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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Ringel-Hall algebras and applications to moduli -
II - Reineke\, M (Bergische Universit㲠Wuppertal)
DTSTART;TZID=Europe/London:20110113T113000
DTEND;TZID=Europe/London:20110113T123000
UID:TALK28841AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28841
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\, \narXiv:
0802.2147. Although this paper was written for an
audience of representation theorists\, it might as
well be helpful \nfor the participants of the Sch
ool on Moduli Spaces. \nThe more recent applicatio
ns to wall-crossing formulae are developed in Pois
son automorphisms and quiver moduli\, arXiv:0802.2
147.\n
LOCATION:Seminar Room 1 Newton Institute
CONTACT:Mustapha Amrani
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