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58 labs · 2 student voices
Other departments in Faculty of Science ›Faculties at The University of Tokyo ›
Ryo Takada, Associate Professor
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The Takada Lab studies nonlinear partial differential equations arising in fluid dynamics from the viewpoint of mathematical analysis. Its goal is to clarify mathematically the various patterns of flow that fluids create and the mechanisms behind them. Focusing on the Euler equations, the Navier-Stokes equations, the Boussinesq equations, and others, the lab investigates well-posedness, stability of solutions, and asymptotic behavior, using methods from harmonic analysis and functional analysis. Recently, the lab has become interested in the mathematical analysis of the dispersive and anisotropic effects of rotation and stable stratification in large-scale fluids.
Asuka Takatsu, Professor
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The Takatsu Lab studies the curvature of space in the field of geometric analysis. The objects of study are often Riemannian manifolds, or more general spaces equipped with a distance and a measure. The lab mainly uses optimal transport theory, which considers how to move things with minimum energy, as its main tool.
Shigeharu Takayama, Professor
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Takayama Lab studies complex algebraic varieties in the field of complex geometry, using analytic methods. The lab applies singular Hermitian metrics on line bundles, multiplier ideal sheaves, and Kodaira-type cohomology vanishing theorems to investigate the algebraic and geometric properties of varieties. Recently, the lab has been particularly interested in Hodge metrics associated with pluricanonical bundles and their relative versions.
Takeshi Tsuji, Professor
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The Tsuji Lab studies p-adic Hodge theory and p-adic cohomology in the field of arithmetic geometry. The lab investigates the p-adic cohomology of algebraic varieties defined over p-adic fields. It also studies special values of L-functions and their applications to p-adic L-functions.
Yukinobu Toda, Professor
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Toda Lab studies derived categories and enumerative invariants on algebraic varieties in the field of algebraic geometry. An algebraic variety is a geometric object defined as the zero set of polynomials, and Calabi-Yau manifolds, among them, play an important role in superstring theory in physics. There are various invariants for counting curves on Calabi-Yau 3-folds, and all of them are expected to be equivalent.
Ryu Hasegawa, Associate Professor
Software & Computing0 student voices
The Hasegawa Lab studies the foundational frameworks of programming languages, mainly from a theoretical standpoint. Its central theme is analyzing the mathematical structures that appear in type theory and, through them, exploring how computation works. Type theory adds the notion of types to the lambda calculus, and it has long been studied as a theoretical foundation for designing programming languages. In particular, investigating the properties of type theories with polymorphism is one of the lab's central challenges.
Kazuo Habiro, Professor
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The Habiro Lab works in topology, studying the relationships between topology and various algebraic structures. Until now, the lab has mainly studied quantum invariants of 3-manifolds and links. Recently, the lab has also become interested in homological algebra, including group homology and Hochschild homology.
Shuhei Hayashi, Associate Professor
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The Hayashi Lab studies differentiable dynamical systems on manifolds, in the fields of dynamical systems and ergodic theory. The lab is working on a conjecture asking whether dynamical systems that exhibit homoclinic bifurcations, together with hyperbolic dynamical systems, are dense in the space of all dynamical systems. To this end, the lab has brought in the perspective of ergodic theory and has tried to build hyperbolicity from invariant measures.
Kengo Hirachi, Professor
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The Hirachi Lab studies CR geometry and conformal geometry in the fields of several complex variables and parabolic geometry. CR geometry is the geometry of real hypersurfaces in complex manifolds. Using methods from differential geometry, partial differential equations, and representation theory, the lab investigates the two geometries from the unified viewpoint of parabolic geometry.
Neal Bez, Professor
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The Bez Lab studies themes related to the Fourier restriction conjecture and the Kakeya conjecture in harmonic analysis and real analysis. The two conjectures are closely and fruitfully interrelated, and have contributed greatly to recent progress in harmonic analysis and geometric measure theory. The Brascamp-Lieb inequality is a broad generalization of inequalities such as Hölder's inequality, and it connects to other fields including convex geometry and information theory. Strichartz estimates, which control the size and decay of solutions to dispersive equations such as the Schrödinger equation, are also one of the lab's research topics.
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