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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Ringel-Hall algebras and applications to moduli -
I - Reineke\, M (Bergische Universite Wuppertal)
DTSTART;TZID=Europe/London:20110112T113000
DTEND;TZID=Europe/London:20110112T123000
UID:TALK28838AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28838
DESCRIPTION:Moduli spaces of representations of quivers\, para
metrizing configurations of vector spaces and line
ar maps up to base change\, provide a prototype fo
r many moduli spaces of algebraic geometry.\n\nThe
Hall algebra of a quiver\, a convolution algebra
of functions on stacks of its representations\, ca
n be used to obtain quantitative information on th
e moduli spaces: algebraic identities in the Hall
algebra\, proved by representation-theoretic techn
iques\, yield identities for e.g. Betti numbers or
numbers of points over finite fields.\n\nWe will
develop several such identities and discuss more r
ecent applications to wall-crossing formulae.\n\nN
otes: Several of the Hall algebra techniques whic
h I would like to discuss are reviewed in the surv
ey "Moduli of representations of quivers"\, arXiv:
0802.2147. Although this paper was written for an
audience of representation theorists\, it might as
well be helpful for the participants of the Schoo
l on Moduli Spaces. The more recent applications t
o wall-crossing formulae are developed in "Poisson
automorphisms and quiver moduli"\, arXiv:0802.214
7.\n
LOCATION:Seminar Room 1 Newton Institute
CONTACT:Mustapha Amrani
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