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58 labs · 2 student voices
Other departments in Faculty of Science ›Faculties at The University of Tokyo ›

Osamu Iyama, Professor
0 student voices
The Iyama Lab studies ring theory and representation theory, both areas of algebra. The lab works with rings such as quivers, orders, commutative rings, and dg categories, together with their representations. The lab also studies the structure of categories associated with representations, such as derived categories, and their applications to cluster algebras and noncommutative resolutions of singularities.

Kohei Iwaki, Associate Professor
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The Iwaki Lab studies differential equations containing a small parameter, such as the Planck constant, using a method called exact WKB analysis. Exact WKB analysis combines the WKB method, long used for approximate calculations in quantum mechanics, with Borel summation, a technique for summing divergent series. Using this theory, the global structure of solutions to second-order linear differential equations can be described as an infinite sum of certain period integrals on an algebraic curve. The lab also works on resurgence theory, its relations to cluster algebras and topological recursion, and applications to Painlevé equations.

Ralph Willox, Professor
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The Willox Lab studies "integrable nonlinear equations" that arise in mathematical physics. In particular, it focuses on soliton equations and Painlevé equations, as well as their discretized counterparts. Using Hirota's bilinear method and Sato theory as its main tools, the lab aims to extend ideas known from continuous systems, such as symmetries and conserved quantities, to difference equations and cellular automata. The lab also investigates the discretization of continuous models that describe natural phenomena, using both computer simulation and analytical methods.

Kazushi Ueda, Associate Professor
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Ueda Lab studies algebraic geometry and symplectic geometry. Its research centers on relationships with mathematical physics, as exemplified by mirror symmetry.

Masayuki Uchida, Professor
Data Science & Statistics0 student voices
Uchida Lab works in mathematical statistics, studying the statistical modeling of stochastic differential equations based on high-frequency time series data. The lab develops asymptotic theory for model estimation and hypothesis testing, and works on information criteria for model selection together with their mathematical justification. The lab also studies statistical asymptotic theory for stochastic partial differential equations using high-frequency spatio-temporal data. The lab is also interested in empirical research using data analysis, and aims to advance statistical modeling from both theoretical and applied perspectives.

Yoshiki Oshima, Associate Professor
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The Oshima Lab studies representations of Lie groups in the field of representation theory. In particular, it investigates the induction and restriction of unitary representations of semisimple Lie groups, using methods based on D-modules and coadjoint orbits.

Izumi Okada, Associate Professor
Data Science & Statistics0 student voices
The Okada Lab uses probability theory to study the long-time behavior of Markov processes. The lab investigates, from a probabilistic perspective, the fundamental properties of simple random walks on the integer lattice and of Brownian motion, their continuous-time version. The objects of study include hitting probabilities, intersections, and local times. In particular, the lab examines the geometric structure of thick points, the exceptional points at which the local time of a random walk takes large values.

Keiji Oguiso, Professor
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The Oguiso Lab has mainly studied Calabi-Yau manifolds in a broad sense, within the field of algebraic geometry. The lab currently approaches its research from the perspectives of both birational algebraic geometry and complex dynamics. It is particularly interested in the existence of primitive automorphisms, problems related to the cone conjecture, and the problem of lifting automorphisms to characteristic zero.

Takahito Kashiwabara, Associate Professor
Software & Computing0 student voices
Kashiwabara Lab works in numerical analysis, studying the mathematical justification of numerical simulations performed on computers. Its goal is to prove that the approximate solutions obtained from numerical simulations are truly close to the exact solutions of the mathematical models, thereby guaranteeing the correctness of approximation and discretization. The main subject is partial differential equations, in particular the Navier-Stokes equations, the fundamental equations of fluid dynamics. Recently, the lab has also become interested in the mathematical analysis of the Primitive equations that arise in geophysics, and in finite element analysis in the maximum norm.

Akishi Kato, Associate Professor
0 student voices
The Kato Lab studies the mathematical structures of quantum field theory and string theory within the field of mathematical physics. "Quantization" and "renormalization" are key concepts in modern physics, but their content and meaning have yet to be fully understood mathematically. The lab is interested in objects and structures in which these properties play an essential role. Currently, the lab focuses in particular on the mathematical structures suggested by dualities in field theory, studying them from the perspectives of low-dimensional topology, representation theory, category theory, and combinatorics.
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