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SUMMARY:Ringel-Hall algebras and applications to moduli - III - Reineke\, 
 M (Bergische Universit㲠Wuppertal)
DTSTART:20110114T113000Z
DTEND:20110114T123000Z
UID:TALK28843@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"\, arXiv:08
 02.2147. 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 to wall-crossing formulae
  are developed in "Poisson automorphisms and quiver moduli"\, arXiv:0802.2
 147.\n
LOCATION:Seminar Room 1 Newton Institute
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