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Onodera Lab
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The lab explores the mathematical principles of the “forms” that appear in the natural sciences.
AboutAbout the lab
In Search of the Mathematical Principles of Beautiful “Forms”
The Onodera Lab studies the mathematical principles of “forms” through partial differential equations and variational problems.
Phenomena and “forms” that appear in the natural sciences can be understood as states in which an underlying “energy” is at a local minimum.
The lab formulates the problem of finding such states as a calculus problem in infinite-dimensional spaces, and aims to clarify their principles and structures.
Key terms
- Partial differential equation
- An equation containing rates of change with respect to several variables, such as position and time
- Variational problem
- A problem of finding the shape or state that makes a quantity such as energy as small (or as large) as possible
- Local minimum
- A state whose value is smaller than that of any nearby state. It is not necessarily the global minimum, the smallest value overall
- Infinite-dimensional space
- A space made by treating each function or shape as a point, in which there are infinitely many directions to move
ResearchResearch themes
*Illustrative imageLearning About the Interior from Surface Measurements
There is a problem called the “Backus problem”: when the strength of the Earth’s magnetic field is measured at the surface, can the state of the interior be determined uniquely from it? The lab treats this problem as a partial differential equation and shows that the solution is determined locally.
*Illustrative imageMathematics for Optimizing Shapes
What shape makes a certain quantity as small or as large as possible? The lab formulates “shape optimization problems,” in which the shape itself is the variable, as calculus in infinite dimensions, and investigates the properties of optimal shapes.
MembersFaculty
- Associate ProfessorMichiaki OnoderaPublications ↗
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Honda LabSchool of Science, Department of MathematicsComplex geometryThe information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
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: “Minimalfläche mit Seifenhaut Tetraeder 0326” Bin im Garten / CC BY-SA 3.0 (cropped)
- Learning About the Interior from Surface Measurements: “Earth's magnetic field, schematic” Zureks / CC0 (cropped)
- Mathematics for Optimizing Shapes: “Fluid-structure-interaction-pressure-field-topology-optimization-4” Chrlundg / CC BY-SA 4.0 (cropped)
- Related lab
(利根川研究室): “Minimalfläche mit Seifenhaut Würfel 0328” Bin im Garten / CC BY-SA 3.0 (cropped) - Related lab (三浦英之研究室): “Yakushima Island Von Karman Vortex street Oct 12 2012” NASA, MODIS Rapid Response System / Public domain (cropped)
- Related lab (馬研究室): “Kummer surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Related lab (本多研究室): “Calabi yau” Jbourjai / Public domain (cropped)
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