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Toda Lab
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A lab that counts curves on Calabi-Yau manifolds using the language of derived categories.
AboutAbout the lab
Mathematics where invariants and categories intertwine.
Toda Lab studies derived categories and enumerative invariants on algebraic varieties in the field of algebraic geometry.
An algebraic variety is a geometric object defined as the zero set of polynomials, and Calabi-Yau manifolds, among them, play an important role in superstring theory in physics.
There are various invariants for counting curves on Calabi-Yau 3-folds, and all of them are expected to be equivalent.
Key terms
- Algebraic variety
- A geometric object defined as the zero set of polynomials. Parabolas and circles are examples.
- Calabi-Yau manifold
- One important class in the classification of algebraic varieties. It also appears in superstring theory.
- Derived category
- An abstract framework that handles objects such as sheaves on a geometric object, together with the relations between them.
ResearchResearch themes
The lab's field is algebraic geometry, and it studies derived categories of coherent sheaves on algebraic varieties and stability conditions on them. It is interested in the moduli theory of stable objects and in enumerative invariants.
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MembersFaculty
- ProfessorYukinobu TodaPublications ↗
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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: “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
- Derived Categories and Enumerative Invariants: “CY5-6D-lattice” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
- Related lab (Ito Lab): “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
- Related lab (Oguiso Lab): “Calabi yau” Jbourjai / Public domain (cropped)
- Related lab (Kawakami Lab): “BarthSextic” Mike Williams / Public domain (cropped)
- Related lab (Kelly Lab): “Spectral Sequence Visualization” L.penguu / CC BY-SA 4.0 (cropped)
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