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### ABOUT AMS

The essence of science is to derive principles from observations, thus
revealing simple structures behind what appears to be a complex
phenomenon. Mathematical sciences, in particular, use mathematical
approaches to investigate "mathematical models", which are derived
experimentally. The modern frontier of mathematical sciences considers
various new mathematical models including those for biological and
social phenomena, in addition to more traditional ones in natural
sciences. These models are investigated through analytical approaches
as well as numerical simulations for understanding of the
phenomena. The knowledge thus obtained is employed to develop
innovative technologies or to predict the future, while new
methodologies are devised for deeper understanding of phenomena.
Our department pays particular attention to large scale and/or highly
non-linear complex phenomena in its research and
education. Particularly in education, we aim at providing students
with both scientific viewpoints which help them understand principles
as well as engineering viewpoints which are useful in solving real
problems in manufacturing. These double viewpoints will give students
comprehensive perspectives over science and engineering in
mathematical sciences. We look forward to ambitious applicants
interested in advanced mathematical sciences.

### Division of Applied Analysis

Professor
ISO, Yuusuke, D.Sc.(Kyoto Univ.),
Numerical Analysis,
Mathematical Analysis of Inverse and Ill-posed Problems
Professor
KIGAMI, Jun, D.Sc.(Kyoto Univ.),
Analysis and Dynamical System,
Analysis on Fractals
Associate Professor
FUJIWARA, Hiroshi, Ph.D.(Informatics, Kyoto Univ.),
Numerical Analysis of Inverse and Ill-Posed Problems,
Computer Arithmetic
Associate Professor
CROYDON, David, Ph.D.(Univ. Oxford),
Probability theory
Senior Lecturer
KUBO, Masayoshi, D.Sc.(Kyoto Univ.),
Mathematical Analysis of Inverse and Ill-posed Problems,
Numerical Analysis
Senior Lecturer
SHIRAISHI, Daisuke, Ph.D. (Science, Kyoto Univ.),
Probability Theory

### Division of Nonlinear Physics

Professor
AOYAGI, Toshio, D.Sc.(Kyoto Univ.), Theory of Neural Networks,
Nonlinear Dynamics, Nonequilibrium Statistical Physics
Associate Professor
TERAMAE, Jun-nosuke, D.Sc.(Kyoto Univ.), Theory of Neural Networks
Senior Lecturer
MIYAZAKI, Syuji, D.Sc.(Kyushu Univ.), Large Deviation Theoretical Analysis,
Spatiotemporal Dynamics
Assistant Professor
HARADA, Kenji, D.Eng.(Kyoto Univ.), Statistical Physics, Computational Physics
Assistant Professor
TUTU, Hiroki, D.Sc.(Kyushu Univ.), Ordering Process and Pattern Formation

Current research activities cover the following fields:

Group of Nonlinear Dynamics and Computational Physics

(Senior Lecturer: MIYAZAKI Syuji, Assistant Professor: HARADA Kenji）

- Nonlinear dynamics and chaos
- Nonequilibrium statistical physics
- Condensed matter theory
- Numerical algorithm for many-body problem : Monte Carlo, tensor network

Group of Nonequilibrium Physics and Theoretical Neuroscience

(Professor: AOYAGI Toshio, Associate Professor: TERAMAE Jun-nosuke, Assistant Professor: TUTU Hiroki)

- Theoretical neural science (mathematical modeling of the brain)
- A collection of dynamical systems linked through a network with evolving structure (neurons, social networks, etc.)
- Analysis of rhythm phenomena (entrainment transition)
- Stochastic modeling for molecular machines
- Modeling social systems based on game dynamics on networks

### Division of Applied Mathematical Sciences

Professor
NISHIMURA, Naoshi, D.Eng.(Kyoto Univ.),
Computational Mechanics, Applied Mechanics,
Boundary Integral Equation Methods, Fast Multipole Methods
Associate Professor
YOSHIKAWA, Hitoshi, D.Eng.(Kyoto Univ.),
Computational Mechanics, Applied Mechanics
Assistant Professor
NIINO, Kazuki, Ph.D.(Informatics, Kyoto Univ.),
Boundary Integral Equation Methods, Computational Electromagnetics

Computer simulations provide powerful means of solving various problems in science and engineering. Computational mechanics is one of such approaches which, along with theoretical and experimental mechanics, investigates mechanical phenomena efficiently. This division develops various approaches of the Boundary Integral Equation Method (BIEM), which is one of major techniques of computational mechanics and is considered suitable for the analyses of phenomena such as waves, fracture, etc. We are currently interested in fast BIEMs and their applications to large scale problems.

Associate Professor
TAGUCHI Satoshi, D.Eng.(Kyoto Univ.),
Fluid Dynamics, Non-equilibrium Gas Dynamics, Kinetic Theory

Our main research interest is to clarify the behavior of non-equilibrium gas flows and to establish theories to describe them. Through theoretical and/or computational investigations applied to kinetic equations, describing the statistical behavior of many particles, we elaborate new continuum theories applicable to non-equilibrium flows. We also derive and construct related mathematical models for non-equilibrium flows and clarify the relations between various fluid models.