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Ikeda Lab
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The lab links enumerative geometry, which counts geometric figures, with representation theory.
AboutAbout the lab
A geometry lab that counts the number of figures.
The Ikeda Lab studies enumerative geometry, a branch of algebraic geometry.
This field determines how many geometric figures satisfy given conditions, working on spaces such as Grassmannians.
Enumerative problems are deeply connected to problems in representation theory, where special functions such as Schur polynomials play an important role.
In recent years, the lab has also studied extensions to K-theory and quantum K-theory, beyond cohomology, as well as the relationship with integrable systems.
Key terms
- Enumerative geometry
- A branch of geometry that counts how many figures satisfy given conditions
- Representation theory
- A field of mathematics that studies the symmetries of figures and groups using the language of matrices and vectors
- K-theory
- A theory that studies the properties of a figure using the collection of vector bundles defined on it
ResearchResearch themes
The lab studies enumerative geometry, a field of algebraic geometry, determining the number of geometric figures that satisfy given conditions. Using methods from representation theory and K-theory, it also investigates the relationship with integrable systems.
*Illustrative imageEnumerative Geometry
The lab studies problems in algebraic geometry that ask how many figures satisfy given conditions, working on spaces such as Grassmannians.
*Illustrative imageRepresentation Theory and Schur Polynomials
Enumerative problems are deeply connected to the representation theory of linear algebraic groups, and special functions such as Schur polynomials play a central role.
*Illustrative imageExtension to K-Theory and Quantum K-Theory
The lab extends enumerative geometry beyond cohomology to the frameworks of K-theory and quantum K-theory, studying new special functions.
*Illustrative imageRelationship with Integrable Systems
Integrable systems, which are highly symmetric differential equations, are also a subject of study. It has become clear that the structure of integrable systems is related to quantum K-theory.
MembersFaculty
The members of the Ikeda Lab consist of faculty members and doctoral, master's, and undergraduate students.As of 2026
- ProfessorTakeshi Ikeda
- Lecturer (Fixed-Term)Takashi Kono
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: “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
- Enumerative Geometry: “Cannonballs mg 3393” Rama / CC BY-SA 2.0 fr (cropped)
- Representation Theory and Schur Polynomials: “Terrace field yunnan china denoised” Jialiang Gao / CC BY-SA 3.0 (cropped)
- Extension to K-Theory and Quantum K-Theory: “Ring van Möbius - Hans Kalkhoven” Alex P. Kok / CC BY-SA 4.0 (cropped)
- Relationship with Integrable Systems: “Tidal bore at the Qiantang river, Hangzhou” gwydionwilliams / CC BY 2.0 (cropped)
- Related lab (本間研究室): “Spinning top shadow” Armenak Margarian / CC BY-SA 4.0 (cropped)
- Related lab (楫研究室): “Modell einer Kubik mit vier Doppelpunkten -Schilling VII, 5 - 48” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (永井研究室): “Klein bottle glass2” PaulT (Gunther Tschuch) / CC BY-SA 4.0 (cropped)
- Related lab (金沢研究室): “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
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