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58 labs · 2 student voices
Other departments in Faculty of Science ›Faculties at The University of Tokyo ›
Takeshi Saito, Professor
0 student voices
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.
Hidetaka Sakai, Associate Professor
0 student voices
The Sakai Lab studies differential and difference equations in the complex domain from the perspective of the theory of special functions and integrable systems. The lab aims to apply the methods and questions developed in the study of elliptic functions and hypergeometric functions to functions defined by nonlinear differential and difference equations. From an algebro-geometric perspective, the lab works on characterizing integrable systems, including the Painlevé differential equations. By studying geometric objects called spaces of initial conditions, the lab seeks to understand the various properties of these equations.
Hiroshi Sakai, Professor
0 student voices
The Sakai Lab studies axiomatic set theory, a branch of the foundations of mathematics. ZFC, the standard axiom system of set theory, allows almost all of ordinary mathematics to be developed, but it is known that many statements concerning infinity, such as the continuum hypothesis, can be neither proved nor disproved in ZFC. The lab studies what statements can be proved in axiom systems obtained by adding large cardinal axioms, forcing axioms, and reflection principles to ZFC.
Takuya Sakasai, Associate Professor
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The Sakasai Lab studies mapping class groups of surfaces from the perspective of topology. The mapping class group is the group of isotopy classes of self-diffeomorphisms of a surface. It appears not only in topology and differential geometry but also in many other areas of mathematics, such as algebra and mathematical physics. The lab aims to elucidate the structure of cohomology rings through the structure of these groups and the topology of moduli spaces. Recently, it has been investigating the structure of related infinite-dimensional Lie algebras through both theoretical analysis and computer experiments. Using the homology cobordism group of surfaces as a starting point, the lab also works on constructing new invariants of knots and 3-manifolds.
Makiko Sasada, Professor
Data Science & Statistics0 student voices
The Sasada Lab studies problems in probability theory that originate in statistical physics. The lab works on methods that start from microscopic systems described by stochastic processes and use scaling and limiting procedures to rigorously derive the macroscopic behavior of those systems.
Atsushi Shiho, Professor
0 student voices
The Shiho Lab studies p-adic objects in arithmetic geometry. The lab investigates p-adic cohomology and p-adic fundamental groups of (logarithmic) algebraic varieties in positive characteristic. It also studies p-adic differential equations on (logarithmic) p-adic analytic spaces.
Akihiro Shimomura, Associate Professor
0 student voices
The Shimomura Lab studies functional equations and the theory of evolution equations, within the field of analysis. The lab carries out its research using methods from functional analysis and real analysis.
Hideko Sekiguchi, Associate Professor
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Sekiguchi Lab studies the Penrose transform, which appears in mathematical physics, from the standpoint of the representation theory of semisimple Lie groups. When infinite-dimensional representations of Lie groups are realized on spaces of functions, the more degenerate a representation is, the more differential equations it is thought to satisfy. Just as the Radon transform is defined by integrating functions on a real manifold over submanifolds, a similar integral transform can be defined by integrating the cohomology of a complex manifold over cycles. Using the geometric structure of homogeneous manifolds, the lab generalizes the Penrose transform to higher dimensions, aiming to describe singular infinite-dimensional unitary representations explicitly.
Shunsuke Takagi, Professor
0 student voices
Takagi Lab studies singularities of algebraic varieties from the perspectives of commutative algebra and algebraic geometry. The lab studies F-singularities, which are singularities in positive characteristic defined using the Frobenius morphism. As an application, the lab is also interested in the properties of singularities that appear in the minimal model program, and in the geometric properties of Frobenius split varieties.
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