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Applied Mathematics Lab
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A lab in the Department of Mathematics that studies partial differential equations, probability theory, and other areas of mathematics.
AboutAbout the lab
Exploring mathematics through partial differential equations and probability theory
The Applied Mathematics Lab is a research unit in the Department of Mathematics, with professors who study partial differential equations, probability theory, real analysis, and algebraic geometry and group theory.
Associate Professor Itsuko Hashimoto studies the equations that describe the motion of compressible fluids as partial differential equations.
Assistant Professor Kohei Hayashi works on probability theory, which explains macroscopic phenomena starting from random microscopic systems.
The staff page of the Department of Mathematics introduces the research area of each professor.
Key terms
- partial differential equation
- An equation written in terms of the relationship between an unknown function and its partial derivatives. It appears in the description of macroscopic phenomena such as the motion of fluids.
- compressible fluid
- A fluid whose motion is described by the compressible Navier–Stokes equations. These equations are built from conservation laws such as the conservation of mass.
- universality class
- A universal type that appears in interacting systems with many degrees of freedom and has properties different from those of the normal distribution.
ResearchResearch themes
In the Applied Mathematics Lab, each professor studies mathematics such as partial differential equations and probability theory. This page introduces the research of the professors whose research is described on the staff page.
*Illustrative imageAnalysis of Equations for Compressible Fluids
The lab studies initial-boundary value problems for one-dimensional viscous conservation laws, the Burgers equation, and the compressible Navier–Stokes equations. Recently it has also taken an interest in spherically symmetric problems for fluid equations in higher-dimensional space, working on the construction of stationary solutions and on the inviscid limit problem.
*Illustrative imageUniversality in Large-Scale Interacting Systems
This is probability theory originating in statistical physics, which explains macroscopic phenomena described by partial differential equations starting from microscopic systems with randomness. It aims to mathematically elucidate the universality classes that appear in interacting systems with many degrees of freedom.
MembersFaculty
- ProfessorNaohito Tomita
- Associate ProfessorItsuko Hashimoto
- Assistant ProfessorTakao Iohara
- Assistant ProfessorKohei Kikuta
- Assistant ProfessorKohei Hayashi
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique ( )” Ecole polytechnique Université Paris-Saclay / CC BY-SA 2.0 (cropped)
- Analysis of Equations for Compressible Fluids: “Oblique Shock Wave” Gtv5007 / CC BY-SA 3.0 (cropped)
- Universality in Large-Scale Interacting Systems: “DLA spiral” Karsten Schmidt / CC BY-SA 2.0 (cropped)
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