Open Mathematics Courses

Microlocal sheaves

A research course developing conic sheaves and kernel operations into specialization, microlocal morphisms and microsupport geometry. The lessons are incomplete drafts.

  1. SH02-COURSE-CONTRACT — How to use this course draft
  2. SH02-PREREQ-OPEN — Open prerequisites and exact import contracts
  3. SH02-PREREQ-PROOFS — Supporting verifications for open prerequisites
  4. Open extensions and ambient supports
  5. SH02-SIX-BRIDGE — Proper supports and the bounded classical comparison
  6. Proper-support composition through a change of base
  7. SH02-CA — Extending sections on convex sets
  8. SH02-SUP-EXH-001 — Recovering sheaf cohomology from closed pieces
  9. SH02-NCD — Continuing cohomology through a moving boundary
  10. SH02-EXCEPTIONAL-OPERATIONS — Exceptional inverse image from a finite resolution
  11. SH02-UR — Finite resolutions without a lower bound
  12. SH02-MD — Local orientations, dimension, and integration
  13. Transport along a scaling action
  14. Composing sheaf operators through an intermediate space
  15. SH02-SPH — Inverse operators from complementary hemisphere boundaries
  16. Fourier kernels as radial averaging
  17. Fourier duality through a test complex on the base
  18. SH02-UFD — Duality when the dual leaves the original transform category
  19. SH02-FTC. Comparing traces after Fourier transformation
  20. Moving Fourier kernels across maps and products
  21. SH02-LFT. A linear map inside the Fourier comparison
  22. SH02-FGC-UNIT. The graded line in a Fourier support comparison
  23. SH02-FTE-UNIT. Transposing the complete Fourier trace comparison
  24. SH02-NDF-UNIT. The geometric normalization of Fourier adjunctions
  25. SH02-MEP-UNIT. Following the comparison maps into the normal bundle
  26. SH02-GAM — Directional neighborhoods and a sheaf projector
  27. SH02-FSB — Formal stabilization over arbitrary neighborhood sets
  28. SH02-CB-UNIT — Finite local data and sheaf biduality
  29. SH02-DA-UNIT — Supports, characteristic classes, and finite duality
  30. Boundary conditions, incidence operators, and trace identities
  31. Convex tests and radial comparisons
  32. SH02-NG-UNIT — Normal geometry as a family with a central fibre
  33. Reading a sheaf at the normal scale
  34. Covector tests of normal limits
  35. SH02-SA — What a normal limit preserves
  36. SH02-MST — Detecting and removing directional obstructions
  37. SH02-MSD — Comparing sheaves through local support tests
  38. Local morphisms in cotangent directions
  39. SH02-MHPR — Product recovery for microlocal composition
  40. SH02-MHPC — Transporting both inputs before forming internal Hom
  41. SH02-SUB-UNIT — Reading a subset through its sheaf
  42. SH02-MO-UNIT — Transporting directional obstructions
  43. SH02-FAG-UNIT — Analytic geometry for finite maps
  44. SH02-NMC-UNIT — Normal Morse data and change of coefficients
  45. SH02-PNM-UNIT — Perverse degrees and normal Morse complexes
  46. SH02-IHM-UNIT — An isolated holomorphic test and its Morse filtration
  47. SH02-FH-UNIT — Directional information under a finite holomorphic map
  48. Directional constraints under algebraic and geometric constructions
  49. SH02-MC — Categories and operations in one cotangent direction
  50. SH02-AE-UNIT — Covectors at a boundary and at infinity
  51. SH02-CHE-UNIT — Cotangent directions that survive a limiting operation
  52. SH02-UCE — Uniform tests for an unbounded Hom complex
  53. SH02-INV — Hamiltonian motion forced by a sheaf
  54. SH02-LFI — Local models and change of ambient manifold
  55. SH02-MA — Continuing coefficients and transporting local morphisms
  56. SH02-RR — From directional tests to further microlocal theories

Original text CC0 1.0 unless the lesson states other terms.