Analytic toric geometry to Real Algebraic
- Analytic toric geometry
- Complex manifolds, Dolbeault theory, and Kähler geometry
- Complex manifolds: transport, quotients, bundles, and gluing
- Curvature, Jacobi fields, submanifolds, and Bochner geometry
- Differential geometry — forms, de Rham cohomology, flows, and degree
- Geodesics, the exponential map, and the Hopf–Rinow theorem
- Geometric topology and the solved Kirby-list problems
- Hamiltonian Floer operations: geometric product and multiplicative PSS
- Hodge structures (pure, mixed, and polarized)
- Morse functions, sublevel topology and Morse–Bott attachments
- Positive scalar curvature, surgery and bordism
- Real algebraic geometry: sign determination and cylindrical decomposition
- Smooth orbifolds with finite isotropy
- Symplectic geometry and Hamiltonian mechanics
- Taubes–Gromov theory
- The Yamabe problem and conformal scalar curvature
- Convex
- Lie
- Manifold
- Real Algebraic
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