Lecturer:
Course Type:
PhD Course
Academic Year:
2025-2026
Period:
February-May
Duration:
30 h
Description:
This course will provide an introduction to modern enumerative geometry, with special focus on localisation and motivic techniques. We will cover the classical Atiyah-Bott localisation formula, its enhancement to the virtual setup, and use these techniques to compute Donaldson-Thomas invariants of 3-folds. Then we will move to motivic invariants of moduli spaces of sheaves and give examples of their calculation for curves and surfaces, mixing localisation techniques with the Bialynicki-Birula decomposition.
Contents
Equivariant cohomology, localisation formulas, virtual classes. Bialynicki-Birula decomposition. Computations on moduli spaces of sheaves on curves, surfaces and 3-folds.
Prerequisites
Basic theory of schemes.
References
A. T. Ricolfi, An invitation to modern enumerative geometry, Springer SISSA Series, no. 3
Research Group: