2025/10/14-2025/12/31

Every Tuesday 16:20–18:10 and Wednesday 10:20–12:10, October 14 to December 31, 2025

Room 509, Cosmology Building, NTU 

Outline

In the first part, we will cover derived categories of sheaves, the six functors, constructibility, and Verdier duality.  In the second part, we will study nearby and vanishing cycles sheaves, which are used to analyze the topology of degenerating families.

1. Derived categories of sheaves on topological spaces.

2. The six functors: direct and inverse image functors, their compactly supported variants, and the tensor-Hom adjunction; the smooth and proper base change formulas.

3. Constructible sheaves on complex algebraic varieties.

4. Verdier duality.

5. Nearby and vanishing cycles; unipotent and tame variants.

6. Compatibility of vanishing cycles with the six functors and Verdier duality.

7. Thom-Sebastiani for vanishing cycles.

8. Hyperbolic localization for vanishing cycles.

Course Goal 

The goal is to develop a working knowledge of constructible sheaves and vanishing cycles sheaves.  The student will be able to starting reading papers where the theory is applied in enumerative geometry, geometric representation theory, or other areas.

Credit

3

Course Number/ ID

No.: NCTS 5058
ID: V41 U2060
(三校聯盟之學生於課程網選課適用)