Abstract: In this series of lectures, we will give an introduction to Bridgeland stability conditions on derived categories. List of topics include:

(1) Bridgeland Deformation Theorem and the case of curves.

(2) Bridgeland Covering Theorem and the case of K3 surfaces.

(3) Families of stability conditions and the case of non-commutative K3 surfaces.

(4) Moduli spaces of stable objects and applications.

Warm-up references:

• Lectures on Bridgeland Stability, E. Macrì and B. Schmidt, arXiv:1607.01262.

• Lectures on non-commutative K3 surfaces, Bridgeland stability, and moduli spaces, E. Macrì and P. Stellari, arXiv:1807.06169.

Schedule

Thursday 21 March:

11-12:30h. Lecture I

12:30-13h. Coffee break

13-14h. Discussion & problems seassion I

14:00-16:00h. Lunch

16:00-17:30h Lecture II

17:30-18h. Coffee break.

18-19h. Discussion & problems seassion II

21h Dinner (main activity)

Friday 22 March:

10-11:30h Lecture III

11:30-12h Coffee break

12-13h Discussion & problems seassion III

Organizan:

Daniel Hernández Serrano dani@usal.es, José Ignacio Iglesias Curto joseig@usal.es, Darío Sánchez Gómez dario@usal.es

Colabora: Departamento de Matemáticas USAL, IUFFyM-Instituto Universitario de Física Fundamental y Matematicas USAL.