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287 labs · 116 student voices
Faculties at The University of Tokyo ›
Nariya Kawazumi, Professor
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The Kawazumi Lab works in topology, studying the topology of Riemann surfaces themselves and of the moduli spaces of Riemann surfaces. In its research over the past few years, the (generalized) Magnus expansion of free groups has played a central role. The lab constructed Magnus expansions by geometric methods and extended the Johnson homomorphisms to the whole mapping class group in a geometrically meaningful way. It also constructed a Lie algebra homomorphism from the Goldman Lie algebra, and as an application gave an explicit description of the action of Dehn twists on the completed group ring of the fundamental group of a surface.
Yoshikata Kida, Professor
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The Kida Lab studies group actions on measure spaces and their orbit equivalence relations, in the fields of discrete groups and ergodic theory. Whether a mathematical object can be classified is expressed concretely as a property of a certain equivalence relation. The complexity of that equivalence relation is regarded as reflecting the complexity of the corresponding classification problem. The lab is particularly interested in the connections between orbit equivalence relations and the functional-analytic and geometric properties of groups.
Yukako Kezuka, Associate Professor
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Kezuka Lab specializes in number theory and studies elliptic curves and Iwasawa theory. The lab also studies special values of L-functions and the Birch and Swinnerton-Dyer conjecture.
Shane Kelly, Associate Professor
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Kelly Lab studies motivic homotopy theory and algebraic K-theory in the field of algebraic geometry. Recently, the lab has been working on generalizing the topological methods in algebraic geometry developed by Voevodsky and others. The lab also targets objects that Voevodsky's methods could not capture, such as non-reduced schemes, additive groups, and wild ramification in number theory. The lab applies topological methods to frameworks that can handle these objects, such as modulus pairs and derived schemes.
Yuta Koike, Associate Professor
Data Science & Statistics0 student voices
Koike Lab works in probability and statistics, studying statistical inference for continuous-time stochastic process models. Such models typically arise as high-frequency trading data of financial assets. Specifically, the lab works on the problem of estimating the covariance structure of stochastic process models from data observed at high frequency. Recently, the lab has been interested in modeling the lead-lag effect, in which a time lag arises in the covariance structure, and in the connection between high-frequency data analysis and high-dimensional statistics.
Toshiyuki Kobayashi, Professor
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The Kobayashi Lab studies Lie groups and infinite-dimensional representation theory in the fields of symmetry, global geometry, and global analysis. The lab works on the global geometry of locally homogeneous spaces (discontinuous group theory) and on a theory that algebraically describes symmetry breaking in infinite-dimensional settings (branching laws of representations). The lab also studies global analysis on minimal representations, as well as multiplicity-free representations using the notion of "visible actions" on complex manifolds.
Hokuto Konno, Associate Professor
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The Konno Lab works in geometry, studying the development of four-dimensional gauge theory and its applications to topology and differential geometry. One central part of the lab's research is to formulate problems using ideas from topology and geometry in dimensions other than four, then build a gauge-theoretic framework suited to those problems and solve them. For example, the lab has established the foundations of gauge theory for families of 4-manifolds and has shown that it can be used for purposes such as constructing characteristic classes of 4-manifold bundles. The lab has a strong interest in using gauge theory to open up new research areas in differential topology.
Yoshinori Gongyo, Professor
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The Gongyo Lab studies geometry in the field of algebraic geometry, focusing on the canonical divisors of algebraic varieties. In particular, it studies the abundance conjecture, one of the most important conjectures in higher-dimensional algebraic geometry. The lab has also studied (semi-)log canonical pairs, the canonical bundle formula, the subadjunction formula, log Fano varieties, and applications of techniques for reduction to positive characteristic.
Takeshi Saito, Professor
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Saito Lab works in arithmetic geometry, studying Galois representations and étale cohomology. Arithmetic geometry studies geometric objects, such as schemes, defined over arithmetic rings and fields, such as rings of integers and local fields. The lab studies Galois representations of number fields and local fields, as well as the theory of étale sheaves, which is also used to construct them.
Norikazu Saito, Professor
Software & Computing0 student voices
The Saito Lab studies the numerical analysis of partial differential equations. The lab systematically derives methods for converting differential equations, as mathematical models, into forms that can be computed by finite difference methods, finite element methods, and others, and verifies their mathematical correctness. It uses mathematics to systematize the "artisanal know-how" that has relied on experience, aiming for high-quality simulation methods that even people with little experience can use with confidence. Toward pure mathematics, the lab also aims to present new problem formulations suited to computation and to open up new research areas in the theory of differential equations.
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