Classification of surfaces, 3-folds and higher dimensional varieties.
Calabi-Yau 3-folds, mirror symmetry. Moduli. Relations with other areas
- Classification: problems on existence and moduli of algebraic surfaces and 3-folds, including methods of projective and birational geometry, commutative algebra, toric geometry, etc. The minimal model program, flips and birational contractions. The proof of classification of 3-folds and log 3-folds. Biregular and birational geometry of Fano 3-folds.
- CYs and mirror symmetry: CY 3-folds in classification, problems of existence, moduli and period maps. Kaehler cone, birational changes of models. Resolution of quotient singularities, McKay correspondence and stringy geometry. Special Lagrangian geometry and mirror symmetry. Relation with "physics".
- Moduli: The heading covers two quite different topics: Moduli of varieties, e.g., Abelian varieties or K3s, and moduli of vector bundles, especially over curves, surfaces and special 3-folds.
- Relations with other areas: there are very many of these, not all predictable. Lean towards interested British math community. Algebra, number theory, physics, gauge theory, symplectic geometry and other aspects of differential geometry, hyperK„hler and related "special" geometries.
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