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Applied Mathematics Lab
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A mathematics lab that studies partial differential equations, probability theory, and mathematical logic.
AboutAbout the lab
From irreversible phenomena to the foundations of mathematics
The Applied Mathematics Lab is a research group in the Department of Mathematics, Graduate School of Science, that studies functional analysis and evolution equations, probability theory, mathematical logic and foundations of mathematics, and the theory of partial differential equations and functional inequalities.
Faculty profile pages list research subjects including partial differential equations that describe phenomena involving irreversibility, Brownian motion, arithmetic systems and reverse mathematics, and functional inequalities.
Key terms
- Evolution equation
- A partial differential equation viewed as an ordinary differential equation on an infinite-dimensional space
- Brownian motion
- A stochastic process that mathematically describes the irregular motion of microscopic particles in a liquid
- Reverse mathematics
- Research that examines, from the viewpoint of logic, the strength of mathematical theorems developed within arithmetic systems
ResearchResearch themes
In the Applied Mathematics Lab, faculty members work in functional analysis and evolution equations, probability theory, mathematical logic and foundations of mathematics, and the theory of partial differential equations and functional inequalities. Below are the research subjects described on the faculty profile pages of the Department of Mathematics.
Partial Differential Equations Describing Irreversible Phenomena
Prof. Akagi studies partial differential equations that describe phenomena involving irreversibility, such as diffusion and phase transitions. Viewing a partial differential equation as an evolution equation, that is, an ordinary differential equation on an infinite-dimensional space, Prof. Akagi uses functional analysis and the calculus of variations to address the existence and uniqueness of solutions and their behavior.
*Illustrative imageBrownian Motion and Stochastic Processes
Motivated by an interest in statistical-mechanical phenomena such as phase transitions, Prof. Hariya studies perturbations of Brownian motion by various functionals and the behavior of their thermodynamic limits. Recently, Prof. Hariya has been examining the relationship between a divergence formula on the infinite-dimensional space of entire Brownian paths and a variational formula for the fundamental solution of the heat equation with Dirichlet boundary conditions under domain deformation.
Arithmetic Systems and Reverse Mathematics
Prof. Yokoyama studies arithmetic systems, which axiomatize the basic properties of the natural numbers, from the viewpoints of proof theory, nonstandard model theory, and computability theory. In reverse mathematics, Prof. Yokoyama is interested in classifying and evaluating combinatorial statements and theorems of analysis. Associate Professor Yamazaki studies reverse mathematics, which classifies mathematical theorems using subsystems of second-order arithmetic characterized by set existence axioms, as well as models of those subsystems.
Partial Differential Equations and Functional Inequalities
Associate Professor Ioku studies the structure of solutions to partial differential equations and the functional inequalities that play an important role in analyzing them. Recently, Associate Professor Ioku has been investigating functional inequalities originating in differential geometry and mathematical physics, focusing on their best constants, the special functions that attain them, and the meaning of these.
MembersFaculty
- ProfessorGoro Akagi
- ProfessorYu Hariya
- ProfessorKeita Yokoyama
- Associate ProfessorNorisuke Ioku
- Associate ProfessorTakeshi Yamazaki
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: “Liquid Crystal Phase Transition” KarlGaff / CC BY 4.0 (cropped)
- Brownian Motion and Stochastic Processes: “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (cropped)
- Related lab (Analysis Lab): “Slide Rule Mathematics - DPLA - afb7ca99683dc5a3f82ec3981f6eb04e” 作者不詳 / Public domain (cropped)
- Related lab (Geometry Lab): “Riemann Minimal Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (Correlated Mathematical Analysis Lab): “Mathematical and Simulation Modeling in Neuroscience (NeuroMat 2018) 04” Sturm / CC BY-SA 4.0 (cropped)
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