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UID:20251212T181223EST-0485Rpp7kh@132.216.98.100
DTSTAMP:20251212T231223Z
DESCRIPTION:Title: “Tyurin data\, non-abelian Cauchy kernels and the Goldma
 n bracket”\n\nAbstract:\n\nIn this talk I will start with a review of the 
 notion of moduli of (stable) vector bundles expressed by Tyurin in late ‘6
 0s. For each (stable) vector bundle E of rank n and degree ng we can assoc
 iate a matrix kernel (the non-Abelian Cauchy kernel) which is written expl
 icitly in terms of the Tyurin data and the ordinary third kind differentia
 ls.\n\nUsing the Cauchy kernel (and additional datum of divisor of degree 
 g) we construct a map from the cotangent bundle to the moduli space to the
  space of representations of the fundamental group of the surface.\n\nThe 
 final goal is to show that the complex-analytic canonical symplectic struc
 ture on the cotangent bundle is mapped to the symplectic structure introdu
 ced by Goldman on the space of representations. The main tool is the “Malg
 range-Fay” form\, expressing the tautological form on the cotangent bundle
 \; it has also an interesting algebro-geometric relevance because this for
 m has a pole along the non-Abelian Theta divisor whose residue is interpre
 ted as dimension of an appropriate space.\n\nJoint work (in progress) with
  C. Norton\, G. Ruzza.\n
DTSTART:20200121T203000Z
DTEND:20200121T213000Z
LOCATION:Room 4336\, CA\, Pav. André-Aisenstadt\, 2920\, ch. de la Tour
SUMMARY:Marco Bertola (SISSA and Concordia)
URL:/mathstat/channels/event/marco-bertola-sissa-and-c
 oncordia-303973
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