Advanced Topics In Geometry Revision as of 17:18, 2 February 2017 (edit)LSGNT (talk | contribs)← Older edit Latest revision as of 11:12, 25 February 2017 (edit) (undo)Valsdav (talk | contribs) (3 intermediate revisions by one other user not shown)(No difference) Latest revision as of 11:12, 25 February 2017 Edit Course Spec and Proj Introduction Spec Proj Solution to exercises Blow ups Introduction First Example: Blowing up C^2 at the origin Blowing up an affine variety along an ideal Blowing up a complex manifold Key examples The general definition Solution to exercises Complex manifolds and the Kähler condition Almost Complex structures Integrability The Kähler Condition Exercises Solutions to exercises Chern Classes Introduction and Basic Definitions Bundles on spheres Chern classes as degeneracy loci of generic sections Suggested Reading Additional exercises Solutions to exercises Classifying spaces, equivariant cohomology and localisation Classifying spaces Equivariant cohomology Localisation Solutions to exercises Symplectic reduction Basic Symplectic Geometry Hamiltonian group actions and moment maps Symplectic reduction Geometric Invariant Theory Introduction Reductive groups Introduction and first examples Quotients GIT in the projective setting Solutions to exercises Symplectic toric varieties Introduction Symplectic toric manifolds from polytopes Another way to get toric symplectic manifolds Where is the fan? Toric blow-up Solution to exercises Lefschetz pencils in algebraic and symplectic geometry Lefschetz hyperplane theorem Local study of ordinary double points Monodromy Hard Lefschetz Theorem Moduli Spaces and Stable Bundles Introduction Brief aside on schemes Back to Moduli Spaces Moduli Space of Bundles Mixed Hodge Structures Introduction Linear Algebra and Hodge Theory Mixed Hodge Structures The open smooth case Applications The Weil conjectures Introduction The Weil conjectures Introduction Transfer Counting Points Zeta functions The Weil Conjectures Atiyah-Singer Index theorem K-theory Fredholm Operators The Atiyah-Singer Index formula (INCOMPLETE) Tropical Curves Introduction Amoebas of Curves The Graph of an Amoeba Corner Loci and Tropical Curves The Tropical Semiring Weights and the Balancing Condition Degree and the Number of Tentacles Newton Polygons Puiseux Series Edit Metadata Hidden category: CourseRoot