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Kumagai Lab
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A lab that builds probability theory on fractals to explain physical phenomena.
AboutAbout the lab
Building probability theory on fractals
Kumagai Lab uses probability theory to study the properties of complex shapes such as fractals.
The lab constructs random walks and Brownian motion on complex shapes and investigates physical properties such as how heat propagates.
Fractals have no smoothness, so ordinary differentiation cannot be used, but the methods of probability theory remain effective even on non-smooth spaces.
In addition to probability theory, the lab conducts interdisciplinary research connected to a wide range of fields, including harmonic analysis and function space theory.
Key terms
- Probability theory
- A field of mathematics that studies phenomena governed by chance, such as rolling dice
- Fractal
- A complex shape in which, when a part of it is magnified, forms similar to the whole appear repeatedly
- Random walk
- The path of a point that keeps moving in randomly chosen directions
NewsLab news
Prof. Kumagai was elected a Fellow of the Institute of Mathematical Statistics (USA)
Prof. Kumagai received the Medal with Purple Ribbon in autumn 2025
Prof. Kumagai received the Prize for Science and Technology in the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (FY2024, Science and Technology field)
ResearchResearch themes
The lab uses probability theory to study physical phenomena that occur on complex shapes such as fractals. Through random walks and Brownian motion, it analyzes how heat propagates, among other things.
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MembersFaculty
- ProfessorTakashi Kumagai
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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: “Mandelbrot Set Image 112” Aokoroko / CC0 (cropped)
- Probability Theory on Fractals: “Mandelbrot Set Image 107” Aokoroko / CC0 (cropped)
- Related lab (福泉研究室): “Rogue wave (03)” F1jmm / CC0 (cropped)
- Related lab (田中研究室): “Minimalfläche mit Seifenhaut Tetraeder 0326” Bin im Garten / CC BY-SA 3.0 (cropped)
- Related lab (小川研究室): “Chladni plate 14” Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tetsuo Argenton / CC BY-SA 4.0 (cropped)
- Related lab (池田研究室): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
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