(B02-1) Obata Laboratory
• Quantum (Non-commutative) Probability
Fundamentals and applications to spectral analysis of graphs and networks, random matrices, and orthogonal polynomials.
• Complex Networks
Mathematical study with broad applications, in particular, to life and social science.
• Infinite Dimensional Stochastic Analysis
Our main concern is to develop the quantum white noise theory with applications to quantum and classical differential equations.
• Applied Mathematics Forum (AMF)
promoting interdisciplinary studies together with international joint research projects.
(B02-2) Fukuizumi Laboratory
• Stochastic Partial Differential Equations
We study, by Ito calculus, the existence, blow-up, asymptotic behavior of solutions of a nonlinear dispersive equation with a stochastic perturbation. In particular, model equations arising in Optical fiber or in Bose-Einstein Condensation are objects of study as applications in Engineering or Physics.
• Stability of Solitary Waves and Travelling Waves
We treat the stability and instability problem of solitary waves. Main tools are variational methods related to nonlinear elliptic equations, and spectral analysis of operators on an infinite dimensional Hilbert space.
• Numerical Analysis
We are interested in numerical simulations using MATLAB which give effectively some intuitive ideas to solve the phenomena mentioned above rigorously.
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