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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260312T150000
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URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-180
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:AMANDA PETCU\, UNIVERSITY OF WATERLOO\n\n_Some results on hype
 rsymplectic structures_\n\nA conjecture of Simon Donaldson is that on a co
 mpact 4-manifold X^4\none can flow from a hypersymplectic structure to a h
 yperkahler\nstructure while remaining in the same cohomology class. To thi
 s end\nthe hypersymplectic flow was introduced by Fine-Yao. In this thesis
 \nthe notion of a positive triple on X^4 is used to define a\nhypersymplec
 tic and hyperkahler structure. Given a closed positive\ntriple one can def
 ine either a closed G2 structure or a coclosed G2\nstructure on T^3 x X^4.
  The coclosed G2 structure is evolved under the\nG2 Laplacian coflow. This
  descends to a flow of the positive triple on\nX^4\, which is again the Fi
 ne-Yao hypersymplectic flow. In the second\npart of this thesis we let X^4
  = R^4 \\0 with a particular\ncohomogeneity one action. A hypersymplectic 
 structure invariant under\nthis action is introduced. The Riemann and Ricc
 i curvature tensors are\ncomputed and we verify in a particular case that 
 this hypersymplectic\nstructure can be transformed to a hyperkahler struct
 ure. The notion of\na soliton for the hypersymplectic flow in this particu
 lar case is\nintroduced and it is found that steady solitons give rise to\
 nhypersymplectic structures that can be transformed to hyperkahler\nstruct
 ures. Some other soliton solutions are also discussed.\n\nMC 5403
DTSTAMP:20260408T060720Z
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