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28 labs · 0 student voices
Faculties at Kyoto University ›
Tatsuki Kuwagaki, Associate Professor
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The Kuwagaki Lab uses sheaves to study topics related to symplectic geometry and algebraic analysis. It is especially interested in problems related to mathematical physics, such as mirror symmetry and, more broadly, field theory. Its main tool is microlocal sheaf theory, and it carries out research with methods motivated by microlocal sheaf theory and its interpretation in terms of Fukaya categories. In its research description, the lab says that students do not particularly need to work on the same research as the professor. It asks anyone who wants to do research in a neighboring field and to study here as a graduate student to get in touch first.
Takuro Mochizuki, Professor
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Professor Takuro Mochizuki studies differential geometry and algebraic geometry in the Fundamental Mathematical Sciences Division of the Research Institute for Mathematical Sciences. Beginning with research on the singularities of harmonic bundles, Professor Mochizuki established the theory of objects known as mixed twistor D-modules. In recent years, Professor Mochizuki has been trying to apply the results and insights obtained so far to related objects and more concrete subjects. Specifically, the lab studies solutions of the two-dimensional Toda equation, and instantons and monopoles with periodicity.
Yoshiko Ogata, Professor
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The Ogata Lab studies quantum spin systems, a fundamental model of quantum statistical mechanics, in the field of mathematical physics. It focuses on the state of matter cooled to absolute zero (the ground state) and the gap just above its energy (the spectral gap). Models with a spectral gap are also related to quantum computers that are robust against noise, and the lab works on the problem of classifying such models. The lab pursues research that shows, with mathematical rigor, what physicists have conjectured.
Narutaka Ozawa, Professor
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The Ozawa Lab studies the relationship between operator algebras and discrete groups. A group is a mathematical language for describing the symmetry of an object. For example, the set of all transformations, such as rotations and reflections, that leave the structure of a crystal unchanged forms a group. The lab treats the elements of a group as operators and investigates problems about groups using analytic techniques from operator algebra theory, while also pursuing applications in the opposite direction. In addition to traditional operator algebra theory, the lab also studies operator theory, Banach algebra theory, Banach space theory, and discrete metric geometry.
Kazushige Terui, Associate Professor
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The Terui Lab studies proofs themselves from the standpoint of mathematical logic. A proof is a means of doing mathematics, but it can also be an object of mathematics: when represented appropriately, the mathematical structure behind it comes into view. Under the Curry–Howard correspondence, a proof can be regarded as (to a certain extent) the same thing as a functional program, so it also has an aspect as a "medium of computation." The lab approaches the subject from various perspectives, including computational complexity, games, denotational semantics, and algebraic semantics.
Kaoru Ono, Professor
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The Ono Lab studies the geometric structure of space, especially the geometry of symplectic structures, in the fields of differential geometry and topology. Floer theory arose by combining the variational framework for studying periodic solutions of Hamiltonian systems with the method of holomorphic curves introduced by Gromov. With collaborators, the lab works on constructing Floer theory for Hamiltonian diffeomorphisms without technical conditions, and on Floer theory of Lagrangian submanifolds and homological mirror symmetry.
Kenji Nakanishi, Professor
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The Nakanishi Lab studies the mathematical analysis of partial differential equations. Its main subjects are nonlinear partial differential equations describing the spatiotemporal evolution of strongly interacting waves, such as those in plasmas, water surface waves, superfluids, and optical fibers. A variety of time evolutions arise from the competition between the dispersion of waves and nonlinear interaction. Recently, aiming to capture the behavior of general solutions as a whole, the lab has been investigating transitions between typical behaviors, as well as intermediate states.
Kei Irie, Professor
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The Irie Lab studies symplectic geometry, in the fields of topology and differential geometry. It focuses in particular on symplectic capacities and periodic orbits of Hamiltonian dynamical systems. Building on Floer homology, a theory that arose from pseudoholomorphic curves, the lab investigates the computation of capacities, periodic orbits of billiard dynamical systems, closing lemmas, and more. In the future, the lab also has in view establishing a method to compute Floer homology by finite-dimensional Morse theory in situations with a torus action.
Noboru Nakayama, Associate Professor
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The Nakayama Lab studies the birational geometry of algebraic varieties and complex manifolds. Using birational invariants such as the Kodaira dimension and plurigenera, the lab investigates the structure of varieties, placing particular emphasis on invariants related to the canonical divisor. The lab has also long worked on the classification of varieties that admit surjective endomorphisms that are not isomorphisms, and on ℚ-Gorenstein deformations.
Go Yamashita, Lecturer
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The Yamashita Lab studies arithmetic geometry. It lists p-adic Hodge theory, Iwasawa theory, multiple zeta values, Shimura varieties and the Langlands correspondence, and inter-universal Teichmüller theory among its research areas. Students who choose Lecturer Yamashita as their academic advisor are generally expected to study and conduct research in arithmetic geometry. After entering graduate school, students choose a text and present it at a seminar held about once a week, then find a research topic and proceed with their research.
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