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Kakehi Lab
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A lab that studies differential equations and integral geometry on symmetric spaces.
AboutAbout the lab
Studying differential equations on symmetric spaces
The Kakehi Lab studies differential equations and integral geometry on symmetric spaces.
The lab has papers and talks on snapshot problems for the wave equation and the Klein-Gordon equation.
The lab belongs to the Analysis Group of the Degree Program in Mathematics.
Key terms
- differential equation
- An equation that expresses relationships among the rates of change of quantities that vary from moment to moment.
- symmetric space
- A geometric space, including the sphere, that has a symmetric structure around each point.
- integral geometry
- A field that studies the properties of a space by integrating over collections of objects in it, such as lines and planes.
- surjectivity
- The property that every function in the target space is obtained as a result of applying the operator.
ResearchResearch themes
The lab's research areas are differential equations and integral geometry on symmetric spaces. Recently, it has been working on snapshot problems for hyperbolic equations and on geometric analysis on symmetric spaces.
*Illustrative imageSnapshot Problems for Hyperbolic Equations
The lab studies snapshot problems for hyperbolic equations together with geometric analysis on symmetric spaces. It has papers and talks dealing with the wave equation and the Klein-Gordon equation on the sphere.
*Illustrative imageConvolution Operators on Symmetric Spaces
The lab has studied the geometric analysis of convolution operators on symmetric spaces, along with applications to integral geometry and inverse problems. It has a paper on the surjectivity of convolution operators on noncompact symmetric spaces.
MembersFaculty
- ProfessorTomoyuki Kakehi
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: “Wave Interference” Cubitt Robert / CC BY-SA 4.0 (cropped)
- Snapshot Problems for Hyperbolic Equations: “Black alder twig and water ripples at Wolfsberger Mühle” Radomianin / CC BY-SA 4.0 (cropped)
- Convolution Operators on Symmetric Spaces: “Torregrotta geodesic dome 2023” Alphacentauri2007 / CC BY-SA 4.0 (cropped)
- Related lab (Takeuchi Lab): “Soap Films” Ryan Somma / CC BY-SA 2.0 (cropped)
- Related lab (Takeyama Lab): “Portal Math Banner Background ka” User:Alsandro / CC0 (cropped)
- Related lab (Kuwabara Lab): “Matematička gimnazija - Mathematical Gymnasium Belgrade - MGB - Physics Laboratory 1” MGB / Public domain (cropped)
- Related lab (Aiyama Lab): “Schwarz CLP Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
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