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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20241206T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-these-defense
SUMMARY:PhD These Defense
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 thesis\, we extend this correspondence by\nprov
 iding necessary and sufficient conditions for when a co-Higgs\nfield induc
 es a Poisson structure on V and P(V)\, showing that the\nco-Higgs field mu
 st either be a function multiple of a constant matrix\nor have only one no
 n-zero column. Furthermore\, we analyze this\ncorrespondence for co-Higgs 
 fields over curves of genus greater or\nequal to one.  Finally\, we analy
 ze how stability can be interpreted\ngeometrically through the zeros of th
 e induced Poisson structure\,\nestablishing connections between \\Phi -inv
 ariant subbundles\, Poisson\nsubvarieties\, and the spectral curve.\n\nJoi
 n on Zoom\n\nMeeting ID: 971 4907 1044\n\nPasscode: 776121
DTSTAMP:20260505T224703Z
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