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9 labs · 0 student voices
Other departments in Research Institute for Mathematical Sciences ›Faculties at Kyoto University ›
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.
Akio Tamagawa, Professor
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The Tamagawa Lab studies number theory and arithmetic geometry. From the viewpoint of number theory, it investigates coverings and fundamental groups of algebraic curves and their moduli spaces. At the Research Institute for Mathematical Sciences, research in this area is actively pursued, centered on anabelian geometry in the broad sense. For the anabelian geometry of curves, the lab has obtained results over finite fields, over fields finitely generated over the rational number field, and over algebraically closed fields of positive characteristic.
Shinichi Mochizuki, Professor
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The Mochizuki Lab studies arithmetic geometry. Its research focuses on the arithmetic geometry of hyperbolic algebraic curves, including elliptic curves and algebraic curves of genus 2 or higher defined over number fields, local fields, and finite fields. For hyperbolic algebraic curves, the outer action of the absolute Galois group of the base field on the non-abelian fundamental group is a natural starting point for arithmetic geometry. The lab has worked on topics such as p-adic Teichmüller theory, p-adic anabelian geometry, and the Hodge-Arakelov theory of elliptic curves.
Yoshinori Namikawa, Professor
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The Namikawa Lab studies, in the field of algebraic geometry, algebraic varieties whose canonical bundle is trivial. Its subjects are compact Calabi-Yau varieties, hyperkähler varieties, and non-compact algebraic varieties with a complex symplectic structure. The lab investigates such varieties with singularities from the viewpoints of birational geometry, deformation theory, and singularity theory.
Yuji Odaka, Professor
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The Odaka Lab conducts research related to moduli spaces, in the fields of algebraic geometry and complex geometry. It connects the geometry of Kähler-Einstein manifolds, which include many classical and important algebraic varieties, to modern algebraic geometry such as birational geometry. The lab has studied K-stability, a concept equivalent to the existence of canonical metrics on algebraic varieties, from an algebro-geometric perspective. The lab asks students who are considering Prof. Odaka as a graduate school advisor to contact him before applying.
Shin-ichi Takehiro, Associate Professor
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The Takehiro Lab uses fluid dynamics to study fluid phenomena that occur on celestial bodies such as the Earth and other planets. It focuses on the factors that give planetary-scale flows their characteristic features: planetary rotation, gravity and density stratification, phase changes of constituent materials, and spherical geometry. The lab turns phenomena in planetary atmospheres, mantles, and cores into simplified models, obtains the flows through numerical experiments on computers, and builds theories that capture their properties. Faculty members and graduate students describe the research group in person, and lab visits are welcome.
Yuichiro Hoshi, Associate Professor
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The Hoshi Lab studies the arithmetic geometry of hyperbolic algebraic curves from perspectives such as anabelian geometry and p-adic Teichmüller theory. It has worked on the section conjecture, anabelian geometry for algebraic curves and higher-dimensional algebraic varieties, combinatorial anabelian geometry, and more. Inter-universal Teichmüller theory and the geometry of hyperbolic algebraic curves in positive characteristic are also among its research subjects. Recently, the lab has been advancing research on the Galois groups of solvably closed Galois extensions of number fields and on the Grothendieck–Teichmüller group.
David Croydon, Associate Professor
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The Croydon Lab studies probability theory, in particular random walks in random environments. Its main interest is diffusion processes on random fractals and their construction as scaling limits of random walks on random graphs. Its interests also extend to the behavior of discrete integrable systems started from random initial conditions.
Naotaka Kajino, Associate Professor
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The Kajino Lab studies the Laplacian and stochastic processes on fractals, in the field of probability theory. Fractal is a general term for spaces whose geometric properties are entirely different from those of smooth spaces such as Euclidean space or Riemannian manifolds. On such spaces, the lab aims to construct a geometrically natural Laplacian and the corresponding stochastic process, and to analyze them in detail. In recent years, the lab has also been working on constructing and analyzing nonlinear energy functionals of Lp type on fractals.
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