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Ike Lab
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A mathematics lab that studies sheaf theory and the shape of data.
AboutAbout the lab
From geometric theory to data analysis.
The Ike Lab studies microlocal sheaf theory and topological data analysis, in particular persistent homology.
The lab applies microlocal sheaf theory to topology and symplectic geometry, and its recent interest is in using sheaves to handle singular objects.
Topological data analysis is a set of methods that use tools such as persistent homology to investigate the topology of data.
Key terms
- Persistent homology
- A method for extracting shape features such as holes and loops from data such as a set of points, while varying the scale
- Symplectic geometry
- A branch of geometry that arose from mechanics, which describes the motion of objects. It treats position and momentum together as pairs
- Sheaf
- A mathematical tool for handling information given on each small part of a space by gluing it together consistently without gaps
ResearchResearch themes
The lab's research fields are microlocal sheaf theory and topological data analysis, with applications of microlocal sheaf theory to geometry and persistent homology as its themes. The lab works on both the theoretical side and the side of applications to data analysis.
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MembersFaculty
- Associate ProfessorYuichi IkePublications ↗
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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: “Simplicial complex example” Trevorgoodchild at en.wikipedia / Public domain (cropped)
- Microlocal Sheaf Theory and Persistent Homology: “Point cloud torus” Lucas Vieira / Public domain (cropped)
- Related lab (Aida Lab): “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (cropped)
- Related lab (Okada Lab): “2D Random Walk Trace” Purpy Pupple / CC BY-SA 3.0 (cropped)
- Related lab (Sasada Lab): “Brownien2d3000pts” Ipipipourax / CC0 (cropped)
- Related lab (Uchida Lab): “Ornstein-uhlenbeck simulation” Loxley / CC BY-SA 4.0 (cropped)
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