Baby Algebraic Geometry Learning Seminar (BAGeLS)

Fall 2019
Thursdays at 5:15 PM, SC 530

This semester we will cover Hodge theory. Gwyneth Moreland and Geoffrey Smith are organizing.

• Sep 122019 SC 232 Geoffrey Smith
  Organizational meeting abstract±    I'll briefly introduce Hodge theory and we'll discuss what will happen for the rest of the semester.
• Sep 192019 SC 530 Duc Vo
  Kähler manifolds abstract±    Voisin Chapter 3. The relevant section of Griffiths-Harris Chapter 0 is also a decent reference.
• Sep 262019 SC 232 Naomi Sweeting
  Sheaves and cohomology abstract±    Voisin Chapter 4, especially the definitions of the various sorts of cohomology (de Rham, Dolbeault, Cech).
• Oct 32019 SC 530 Maxim Jeffs
  The Hodge decomposition for Kahler manifolds abstract±    Define harmonic forms, state Voisin Theorem 5.2, then Voisin Chapter 6.
• Oct 102019 SC 530 Waqar Ali
  Hodge structures in the abstract abstract±   
• Oct 172019 SC 530 Yujie Xu
  Variations of Hodge structure abstract±    In this talk, I will present Deligne's and Voisin's perspectives on Hodge structures and variation of Hodge structures. I will cover the Kahler case following Voisin, covering the semicontinuity theorem, local constancy of Hodge numbers, Griffith transversality, etc. I will give some examples involving abelian varieties. If time permits, I will discuss how a Shimura datum gives rise to a variation of Hodge structures.
• Oct 242019 SC 530 Kevin Lin
  The Hodge theory of hypersurfaces abstract±    Following Voisin II Chapter 6.
• Oct 312019 SC 530 Vaughan McDonald, at 5:30 PM
  The Hodge theory of hypersurfaces, continued abstract±    Also following Voisin II Chapter 6. But spooky or something.
• Nov 72019 SC 530 Morgan Opie
  Mixed Hodge Structures abstract±    Peters-Steenbrink Chapter 3
• Nov 142019 SC 530 Gwyneth Moreland, at 5:35 PM
  Mixed Hodge structures of smooth varieties abstract±    Peters-Steenbrink Chapter 4
• Nov 212019 SC 530 Geoffrey Smith
  Mixed Hodge structures of singular varieties abstract±    Peters-Steenbrink Chapter 5
• Dec 52019 SC 530 Sasha Petrov
  Mixed Hodge structures of singular varieties, continued abstract±