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11 labs · 0 student voices
Other departments in Research Institute for Mathematical Sciences ›Faculties at Kyoto University ›
Narutaka Ozawa, Professor
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The Ozawa Lab studies the relationship between operator algebras and discrete groups. A group is a mathematical language for describing the symmetry of an object. For example, the set of all transformations, such as rotations and reflections, that leave the structure of a crystal unchanged forms a group. The lab treats the elements of a group as operators and investigates problems about groups using analytic techniques from operator algebra theory, while also pursuing applications in the opposite direction. In addition to traditional operator algebra theory, the lab also studies operator theory, Banach algebra theory, Banach space theory, and discrete metric geometry.
Masahito Hasegawa, Professor
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The Hasegawa Lab studies theoretical computer science, particularly the semantics of programming languages. The lab aims to extract and analyze the mathematical structures underlying computation, so that the wide variety of software on computers can be discussed in a unified and rigorous way. The approach is to understand complex computational phenomena through appropriately abstracted structures; in a sense, it is a "representation theory of computation." The lab mainly uses algebraic and category-theoretic methods, together with the frameworks of proof theory and type theory.
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.
Camila Sehnem, Associate Professor
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The Sehnem Lab studies functional analysis, especially operator algebra theory. The lab is interested in various generalizations of actions of groups and semigroups on C*-algebras (such as correspondences and partial automorphisms), and works on constructing operator algebras, mainly C*-algebras, from such actions. Non-self-adjoint operator algebras and von Neumann algebras have also played important roles in this research.
Tatsuyuki Hikita, Associate Professor
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The Hikita Lab studies geometric representation theory. In mathematics and mathematical physics, a phenomenon called “duality” has been observed, in which seemingly completely different mathematical objects turn out to be equivalent. Mirror symmetry and Langlands duality are well-known examples. One of the lab's research goals is to use problems in combinatorics as probes to find phenomena like duality that lie behind them. The lab has also proved the Stanley–Stembridge conjecture on chromatic symmetric functions of graphs.
Nobu Kishimoto, Lecturer
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The lab studies nonlinear partial differential equations, in particular evolution equations known as dispersive equations. Dispersive equations include the nonlinear Schrödinger equation and the KdV equation. Using methods from harmonic analysis and real analysis, the lab investigates the well-posedness of initial value problems (existence and uniqueness of solutions, and stability with respect to changes in the initial data). The lab also studies global-in-time properties of solutions, such as asymptotics toward linear solutions and finite-time blow-up.
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