Algebra Calabi-Yau manifolds Elliptic space Fourier transformations Geometry Torus (Geometry) (Colo.)homology theory Abelian categories Algebra, Homological Algebraic geometry Algebraic stacks Algebraic topology Applied homological algebra and category theory Categories with structure Category theory; homological algebra Derived categories, triangulated categories Differential topology Double categories, $2$-categories, bicategories and generalizations Families, fibrations Homological algebra Homotopy theory Manifolds and cell complexes Mathematical physics Mirror symmetry Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories Quantum field theory; related classical field theories Quantum theory Sheaves, derived categories of sheaves and related constructions Simplicial sets, simplicial objects (in a category) Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)