System Information Sciences
Mathematical System Analysis II B02
Foundations of Mathematical Analysis and Applications
(B02-1) Obata Laboratory
Quantum (Non-commutative) Probability
Our main concern is to develop the quantum white noise theory with applications to quantum and classical differential equations. Fundamentals and applications to spectral analysis of graphs, random matrices, and orthogonal polynomials.
A graph with some additional structure is generally called a network. We are interested in the structure of growing and random networks as well as the critical behavior of relevant dynamics by means of statistical physics and numerical analysis.
Applied Mathematics Forum (AMF)
promoting interdisciplinary studies together with international joint research projects. In particular, mathematical approach to network science is of our central interest, along with applications to quantum technology, life and social sciences.
(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 quantum device, 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.
We are interested in numerical simulations using MATLAB which give effectively some intuitive ideas to solve the phenomena mentioned above rigorously.
Giant component of a configuration model
Finding critical point by the 1st and 2nd connected components