Labs in Kyushu University, Institute of Mathematics for Industry

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The lab uses mathematics to handle lattices and point configurations, and also works on crystal analysis.

Prof. Tomiyasu's lab develops algorithms and applications for discrete structures such as lattices, rings of integers, and point configurations. The lab's tools come from mathematics such as the geometry of numbers, algebraic number theory, discrete mathematics, and convex optimization. The lab also handles problems with concrete applications in numerical analysis and in materials science dealing with atomic structure. The lab's activities, including cross-disciplinary collaboration, take place in mathematical crystallography, where the geometry of numbers, algebraic computation, harmonic analysis, and the generation of packings and meshes can all be used.

#Applied algebra #Number theory #Mathematical crystallography

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A topology lab that studies the shape of manifolds through the singularities of maps.

The lab studies topology, investigating the overall shape of manifolds, which are geometric objects, by using the singularities of differentiable maps defined on them as clues. By restricting the types of singularities to simple ones, or focusing on low-dimensional cases, the lab investigates how singularities relate to the structure of manifolds. The lab also works broadly across many areas of topology, including knots, 4-manifolds, and isolated singularities of complex hypersurfaces. It also works on applications of topology, such as the visual analysis of DNA knots and multivalued function data, and is interested in studying the properties of matter and materials from a topological viewpoint.

#Topology #Singularity theory #Knots

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A probability theory lab that explores the arrangement of random points and the properties of graphs.

Within probability theory, the lab studies determinantal point processes, which describe how points are scattered at random. By extracting the fermionic nature of eigenvalues of random matrices, the lab constructed this model of point configurations. The lab is also interested in the relationships among random walks on graphs, the spectrum of the Laplacian, and the geometric properties of graphs. Recently, the lab has also been studying random topology.

#Determinantal point processes #Random topology #Random walks

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A lab that studies optimization problems involving continuous variables.

This optimization and mathematical programming lab (Professor Hayato Waki) studies optimization problems involving continuous variables. The lab previously published papers on developing algorithms for optimization problems, but it is now interested in using the properties of optimization problems to investigate the structure of the phenomena and problems they model. The lab works on semidefinite programming problems and studies, for example, the relationship between the convergence rate of the method of alternating projections and the properties of the problem.

#Optimization #Mathematical programming #Semidefinite programming

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The lab studies branching laws for representations of Lie groups using algebraic methods.

Associate Professor Masatoshi Kitagawa studies the representation theory of Lie groups, in particular a problem known as branching laws. A branching law concerns how an irreducible representation of a group behaves when it is restricted to a subgroup. Using modules over Lie algebras and D-modules on algebraic varieties as tools, the lab studies the structure of representations algebraically.

#Lie groups #Representation theory #Branching laws

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The lab researches and develops new statistical analysis methods based on mathematical statistics.

The Hirose Lab researches and develops new statistical analysis methods based on mathematical statistics. It also incorporates ideas from methods used in machine learning. Analyzing large-scale data such as genetic data requires statistical models with tens of thousands to hundreds of millions of parameters. The lab is therefore working on new methods of sparse estimation, which extract useful information by estimating most of a large number of parameters as exactly zero.

#Sparse estimation #Factor analysis #Multivariate analysis

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The lab interprets large-scale data using statistics and optimization.

Professor Hien Duy Nguyen's lab studies computational statistics, which analyzes large volumes of data that accumulate gradually and data too large for ordinary computers to handle. It uses methods such as stochastic optimization and Bayesian inference to deal with the difficulties that come with such data. The lab is also interested in statistical tools for model selection when data are complex, methods for verifying whether that selection is valid, and ways of expressing the confidence that shows how reliable an inference is. The professor also concurrently serves as an Associate Professor at La Trobe University in Australia, and is responsible for building collaboration between the two universities.

#Computational statistics #Stochastic optimization #Bayesian inference

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A lab that studies statistics for estimating values for small subdivisions from survey data.

Associate Professor Masayo Hirose's lab studies statistical small area estimation, which estimates characteristic values for each small subdivision from survey data. The lab studies, from both theoretical and applied perspectives, estimation methods that use statistical models to help improve statistical accuracy. In recent years, the importance of EBPM has been recognized, and expectations are also growing for planning based on an understanding of actual conditions in each subdivision. The research keywords are statistical science, small area estimation, and mixed-effects models.

#Statistical science #Small area estimation #Mixed-effects models

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A lab that uses Bayesian statistics to understand physical phenomena from measurement data without ambiguity.

The Tokuda Lab aims to establish guiding principles for understanding physical phenomena from measurement data without ambiguity. The lab combines mathematical modeling, which represents data with simple equations, and statistical inference, which selects models in light of the data. While exploring the mathematics of Bayesian statistics as the foundation, the lab also conducts joint research with researchers in various sciences and in industry. The lab is recruiting fourth-year students from the Department of Mathematics, Faculty of Science who wish to join, as well as incoming graduate students of the Graduate School of Mathematics and the Joint Graduate School of Mathematics for Innovation.

#Bayesian statistics #Uncertainty quantification #Mathematical modeling

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This is the lab of Professor Fumikazu Sato at the Institute of Mathematics for Industry.

Professor Fumikazu Sato is a Professor in the Liaison Strategy Division of the Institute of Mathematics for Industry. Professor Sato also holds a concurrent faculty appointment in the Department of Mathematics, Faculty of Science. As a social contribution activity, Professor Sato serves as a technical advisor (research guidance) to companies.