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33 labs · 9 student voices
Other departments in School of Science ›Faculties at Hokkaido University ›
Nao Hamamuki, Associate Professor
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Prof. Hamamuki studies nonlinear partial differential equations. The main subjects are equations that describe the motion of surfaces (interfaces) separating two different phases of a substance, as they arise in crystal growth and materials science. Based on the theory of viscosity solutions, a type of weak solution, the lab investigates the existence, uniqueness and long-time behavior of solutions, aiming to give these equations a rigorous mathematical foundation. Recently, the lab has also become interested in understanding phenomena from multiple perspectives through limit procedures, such as the relationship between the discrete and the continuous and between the micro and the macro.
Akira Sakai, Professor
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Prof. Sakai studies problems in mathematical physics, especially probability theory and statistical mechanics, with mathematical rigor. The central interests are phase transitions and critical phenomena, and the limit theorems associated with them. For example, the Ising model, a statistical-mechanical model of a magnet, shows a phase transition in which spontaneous magnetization appears or disappears as the temperature is changed. Critical phenomena are thought to arise from the cooperation of infinitely many components, and they require a theory that goes beyond conventional probability theory dealing with independent variables.
Hirotoshi Kuroda, Associate Professor
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Prof. Kuroda studies variational problems and partial differential equations with variational structure. The main subject is the total variation flow equation, which arises when removing noise from images. Because this equation is strongly singular, the lab uses subdifferentials of convex functions and the nonlinear semigroup theory they generate to study whether solutions exist and how they behave. The lab also covers total variation flow equations that appear in mathematical models of crystal growth, and recently it has taken an interest in phenomena that occur when a domain becomes thin and degenerates.
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