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16 labs · 4 student voices
Other departments in School of Fundamental Science and Engineering ›Faculties at Waseda University ›
Toshimichi Usuba, Professor
1 student voices
The Usuba Lab studies axiomatic set theory, a foundational field of mathematics. In particular, it studies set theory related to "large cardinals," which measure the size of sets, and the "axiom of choice," one of the axioms underlying mathematics. As an application, the lab also works on set-theoretic topology, which uses set theory to investigate the properties of spaces.
Takashi Kumagai, Professor
1 student voices
Kumagai Lab uses probability theory to study the properties of complex shapes such as fractals. The lab constructs random walks and Brownian motion on complex shapes and investigates physical properties such as how heat propagates. Fractals have no smoothness, so ordinary differentiation cannot be used, but the methods of probability theory remain effective even on non-smooth spaces. In addition to probability theory, the lab conducts interdisciplinary research connected to a wide range of fields, including harmonic analysis and function space theory.
Kazunaga Tanaka
1 student voices
The Tanaka Lab studies nonlinear partial differential equations using a mathematical technique called variational methods. It targets equations whose solutions do not have simple forms, such as nonlinear elliptic equations and Hamiltonian systems. The lab uses mathematics to determine whether solutions to these equations exist and what form they take.
Hiroaki Narita
1 student voices
The Narita Lab studies number theory, in particular functions called automorphic forms. Number theory is a field of mathematics that investigates the properties of prime numbers and integer solutions, and automorphic forms are one of its research tools. The lab works on constructing automorphic forms explicitly and clarifying their number-theoretic properties.
Takeshi Ikeda, Professor
0 student voices
The Ikeda Lab studies enumerative geometry, a branch of algebraic geometry. This field determines how many geometric figures satisfy given conditions, working on spaces such as Grassmannians. Enumerative problems are deeply connected to problems in representation theory, where special functions such as Schur polynomials play an important role. In recent years, the lab has also studied extensions to K-theory and quantum K-theory, beyond cohomology, as well as the relationship with integrable systems.
Takayoshi Ogawa, Professor
0 student voices
Ogawa Lab studies nonlinear partial differential equations using methods from real analysis and harmonic analysis. The lab investigates the critical structure of nonlinear evolution equations and the functional inequalities related to it. From the standpoint of applied analysis, the lab works to clarify mathematically how the solutions of these equations behave.
Manabu Ozaki, Professor
0 student voices
Ozaki Lab uses Galois theory to study the structure of number fields, a type of number system. In particular, the lab centers its research on Iwasawa theory, which concerns extensions of cyclotomic fields, a special kind of number field. The lab aims to clarify what structure the Galois groups of number fields have, using non-abelian methods as well.
Hajime Kaji, Professor
0 student voices
Kaji Lab studies algebraic geometry, and within it the projective geometry of algebraic varieties. The lab investigates figures such as algebraic curves, vector bundles, and homogeneous spaces from the viewpoint of how they behave inside projective space. Specifically, it studies the structure of secant varieties of projective varieties and the properties of Gauss maps. It also works on the phenomena peculiar to the special case where the number system of the coefficients has positive characteristic.
Atsushi Kanazawa, Associate Professor
0 student voices
Kanazawa Lab studies a field spanning complex geometry, symplectic geometry, and mathematical physics. In particular, the lab focuses on shapes called Calabi-Yau manifolds and on a correspondence called mirror symmetry.
Hideo Kozono, Professor
0 student voices
Kozono Lab studies the Navier-Stokes equations, which describe the motion of fluids such as water and air. Using methods of real analysis, the lab mathematically clarifies whether solutions to the equations exist and what properties they have. The lab also studies the properties of turbulence (irregular, disordered flow) by combining nonlinear analysis with computational science.
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