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703 labs · 48 student voices
Johannes Jaerisch, Associate Professor
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Prof. Jaerisch studies dynamical systems, centering on ergodic theory and fractal geometry. The initial values of orbits that behave chaotically often form a fractal set, such as a Julia set. For conformal dynamical systems, Prof. Jaerisch investigates the relationship between their properties as dynamical systems and their properties as fractals, using thermodynamic formalism as a tool. In the message to students, the professor says that fractal geometry is a new field, so students can take on new challenges from a fairly early stage.
Akira Ishii, Professor
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Prof. Ishii studies algebraic geometry, focusing especially on a phenomenon called the McKay correspondence. The McKay correspondence is a beautiful and mysterious relationship between the geometric description of the resolution of two-dimensional singularities (Kleinian singularities) and the representation theory of finite groups. Generalizations of this relationship are also called by the same name. The professor has described resolutions of singularities as moduli spaces and studied the structure of the related derived categories.
Keisuke Izumi, Associate Professor
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Prof. Izumi is an Associate Professor at the Graduate School of Mathematics, Nagoya University, with theory of gravity and cosmology as keywords. In the department's list of research fields, the professor appears under mathematical physics, general relativity, and cosmology. In the graduation research seminar, students learn the mathematics of general relativity, the physical theory that describes the dynamics of spacetime. Starting with an understanding of the Einstein equations, students go on to learn about black holes, the expanding universe, and gravitational waves, depending on their interests.
Yoshimichi Ueda, Professor
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Prof. Ueda studies noncommutative analysis broadly, building on operator algebra theory. Operator algebra theory demands both the power of algebra to handle noncommutativity and the power of analysis to overcome infinite-dimensionality. The lab also conducts research related to harmonic analysis, probability theory, and ergodic theory, aiming to contribute to the analysis of noncommutative quantities based on operator algebras.
Hiroshi Ohta, Professor
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Prof. Ohta studies geometry, centered on symplectic geometry, which has its origins in analytical mechanics. The lab investigates the relationship between singularities and symplectic and contact geometry, as well as Floer cohomology, from the viewpoint of homotopy algebraic structures. Together with collaborators, Prof. Ohta has worked on giving mathematical foundations, from the symplectic geometry side, to the mirror symmetry conjecture predicted by string theory.
Toru Ohira, Professor
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Prof. Ohira builds mathematical models from concrete natural and social phenomena. The core of the research is taking up problems that are not yet part of mathematics and shaping them into mathematical problems. The lab works on the mathematics of systems involving delay and fluctuation (noise) in information transmission, and on "collective pursuit and evasion," in which groups chase and flee. Prof. Ohira believes that building mathematical models also requires sensibilities from outside mathematics, such as those gained from experiments and observation, as well as collaboration with people in other fields.
Soichi Okada, Professor
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Prof. Okada studies the intersection of combinatorics and representation theory. Combinatorics is the mathematics of discrete objects, and representation theory is the mathematics of studying how algebraic systems such as groups are realized as linear transformations. The professor is interested in Young diagrams and symmetric functions related to the representation theory of classical groups, as well as counting problems for plane partitions and alternating sign matrices. In the small-class master's courses, the topics listed include enumerative combinatorics, symmetric functions and their extensions, and quantum groups and crystal bases.
Hisashi Kasuya, Professor
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The Kasuya Lab studies differential geometry and complex geometry. It works on the geometry of spaces that do not have a Kähler structure, noncommutative Hodge theory, and the geometry of Lie groups and homogeneous spaces. Beyond linear algebra and set theory, no prior knowledge is required when joining the lab, and students who have never studied geometry are accepted. The lab encourages students to consult with it before submitting the lab preference form, and online meetings and visits to its seminar are available.
Jun Kato, Associate Professor
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Prof. Kato studies nonlinear partial differential equations. Nonlinear partial differential equations appear as models of a wide range of natural phenomena. The professor examines mathematical well-posedness, such as whether a solution exists and whether it is uniquely determined. In particular, equations describing wave phenomena are studied with methods from functional analysis and harmonic analysis (including Fourier analysis).
Jacques Garrigue, Professor
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Prof. Garrigue studies the theory of programming languages. The goal is to eliminate bugs thoroughly without sacrificing the expressiveness of programming languages. The main subjects are type systems and program proofs. As one of the developers of the functional programming language OCaml, the professor has pursued both expressiveness and safety. The professor is also trying to apply Coq, a proof assistant, to proofs in mathematics and systems.
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