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137 labs · 6 student voices
Faculties at Kyoto University ›
Tetsuya Ito, Professor
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This lab studies low-dimensional topology. Its main research themes include braid groups, ordered groups, mapping class groups, and contact structures on 3-manifolds. It investigates the properties of knots using the language of groups and classification results.
Hiroyuki Inou, Professor
0 student voices
This lab studies dynamical systems, especially complex dynamics. Repeatedly composing a polynomial in one complex variable naturally produces complex fractal sets such as Julia sets and the Mandelbrot set. The lab studies their topological and combinatorial properties, such as self-similarity and local connectivity. Recently, it has also been working on using VR equipment to make fractal sets in complex 2-dimensional (real 4-dimensional) space visible.
Hiroshi Iritani, Professor
0 student voices
The Iritani Lab studies mirror symmetry in differential geometry and mathematical physics. Its main themes are Hodge-theoretic mirror symmetry and the global properties of Gromov–Witten theory. The lab also works on quantum cohomology, the crepant transformation conjecture, and the Gamma conjecture.
Syu Kato, Professor
0 student voices
The Syu Kato Lab studies geometric representation theory. It realizes representations of algebraic systems arising from semisimple Lie algebras and their root systems (Hecke algebras, quantum groups, algebraic groups, and others), mainly by using geometric structures. The lab investigates the classification of irreducible and unitary representations and the structure of categories of representations. By comparing different realizations, it also studies integrable systems, orthogonal function systems, and number-theoretic invariants.
Tsuyoshi Kato, Professor
0 student voices
The Tsuyoshi Kato Lab studies gauge theory and differential topology within differential geometry. Its research themes also include geometric analysis on noncompact spaces, noncommutative geometry, and tropical geometry and dynamical systems. Through collaborative research, the lab investigates Seiberg-Witten theory for 4-manifolds and the properties of noncompact manifolds.
Shu Kawaguchi, Professor
0 student voices
The Kawaguchi Lab studies algebraic geometry over number fields. In joint research, the lab works on tropicalization, which maps a geometric shape to a piecewise-linear shape in order to study it, and on the theory of heights, which measures the complexity of numbers. The lab has also co-authored a book presenting the complete proof of the Mordell conjecture via Diophantine geometry.
Seiichiro Kusuoka, Professor
0 student voices
The Kusuoka Lab studies stochastic analysis within the field of probability theory. Its main themes are stochastic differential equations, Malliavin calculus, and singular stochastic partial differential equations. The lab also works on stochastic quantization, which uses stochastic partial differential equations to construct measures that appear in quantum field theory.
Takashi Sakajo, Professor
0 student voices
The Sakajo Lab studies the mathematical description of complex fluid motion from the standpoint of applied mathematics. It uses the theory of partial differential equations, dynamical systems theory, numerical analysis, and data science (topological data analysis, data assimilation). Its applied research is wide-ranging, covering meteorology, oceanography, and medicine, and even joint research with companies.
Senjo Shimizu, Professor
0 student voices
The Shimizu Lab studies the theory of partial differential equations in the field of analysis. Centered on the idea of maximal regularity, the lab investigates equations describing fluid motion, such as the Navier-Stokes equations. Through joint research, the lab also works on free boundary problems and the equations of magnetohydrodynamics (electrically conducting fluids).
Masaki Tsukamoto, Professor
0 student voices
The Tsukamoto Lab mainly studies the mean dimension of dynamical systems, which are systems that change over time. Mean dimension is the number of degrees of freedom a dynamical system has per unit time, and it was introduced by Gromov in 1999. The lab studies both the application of geometry to differential equations and applications to problems in topological dynamics. In the course of this work, the lab found that rate-distortion theory from information theory is deeply connected to mean dimension.
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