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Analysis Lab
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A division of the Department of Mathematics that studies partial differential equations, probability theory, and algebraic analysis.
AboutAbout the lab
Partial differential equations, probability theory, and algebraic analysis.
The Analysis Lab is one of the divisions of the Department of Mathematics, Graduate School of Science, Osaka University (School of Science, Department of Mathematics), and its faculty specialize in partial differential equations, probability theory, algebraic analysis, and related areas.
The staff list gives the faculty members' specialties as nonlinear partial differential equations, partial differential equations, probability theory, free probability theory, ergodic theory, algebraic analysis, and microlocal analysis.
In probability theory, one faculty member has studied the behavior of Lévy processes, a class of stochastic processes (models describing the random evolution of a phenomenon over time), and stochastic control of models built on them.
Another faculty member takes the viewpoint of algebraic analysis and seeks a unified understanding of the general principles common to problems involving differential equations.
Key terms
- Stochastic process
- A model describing the random evolution of a phenomenon over time. One of the key topics in probability theory.
- Lévy process
- A type of stochastic process. It is the subject of basic research on its behavior and of applications to stochastic control.
- Algebraic analysis
- A field that studies problems involving differential equations from an algebraic standpoint, using unified viewpoints and computational methods.
ResearchResearch themes
This division studies areas of analysis such as differential equations, probability theory, and algebraic analysis. Here we introduce the probability theory and algebraic analysis topics for which the faculty members' profile pages include a description of their research.
*Illustrative imageBehavior of Lévy processes and stochastic control
Associate Professor Noba has studied Lévy processes, a type of stochastic process. Using scale functions, he has characterized the behavior of real-valued stochastic processes with no positive jumps, and he has studied stochastic control of models built on Lévy processes.
*Illustrative imageUnderstanding differential equations through algebraic analysis
Associate Professor Uchida aims to understand the general principles common to analytic problems involving differential equations, using the unified viewpoints and computational methods of algebraic analysis. He hopes that this same approach will advance understanding not only of local problems but also of global ones.
MembersFaculty
- ProfessorSoichiro Katayama
- ProfessorNoriyoshi Sakuma
- ProfessorShinichi Doi
- ProfessorKoji Yano
- Associate ProfessorMotoo Uchida
- Associate ProfessorKei Noba
- Associate ProfessorHaruya Mizutani
- Assistant ProfessorYoshinori Nishii
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: “Graph of argument of square root of complex variable -pi to pi” Dom walden / CC BY-SA 4.0 (cropped)
- Behavior of Lévy processes and stochastic control: “Dice ( )” Daniel Dionne / CC BY-SA 2.0 (cropped)
- Understanding differential equations through algebraic analysis: “Mathematical analysis, Linear algebra, Mathematics lecture notes, Rostov-on-Don, Russia” Vyacheslav Argenberg / CC BY 4.0 (cropped)
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