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Other departments in Division I, Faculty of Science ›Faculties at Tokyo University of Science ›
Tomomi Yokota, Professor
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Yokota Lab studies partial differential equations within analysis. Its main research subject is chemotaxis systems arising in mathematical biology. Chemotaxis is the property by which a chemoattractant induces directed movement in a population, and a representative mathematical model is the Keller-Segel system. Using methods of real analysis, such as integration by parts and maximal regularity, together with operator theory, the lab investigates the boundedness of solutions and finite-time blow-up.
Mieko Tanaka, Associate Professor
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Tanaka Lab uses the calculus of variations to show that solutions to differential equations exist. Variational problems appear in many places: Fermat's principle (light travels along the shortest path) and the Dirichlet principle, both known as variational principles, as well as geodesics and brachistochrones. Such problems can be solved by finding the function that attains the minimum of a real-valued function whose domain is a set of functions (a functional). The lab examines the extrema of functionals to show the existence of solutions to differential equations.
Atsuhide Ishida, Professor
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The Ishida Lab studies the Schrödinger equation, a partial differential equation that is fundamental to quantum mechanics. By analyzing the asymptotic behavior of solutions to this equation as time tends to infinity and at large distances in space, the lab seeks to understand scattering phenomena in quantum mechanics in the language of mathematics. The lab lists the behavior of solutions to the Schrödinger equation, the direct and inverse problems of quantum scattering, and the spectral theory of Schrödinger operators as example themes.
Ayako Itaba, Associate Professor
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The Itaba Lab studies the representation theory of algebras and noncommutative algebraic geometry, both within the field of algebra. The Hochschild cohomology of an algebra is an invariant of Morita equivalence, stable equivalence of Morita type, and derived equivalence of algebras, and it is also an object of interest from the standpoint of the representation theory of algebras. Noncommutative algebraic geometry began with the classification of 3-dimensional AS-regular algebras, which are the coordinate rings of quantum projective planes. Noting that noncommutative algebraic geometry and the representation theory of algebras are closely related, the lab aims to investigate the connection between them.
Ryotaro Tanaka, Associate Professor
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The Tanaka (Ryo) Lab studies Banach spaces, the main objects of functional analysis, from a geometric perspective, such as the shape of the unit ball. Functional analysis is a foundational field with broad applications. Built on linear algebra and topology, it provides basic tools to every area of modern analysis. The lab applies ideas from the geometry of Banach spaces to uniform algebras, operator algebras, and related structures, and explores how far Banach spaces can be classified at the nonlinear level. On the university's lab introduction pages, the lab is listed under the name "Tanaka Lab."
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