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DTSTART;TZID=America/Toronto:20250312T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-179
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:AMANDA PETCU\, UNIVERSITY OF WATERLOO\n\n_Some results on hyper
 symplectic structures_\n\nA conjecture of Simon Donaldson is that on a com
 pact 4-manifold X^4\none can flow from a hypersymplecticstructure to a hyp
 erkahler\nstructure while remaining in the same cohomology class. To this 
 end\nthehypersymplectic flow was introduced by Fine-Yao. In this thesis th
 e\nnotion of a positive triple on X^4 is used todefine a hypersymplectic\n
 and hyperkahler structure. Given a closed positive triple one can\ndefine 
 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 desce
 nds to a flow of the positive triple on X^4\, which\nis again the Fine-Yao
 hypersymplectic flow. In the second part of this\nthesis we let X^4 = R^4 
 \\0 with a particular cohomogeneity oneaction.\nA hypersymplectic structur
 e invariant under this action is introduced.\nThe Riemann and Ricci curvat
 uretensors are computed and we verify in a\nparticular case that this hype
 rsymplectic structure can be transformed\ntoa hyperkahler structure. The n
 otion of a soliton for the\nhypersymplectic flow in this particular case i
 s introducedand it is\nfound that steady solitons give rise to hypersymple
 ctic structures\nthat can be transformed to hyperkahlerstructures. Some ot
 her soliton\nsolutions are also discussed.\n\nMC 5403
DTSTAMP:20260430T201644Z
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