Working Seminar on Derived Algebraic Geometry

Spring Semester 2019

Main source:
  1. Gaitsgory–Rozenblyum’s A study in Derived Algebraic Geometry I and II.
Sources (for Dg schemes, Gromov Witten Invariants and Virtual Fundamental classes):
  1. Cox, Sheldon; Mirror Symmetry and Algebraic Geometry (Chapter 7).
  2. Ciocan-Fontanine, Kapranov; Virtual fundamental classes via dg-manifolds.
  3. Ciocan-Fontanine, Kapranov; Derived Quot Schemes.
  4. Toen; Derived Algebraic Geometry.
  5. Kock, Vainsencher; An invitation to Quantum Cohomology.
Topic Date Speaker
1. Intro + reminders of Higher Category/Algebra (I.1) 20.03.19 Quoc
2.1 Derived algebraic geometry (I.2) 10.4.19 Quoc
2.2 Derived algebraic geometry (I.2) Part II 17.04.19 Quoc
3.1 Dg Schemes (Gromov-Witten Invariants and Virtual Fundamental Class) 26.04.19 Tanya
3.2 Dg Schemes II (Virtual Fundamental Class via dg Schemes) 09.05.19 Tanya
4.1 dg-Affine schemes and Quasi-coherent sheaves on prestacks (I.3) 22.05.19 Penghui
4.2 Special Guest Lecture: Higher Intrinsic Normal Cone 22.05.19 Dhyan Aranha
5. Grothendieck Riemann-Roch in Higher categories 29.05.19 Penghui
6. Correspondences + Duality (I.5) TBA Iordan
7. QCoh vs IndCoh (I.6) TBA Sasha-Penghui (?)
8. Deformation Theory 1 (II.1.1 to II.1.4) TBA Tanya
9. Deformation Theory 2 (II.1.5 to II.1.10) TBA Hongjie
10. Ind-schemes and inf-schemes (II.2) TBA Sasha
11. Ind-coh on ind-inf-schemes (II.3) TBA
12. Crystals (II.4) TBA Hongjie
Organizers: Quoc Ho and Tanya