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SUMMARY:Ringel-Hall algebras and applications to moduli - II - Reineke\, M
  (Bergische Universit㲠Wuppertal)
DTSTART:20110113T113000Z
DTEND:20110113T123000Z
UID:TALK28841@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Moduli spaces of representations of quivers\, parametrizing co
 nfigurations of vector spaces and linear maps up to base change\, provide 
 a prototype for many moduli spaces of algebraic geometry.\n\nThe Hall alge
 bra of a quiver\, a convolution algebra of functions on stacks of its repr
 esentations\, can be used to obtain quantitative information on the moduli
  spaces: algebraic identities in the Hall algebra\, proved by representati
 on-theoretic techniques\, yield identities for e.g. Betti numbers or numbe
 rs of points over finite fields.\n\nWe will develop several such identitie
 s and discuss more recent applications to wall-crossing formulae.\n\nNotes
 :  Several of the Hall algebra techniques which I would like to discuss ar
 e reviewed in the survey Moduli of representations of quivers\, \narXiv:08
 02.2147. 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 applications to wall-crossing form
 ulae are developed in Poisson automorphisms and quiver moduli\, arXiv:0802
 .2147.\n
LOCATION:Seminar Room 1 Newton Institute
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