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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20241126T110000
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URL:https://uwaterloo.ca/pure-mathematics/events/algebraic-geometry-working
 -seminar-82
SUMMARY:Algebraic Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:BRADY ALI MEDINA\, UNIVERSITY OF WATERLOO\n\nCo-Higgs bundles a
 nd Poisson structures.\n\nThere is a correspondence between co-Higgs field
 s and holomorphic\nPoisson structures on P(V) established by Polishchuk in
  the rank 2\ncase and by Matviichuk in the case where the co-Higgs field i
 s\ndiagonalizable. In this talk\, I will extend this correspondence by\npr
 oviding necessary and sufficient conditions for when a co-Higgs\nfield ind
 uces an integrable Poisson structure on V and P(V)\, showing\nthat the co-
 Higgs field must either be a function multiple of a\nconstant matrix or ha
 ve only one non-zero column. We will also analyze\nthis correspondence for
  co-Higgs fields over curves of genus g greater\nthan one. Finally\, I wil
 l show how stability can be understood\ngeometrically through the zeros of
  the induced Poisson structure\,\nestablishing connections between \\Phi-i
 nvariant subbundles\, Poisson\nsubvarieties\, and the spectral curve. As t
 his talk is a preparation\nfor my thesis defense\, please ask me many ques
 tions!\n\nMC 5403
DTSTAMP:20260505T184453Z
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