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DTSTART:20260308T070000
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DTSTART;TZID=America/Toronto:20260324T090000
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URL:https://uwaterloo.ca/pure-mathematics/events/phd-thesis-defense-12
SUMMARY:PhD Thesis Defense
CLASS:PUBLIC
DESCRIPTION:AMANDA MARIA PETCU\, UNIVERSITY OF WATERLOO\n\n_Some results on
  hypersymplectic structures_\n\nA conjecture of Simon Donaldson is that on
  a compact 4-manifold X^4\none can flow from a hypersymplecticstructure to
  a hyperkahler\nstructure while remaining in the same cohomology class. To
  this end\nthehypersymplectic flow was introduced by Fine-Yao. In this the
 sis the\nnotion of a positive triple on X^4 is used todefine a hypersymple
 ctic\nand hyperkahler structure. Given a closed positive triple one can\nd
 efine either a closedG2 structure or a coclosed G2 structure on T^3 x\nX^4
 . The coclosed G2 structure is evolved under the G2Laplacian\ncoflow. This
  descends to a flow of the positive triple on X^4\, which\nis again the Fi
 ne-Yaohypersymplectic flow. In the second part of this\nthesis we let X^4 
 = R^4 \\ {0} with a particular cohomogeneityone\naction. A hypersymplectic
  structure invariant under this action is\nintroduced. The Riemann and Ric
 cicurvature tensors are computed and we\nverify in a particular case that 
 this hypersymplectic structure can\nbetransformed to a hyperkahler structu
 re. The notion of a soliton for\nthe hypersymplectic flow in this particul
 arcase is introduced and it\nis found that steady solitons give rise to hy
 persymplectic structures\nthat can betransformed to hyperkahler structures
 . Some other soliton\nsolutions are also discussed.\n\nMC 5479
DTSTAMP:20260408T024732Z
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