Nick Sheridan (IAS and Princeton University)
This mini-course consists of a series of six one-hour lectures.
- 1. Introduction: The relative Fukaya category.
- Precise statement of result (Calabi-Yau case).
- Versions of the Fukaya category: exact, relative, absolute, orbifold.
- 2. The pair of pants. (1.5 talks)
- Constructing the immersed Lagrangian sphere in the pair of pants.
- Computing its Fukaya endomorphism algebra using pearly trees.
- 3. Deformation theory. (0.5 talk)
The endomorphism algebra is uniquely determined up to a
quasi-isomorphism and a mirror map by its first-order term.
- 4. The B-model.
- Matrix factorizations.
- Dyckerhoff's minimal model via the homological perturbation lemma.
- Equivariant versions.
- Orlov's theorem relating graded matrix factorizations to coherent sheaves.
- 5. Automatic split-generation of the Fukaya category.
- Abouzaid's split-generation criterion.
- Generalized split-generation argument (joint with Perutz):
closed-open string maps and maximally unipotent monodromy.
- 6. The Fano case.
- What the Fukaya category of a Fano looks like: c1 eigenvalue decomposition.
- How the same computations also give HMS for Fanos.
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