeta functions for geodesic flows on the closed manifold with negative sectional curvature. The main results is that the concentration of its zeros along the imaginary axis, which is a generalization of the classical results of Selberg. . |

14. | Decay of correlations and dynamical zeta functions for hyperbolic flows. |

**Membership in Academic Society**

- Japan Mathematical Society

**Awards**

- Functional analytic methods in smooth ergodic theory.

Educational

**Educational Activities**

For education, I am in charge of lectures on basic calculus and linear algebra for freshmen, those for senior students in the technology depatrment and those for students in mathematics department in usual years. This year, I teach Linear Algebra for the first year students for two classes and Basic mathematics 2 for the second year students in mathematics department.

Social

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