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DTSTART;TZID=America/Toronto:20230406T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/moduli-s
 paces-holomorphic-bundles-framed-along-real
SUMMARY:Moduli spaces of holomorphic bundles framed along a real hypersurfa
 ce
CLASS:PUBLIC
DESCRIPTION:ANDREI TELEMAN\, AIX-MARSEILLE UNIVERSITY\n\nLet \\(X\\) be a c
 onnected\, compact complex manifold\, and \\(S\\subset X\\)\nbe a separati
 ng real hypersurface. \\(X\\) decomposes as a union of\ncompact complex ma
 nifolds with boundary \\(\\bar X^\\pm\\) with \\(\\bar\nX^+\\cap \\bar X^-
 =S\\). Let \\(\\mathcal{M}\\) be the moduli space of\n\\(S\\)-framed holom
 orphic bundles on \\(X\\)\, i.e. of pairs\n\\((E\,\\theta)\\) (of fixed to
 pological type) consisting of a _\nholomorphic _ bundle \\(E\\) on \\(X\\)
  endowed with a _ differentiable _\ntrivialization \\(\\theta\\) on \\(S\\
 ). This moduli space is the main\nobject of a joint research project with 
 Matei Toma.\n\nThe problem addressed in my talk: compare\, via the obvious
  restriction\nmaps\, the moduli space \\(\\mathcal{M}\\) with the correspo
 nding\nDonaldson moduli spaces \\(\\mathcal{M}^\\pm\\) of boundary framed\
 nholomorphic bundles on \\(\\bar X^\\pm\\). The restrictions to \\(\\bar\n
 X^\\pm\\) of an \\(S\\)-framed holomorphic bundle \\((E\,\\theta)\\) are\n
 boundary framed formally holomorphic bundles \\((E^\\pm\,\\theta^\\pm)\\)\
 nwhich induce\, via \\(\\theta^\\pm\\)\, the same tangential Cauchy-Rieman
 n\noperators on the trivial bundle on \\(S\\). Therefore one obtains a\nna
 tural map from \\(\\mathcal{M}\\) into the fiber product\n\\(\\mathcal{M}^
 -\\times_\\mathcal{C}\\mathcal{M}^+\\) over the space\n\\(\\mathcal{C}\\) 
 of Cauchy-Riemann operators on the trivial bundle on\n\\(S\\).\n\nOur resu
 lt states: _ this map is bijective. _ Note that\, by theorems\ndue to S. D
 onaldson and Z. Xi\, the moduli spaces \\(\\mathcal{M}^\\pm\\)\ncan be ide
 ntified with moduli spaces of boundary framed Hermitian\nYang-Mills connec
 tions.\n\nThis seminar will be held both online and in person:\n\n* Room: 
 MC 5417\n * Zoom\nlink: https://uwaterloo.zoom.us/j/96883292635?pwd=KytGY
 nEvRmhyTTV1NC9Gc2dnT05oQT09
DTSTAMP:20260320T000641Z
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