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900 labs · 77 student voices
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.
Kazuhisa Makino, Professor
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The Makino Lab analyzes discrete structures such as those in graph theory and combinatorics, and studies optimization and algorithms that exploit those structures. Its representative research is on the dualization problem for monotone Boolean functions. This problem is known to be equivalent, in the sense of polynomial-time reductions, to many problems arising in diverse fields such as mathematical programming, artificial intelligence, databases, distributed systems, and learning theory. The lab also studies systems of integer linear inequalities, complementarity problems, online optimization problems, robust optimization, and equilibria in game theory.
Masayuki Kawakita, Associate Professor
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The Kawakita Lab studies the birational geometry of algebraic varieties, within the field of algebraic geometry. The minimal model program is a method that picks out a representative variety from each birational equivalence class by comparing canonical divisors. The lab works on the classification of threefold divisorial contractions, and on research guided by minimal log discrepancies, an invariant of singularities. Building on the research so far, a book has also been written.
Yusuke Kobayashi, Associate Professor
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The Kobayashi Lab studies the theory of algorithms for discrete optimization problems. Discrete optimization problems ask for maximizing or minimizing some measure over discrete structures such as networks and graphs, and they appear in every part of modern society. The lab investigates where the essential difference lies between problems that can be solved efficiently (solvable in polynomial time) and hard problems. It works on the design and theoretical analysis of efficient algorithms, mathematical proofs of hardness, and the construction of mathematical frameworks that encompass a wide variety of efficiently solvable problems.
Akitoshi Kawamura, Associate Professor
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The Theory of Computation Lab (Kawamura Lab) studies the foundational theory of the methods, efficiency, and limits of information processing (the theory of computation). Whether in computer computation or in human mathematical reasoning, information processing is expressed as an algorithm, a procedure made up of finite operations, and the theory of computation explores what can and cannot be done with it. The lab approaches this from both sides: designing useful computational methods and investigating their limits. Centering on the theory of computation, it also takes up topics at the boundary of mathematics and computer science, such as computer mathematics and computer-assisted proofs.
Yusuke Isono, Associate Professor
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The Isono Lab studies the relationship between von Neumann algebras and ergodic theory, in the field of operator algebras. An operator algebra is a subalgebra of the algebra of all bounded linear operators on a Hilbert space. The concept first appeared when von Neumann gave a mathematical formulation of quantum mechanics. The lab mainly investigates von Neumann algebras constructed from discrete groups, from the viewpoint of deformation/rigidity theory.
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