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33 labs · 9 student voices
Other departments in School of Science ›Faculties at Hokkaido University ›
Masanori Asakura, Professor
1 student voices
Prof. Asakura studies arithmetic geometry using the theory of motives as a guide. Motives are a vision conceived by Grothendieck in the 1960s; refined by many mathematicians since, they are now an active area of research. Two of the Millennium Prize Problems, the Hodge conjecture and the Birch and Swinnerton-Dyer conjecture, are also deeply connected to this field. Centered on the still-unsolved Beilinson conjecture, the research has recently been tackling problems by making active use of p-adic theory.
Yoichi Shibukawa, Professor
1 student voices
Prof. Shibukawa studies the Yang–Baxter equation and its solutions, within the field of integrable systems. In statistical mechanics, the (quantum) Yang–Baxter equation is the equation that guarantees a lattice model is solvable. The braid relation, which is equivalent to this equation, also makes sense as an equation on morphisms in a tensor category. The lab considers solutions in various tensor categories, seeking to grasp connections with representation theory, Hopf algebras, and solitons from a unified perspective.
Naohiko Kasuya, Associate Professor
1 student voices
Prof. Kasuya studies complex surfaces and the contact structures that appear on their boundaries. A typical example is a Stein surface and its strongly pseudoconvex boundary. Of particular interest are the Milnor fibers and singularity links of complex hypersurface singularities known as cusp singularities. Building on differential topology, the work also intersects with complex geometry, several complex variables, and singularity theory.
Masaharu Nagayama, Professor
1 student voices
The lab studies methods for understanding natural and biological phenomena from the viewpoint of mathematical sciences. A mathematical model imitates a phenomenon with equations, and when it is reproduced on a computer through numerical computation, the mechanisms hidden in the phenomenon become visible. Adding mathematical analysis makes it possible to extract mathematical structures shared by different phenomena. The lab investigates the motion of droplets and particles, the barrier function of the epidermis, and the motion of cells, in collaboration with experimental groups and companies.
Takao Namiki, Professor
1 student voices
Prof. Namiki studies the field collectively known as complex systems. A cellular automaton is a dynamical system that simply updates the 0s and 1s in a row of cells according to a simple rule, yet shows a wide variety of behavior. The lab treats this using ideas from thermodynamics and statistical mechanics, aiming to grasp the properties of the system from how its entropy decreases. The lab also works on quantum walks, which are related to quantum computation, chaotic time-series analysis of EEG (brainwave) data, and the construction of a digital library of mathematics.
Satoshi Masaki, Professor
1 student voices
Prof. Masaki works mainly on nonlinear dispersive equations within the theory of partial differential equations. Roughly speaking, dispersive equations are equations about “waves.” The lab deals with the nonlinear Schrödinger equation, the nonlinear Klein-Gordon equation, the KdV equation, and others. A major goal is to understand how nonlinearity affects the behavior of solutions after a long time.
Yuzuru Sato, Associate Professor
1 student voices
Prof. Sato studies nonlinear dynamical systems and complex systems, especially the complexity of spatiotemporal chaos. From the standpoint of random dynamical systems, the lab investigates what happens when deterministic chaos and stochastic noise are mixed. Main themes also include the phenomenology and time series analysis of dynamical systems with many degrees of freedom, and information-theoretic and computational analysis of chaotic dynamics. Building on dynamical systems theory and nonlinear physics, the lab extends its applications to neighboring fields such as computation theory, information theory, and predictive control.
Sohei Tasaki, Associate Professor
1 student voices
Prof. Tasaki studies, from a mathematical standpoint, how the complex structures of living systems arise and how they achieve their sophisticated functions. The lab looks across multiple levels: gene-level regulation that determines cell states, the movement of cell populations, the shapes of tissues, and the relationship with the surrounding environment. For each level, and for the links between levels, the lab builds mathematical models fitted to experimental data. The lab also develops new data analysis methods to extract the necessary information from high-dimensional life science data.
Yushi Nakano, Associate Professor
1 student voices
Prof. Nakano studies dynamical systems theory and ergodic theory. Dynamical systems theory is a field that examines how a system behaves after a long time has passed, given the law of its evolution over one unit of time. The objects of study are not limited to mechanical models, but also include mathematical models of natural and social phenomena such as population, stock prices, and rainfall. The property by which a small change in the initial state later has a large effect is called chaos, and the lab studies the statistical properties of such systems.
Toshiyuki Akita, Professor
0 student voices
The Geometry Lab approaches geometry as the study of measuring the shape of things. It extracts quantities that capture the features of a shape, and investigates whether those quantities truly describe the shape well and how they can be computed. Beyond triangles and surfaces, it treats physical phenomena, complex figures, solution sets of equations, groups, and information as “things that have shape.” Its research is broad, spanning topology, algebraic geometry, differential geometry, singularity theory, and mathematical physics, and members collaborate while preserving diversity.
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