course: Stability conditions
speaker: Tom Bridgeland (University of Sheffield)abstract: These five lectures will introduce the space of stability conditions on a triangulated category, give some geometric examples and touch on some of the recent work on wall-crossing behaviour in this context.
A rough plan (which may well change) is
(A) Brief recall of derived and triangulated categories. T-structures and tilting. Examples (e.g. P1).
(B) Stability in abelian and triangulated categories. Spaces of stability conditions. Examples (e.g. elliptic curve, K3 surface).
(C) Hall algebras. Reieneke's formula. Stokes factors and wall-crossing.
The main prerequisites apart from standard algebraic geometry will be a certain familiarity with derived categories, and the basic definitions concerning representations of quivers. The following two papers are useful introductions
Bernhard Keller 'Derived categories and tilting'
Richard Thomas 'Derived categories for the working mathematician'
Alternatively, consult the first chapter of Robin Hartshorne `Residues and duality' or the textbook Gelfand and Manin `Methods of homological algebra'.
The first section (pages 3-8) of William Crawley-Boevey's 'Lectures on representations of quivers' will give the necessary background on those. Also to be found on page 99 of Benson's book Representations and Cohomology I.
timetable:
Mon 16 Jun, 10:45 - 11:45, Aula Dini
Tue 17 Jun, 9:00 - 10:00, Aula Dini
Wed 18 Jun, 9:00 - 9:50, Aula Dini
Thu 19 Jun, 9:00 - 10:00, Aula Dini
Fri 20 Jun, 9:00 - 10:00, Aula Dini
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