Spring 2024 Algebraic geometry learning seminar:
Decomposition of the diagonal

Time: Friday 1:45 – 3:00pm.
Place: 307 Math Building.
Book: Voisin, Chow rings, decomposition of the diagonal, and the topology of families: link.
Organizers: Nathan Chen and Yoonjoo Kim.

Scheduled talks:

Date Speaker Section Topic Note
Jan 26 Nathan Chen 1
Introduction pdf
Feb 2
Yoon-Joo Kim 2.1.1 – 2.1.3
Chow groups and their functoriality
pdf
Feb 9 Simon Felten 2.1.3.1 – 2.1.4
Motives, cycle classes, and examples pdf
Feb 16 Nicolás Vilches Reyes 2.2.1 – 2.2.3
Pure Hodge structures and standard conjectures pdf
Feb 23 Matthew Hase-Liu 2.2.4 – 2.2.5
Mixed Hodge structures
Mar 1 Ivan Zelich 3.1 – 3.1.1
General principle and Mumford's theorem
Mar 8 TBA
3.1
Proof of Theorem 3.1

Mar 15 (Spring break)
-
-

Mar 22 TBA 3.1.2 Further applications (theorems of Bloch-Srinivas)
Mar 29 TBA 3.2.1 – 3.2.2 Generalized decomposition of the diagonal (due to Paranjape and Laterveer)
and generalized Bloch conjecture

Apr 5
Morena Porzio
3.2.3
Nilpotence conjecture and Kimura's theorem

Apr 12 Kuan-Wen Chen 4.1 – 4.1.1 Hodge coniveau of hypersurfaces