Takashi Hara | Last modified date：2015.10.29 |

Graduate School

Undergraduate School

Administration Post

Dean of the Faculty of Mathematics

Homepage

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This web page is on my research and teaching activities. Contains list of publications and some of my lecture notes for my class..

Academic Degree

Doctor of Philosophy

Field of Specialization

Mathematical Physics

Outline Activities

On research: I have been studying crical phenomena and continuum limits of stitistical mechanical models in a mathematically rigorous way. These problems arise as a result of cooperative phenomena in systems of infinite degrees of freedom. Mathematically, these phenomena can be interpreted as a consequence of (yet unknown) limit theorems in probability theory. Currently, I am using Renormalzation Group Methods to study these problems. Recently, I am also studying problems related to foundations of quantum statistical mechanics.

Education: Have taught a lot of basic courses on undergraduate and gradute levels. Also acted as thesis advisors based on my

research interests explained above.

Education: Have taught a lot of basic courses on undergraduate and gradute levels. Also acted as thesis advisors based on my

research interests explained above.

Research

**Research Interests**

- Foundations of Quantum Statistical Mehanics

keyword : Quantum Statistical Mechanics

2012.04～2017.12. - critical behavior of classical spin systems

keyword : renormalization group, spin systems, critical behavior, low-temperature phase

2011.09～2013.05. - Critical Behaviour of four dimensional self-avoiding walk

keyword : critical phenomena, self-avoiding walk

2005.01. - Critical behaviour of q-lattice animals

keyword : critical phenomena, q-lattice animals, percolation

2004.01. - Critical behaviour of hierarchical self-avoiding walk

keyword : critical phenomena, hierarchical model, renormalization group, self-avoiding walk

2002.04. - Critical Behaviour and Continuum Limits of Hierarchical Ising Model

keyword : critical phenomena, quantum field theory, hierarchical model, Ising model

1998.04～2002.02. - Asymptotic behaivour of 2-point functions for stochastic geometric models

keyword : critical phenomena, percolation, self-avoiding walk, 2-point function, critical point, lace expansion

1998.09～2004.08.

**Academic Activities**

**Papers**

1. | Takashi HARA,Decay of Correlations in Nearest-Neighbor Self-Avoiding Walk, Percolation, Lattice Trees and Animals,Annals of Probability,vol. 36, pp.530-593,2008.03. |

**Presentations**

1. | q-Lattice Animals. |

2. | Decay of Correlations in Nearest Neighbour Self-Avoiding Walk, Percolation, Lattice Trees and Animals. |

Educational

**Educational Activities**

The following list contains courses taught at Kyushu University, Nagoya University, Tokyo Institute of Technology.

For undergraduates: Calculus, Linear Algebra, Complex Analysis, Vector Analysis, Functional Analysis (basics only), Theory of ordinary differential equations, Theory of Electricity and Magnetism, Mathematical Methods in Physics, Quantum Mechanics (advanced level), Introduction to Probability Theory

For graduates: Introduction to Probability Theory, Critical Phenomena and Quantum Field Theory, Special Lectures in Mathematical Physics (Rigorous Analysis of Critical Behaviour, Theory of Renormalization Group)

In addition to tbe above, I have been thesis advisors for several graudate students.

For undergraduates: Calculus, Linear Algebra, Complex Analysis, Vector Analysis, Functional Analysis (basics only), Theory of ordinary differential equations, Theory of Electricity and Magnetism, Mathematical Methods in Physics, Quantum Mechanics (advanced level), Introduction to Probability Theory

For graduates: Introduction to Probability Theory, Critical Phenomena and Quantum Field Theory, Special Lectures in Mathematical Physics (Rigorous Analysis of Critical Behaviour, Theory of Renormalization Group)

In addition to tbe above, I have been thesis advisors for several graudate students.

**Other Educational Activities**

- 2013.09,I have given a series of lectures in "Mathematical Physics 2013", held in Tokyo. .
- 2013.06,I have given a series of lectures at the Feza Gursey Summer School on Mathematical Physics held in Istanbul. .
- 2005.08,Have given a lecture in an extramural course, organized by the Faculty of Mathematics.

Social

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