New Research


2009/10/01

Mathematical Sciences as Critical Studies of Natural Sciences

Partial differential equations, Dynamical systems, Numerical computations, Stochastic analysis

Professor Hayato NAWA, Associate Professor Toshiyuki Ogawa

Regarding mathematical sciences as critical studies of natural sciences, we are left with various problems to be studied and formulated in rigorous, mathematical ways. Activity of a research group is limited however; we are now working on the following problems mainly:

1. Laser beam propagation and nonlinear Schrodinger equations,
2. Chemical reactions, bifurcation analysis and reaction diffusion equations,
3. Self-Validation algorithm in numerical computation and Homology,
4. Mathematical modeling of turbulence from a stochastic point of view.

It is one of the important issue of mathematical sciences not only to justify and to verify the mathematical models but also to establish the fundamental concepts in the models as firm mathematical notions, and such studies seem to be still more significant nowadays, considering the recent advances of science and technology.

To deepen, enrich and exchange our knowledge and technique etc on mathematical sciences, we run two seminars with researchers from other Universities: “KATAROU SUURIKAISEKI (Let’s Enjoy Mathematical Sciences, Fun! Fun! Fun!)” and “Kyoto EKIMAE Seminar (Seminar on mathematical sciences in front of Kyoto Station)”, broadly going to topics of mathematical sciences and natural phenomena other than the problems listed above.

Students in our Laboratory choose their themata of mathematical sciences relevant to various area of mathematics, e.g., partial differential equations, dynamical systems, numerical computations, probability, to accomplish their theses.


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