Rutgers University Algebra and Geometry learning seminar

Zeyu Shen organized the Rutgers University Algebra and Geometry learning seminar in fall 2023.

Daniel Huybrechts’s book Fourier-Mukai transforms in algebraic geometry was the reference.

The talks given were:

1. September 5th, Tim, additive categories and Serre functor.

2. September 12th, Nilava, triangulated categories and exact functor.

3. September 19th, Zengrui Han, criteria for exact functors between triangulated categories to be fully faithful.

4. September 26th, Zengrui Han, exceptional sequences and semi-orthogonal decompositions.

5. October 3rd, Zengrui Han, construction of the derived category.

6. October 10th, Zeyu Shen, boundedness condition on the derived category.

7. October 17th, Zengrui Han, derived functors between derived categories.

8. October 24th, Zengrui Han, derived category of coherent sheaves on a Noetherian scheme.

9. October 31st, Zengrui Han, derived category of ample (anti)-canonical bundle.

10. November 7th, Zengrui Han, point-like and invertible objects in a triangulated category with a Serre functor.

11. November 14th, Zengrui Han, proof of Orlov and Bondal’s theorem that two smooth projective varieties are isomorphic if

there is an exact equivalence between their bounded derived categories and that one of them has ample (anti)-canonical bundle.

12. November 21st, Zengrui Han, derived functors in algebraic geometry.

13. November 28th, Zengrui Han, Grothendieck-Verdier duality and Fourier-Mukai transforms.

14. December 5th, Zengrui Han, passage to cohomology for Fourier-Mukai transforms.