Lectures

  • 08/23 Lecture 1. Introduction to GAGA. (Notes / Video)

  • 08/25 Lecture 2. O-minimal structures. (Notes / Video)

  • 08/27 Lecture 3. Definable cylindrical cell decomposition I: statement. (Notes / Video)

  • 08/29 Lecture 4. Definable cylindrical cell decomposition II: monotonicity. (Notes)

  • 09/01 Lecture 5. Definable cylindrical cell decomposition III: uniform finiteness. (Notes)

  • 09/03 Lecture 6. Definable cylindrical cell decomposition IV: end of proof in R^2. (Notes / Video)

  • 09/08 Lecture 7. Bialgebraic varieties for the exponential. (Notes / Video)

  • 09/10-15 Lecture 8, 9. Definable Chow. (Notes / Video 8, 9)

  • 09/17 Lecture 10. The Pila--Wilkie counting theorem. (Notes / Video)

  • 09/20 Lecture 11. Definable topological spaces. (Notes / Video)

  • 09/22 Lecture 22. Definable complex manifolds. (Notes / Video)

  • 09/24 Lecture 13. Examples of definable complex manifolds. (Notes / Video)

  • 09/27 Lecture 14. Cell decomposition for definable topological spaces. (Notes / Video)

  • 09/29 Lecture 15. The definable site. (Notes / Video)

  • 10/01 Lecture 16. Coherent sheaves. (Notes / Video)

  • 10/04 Lecture 17. Definable Noether normalization. (Notes / Video)

  • 10/06 Lecture 18. Definable Weierstrass division. (Notes / Video)

  • 10/08 Lecture 19. Definable Oka coherence. (Notes / Video)

  • 10/11 Lecture 20. Faithfulness of analytification. (Notes / Video)

  • 10/13 Lecture 21. Definabilization. (Notes / Video)

  • 10/18 Lecture 23. Definable Noetherian induction. (Notes / Video)

  • 10/20-22 Lecture 24, 25. Definable GAGA. (Notes / Video 24, 25)

  • 10/25-29 Lecture 26, 27, 28. Definable images. (Notes)

  • 11/01-05 Lecture 29, 30. Reduced spaces. (Notes)

  • 11/08 Lecture 31. Subvarieties of complex tori. (Notes)

  • 11/10 Lecture 32. Hodge structures. (Notes)

  • 11/12 Lecture 33. Examples of Hodge structures I. (Notes)

  • 11/15 Lecture 34. Examples of Hodge structures II. (Notes)

  • 11/17 Lecture 35. Moduli of Hodge structures. (Notes)

  • 11/19 Lecture 36. Period domains and their compact duals. (Video)

  • 11/22 Lecture 37. Moduli spaces of Hodge structures aren't algebraic. (Video)

  • 11/24 Lecture 38. Definable fundamental sets. (Video)