ZMP Seminar - Summer Term 2021

About

• The topic of this term's ZMP seminar is Stability conditions.
• Abstract: Approximately 15 years ago Tom Bridgeland introduced the notion of stability condition on a triangulated category as a mathematical framework to understand Douglas' Pi-stability for D-branes in string theory. It turns out that the space Stab(D) of stability conditions on a fixed triangulated category D is a (possibly infinite-dimensional) complex manifold. If D is a triangulated three-dimensional Calabi-Yau category, then its Donaldson-Thomas invariants can be encoded into a geometric structure on Stab(D), called a Joyce structure, which in turn gives rise to a complex hyperkähler structure on the total space of the tangent bundle of Stab(D). In this seminar we would like to explore this circle of ideas starting from its physical origin in the work of Douglas.
• Download notes here.

Schedule

Matrix chat

If you're interested in giving a talk or simply want to discuss anything related to the topic, please join us in the matrix chat room

#zmp:matrix.math.uni-hamburg.de

There, we will coordinate the topics and discuss what makes most sense to present. Every member of the math department already has a chat account on https://riot.math.uni-hamburg.de/ with login

firstname.lastname

and your usual Kerberos password. Every member of the physics department should have an account on https://riot.physnet.uni-hamburg.de/. Everybody else can get a free account on https://matrix.org/. See you there!

Literature

• Aspinwall et al, "Dirichlet Branes and Mirror Symmetry", Clay Mathematics Monographs Volume 4
• Bridgeland "Stability conditions on triangulated categories", Ann. Math. 166 (2007), 317 - 345
• Bridgeland "Spaces of stability conditions" (survey) arXiv:math/0611510
• Bridgeland "Geometry from Donaldson-Thomas invariants" arXiv:1912.06504
• Bridgeland, Strachan "Complex hyperkähler structures defined by Donaldson-Thomas invariants" arXiv:2006.13059