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703 labs · 48 student voices
Tomomi Kawamura, Associate Professor
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Prof. Kawamura studies knot theory and low-dimensional topology. Put simply, knot theory is a branch of geometry that examines how tangled a piece of string is. The professor studies the properties of invariants of knots and links, that is, numbers, polynomials, and the like that express their complexity. The professor reportedly never stops being amazed by the depth of the field: results from advanced theories such as gauge theory, which developed in physics, are applied to proving formulas that look simple at first glance.
Nanao Kita, Associate Professor
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Prof. Kita studies discrete mathematics and theoretical computer science, centered on graph theory, combinatorial optimization, and algorithms. Motivated by optimization theory and algorithm design, the professor investigates the structure of graphs. The lab does not do applied research; its style is to build theory by accumulating theorems and proofs. The lab accepts undergraduate students from the Department of Mathematics in the School of Science for graduation research, and accepts graduate students through the Graduate School of Mathematics.
Shinya Kinoshita, Associate Professor
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Prof. Kinoshita studies the theory of partial differential equations and harmonic analysis. The focus is on dispersive and wave equations, which describe a wide range of wave phenomena arising in quantum mechanics, plasma engineering, and fluid dynamics. Given information at a certain time (the initial data), the research shows that a solution exists and is unique, and then examines how that solution behaves. Harmonic analysis, especially Fourier restriction theory, plays a major role as a tool for this.
Takayuki Kihara, Professor
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Prof. Kihara studies the foundations of mathematics and mathematical logic. The foundations of mathematics is a field that takes mathematics itself as its object and explores its premises and limits. Prof. Kihara is interested in theories that classify fundamental mathematical concepts such as computation, proof, and definition by their complexity. The core of his recent research is the analysis of the internal logic of sheaf toposes through "oracle sites."
Masashi Kubo, Associate Professor
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Prof. Kubo studies the fundamental theory of communication within information theory. The specialties are source coding, the theory of data compression, and channel coding. Although the field has a name like information engineering, it is approached as a branch of mathematics based on probability theory, and sometimes hardly uses computers. In small-class courses, the basic approach is to choose topics that involve probability in some form.
Tetsuya Shiromizu, Professor
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Prof. Shiromizu studies general relativity and cosmology. Prof. Shiromizu applies geometry to relativity, particle physics, and cosmology, and proposes original and universal insights and formulations. The professor takes a distinctive strategy of approaching, through geometry, the mysteries of the universe revealed by observation. The lab accepts students for senior thesis research in the Department of Mathematics, School of Science, in principle every other year.
Mitsuru Sugimoto, Professor
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Prof. Sugimoto studies partial differential equations and Fourier analysis. Expressing various natural phenomena as partial differential equations makes it possible to treat them mathematically. Through the analysis of these equations, the lab aims to extract new principles that can explain concrete phenomena in a unified way. In particular, the lab aims to apply methods that derive properties of solutions from the structure of the equations to the analysis of quantitative properties, such as the size and smoothness of solutions.
Ryo Takahashi, Professor
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Prof. Takahashi studies commutative algebra. Commutative algebra is a field closely related to algebraic geometry, algebraic combinatorics, and the representation theory of algebras. The professor mainly studies the "representation theory of commutative rings," which is commutative algebra approached from the direction of the representation theory of algebras. The aim is to understand the structure of the module category (the category of all finitely generated modules) of commutative Noetherian rings, especially Cohen–Macaulay rings.
Sho Tanimoto, Professor
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Prof. Tanimoto studies algebraic geometry and arithmetic geometry. For equations with rational coefficients, the field that investigates solutions whose coordinates are rational numbers is called Diophantine geometry, and it has been studied since the time of ancient Greece. In modern mathematics, rational solutions are regarded as points on the geometric object (algebraic variety) defined by the equation, and are studied with the methods of algebraic geometry. The professor has applied methods from higher-dimensional algebraic geometry, which have developed in recent years, to this problem and has achieved results.
Mayu Tsukamoto, Associate Professor
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Prof. Tsukamoto studies the representation theory of algebras. An algebra is a ring that also has the structure of a vector space. Rather than studying an algebra directly, the approach of representation theory is to study the structure of the entire collection of modules that reflects its properties (the module category). Established in the 1970s, this is a relatively new field that continues to develop in close connection with commutative ring theory, algebraic geometry, and the representation theory of Lie algebras and quantum groups.
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