BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Drupal iCal API//EN
X-WR-CALNAME:Events items teaser
X-WR-TIMEZONE:America/Toronto
BEGIN:VTIMEZONE
TZID:America/Toronto
X-LIC-LOCATION:America/Toronto
BEGIN:DAYLIGHT
TZNAME:EDT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
DTSTART:20230312T070000
END:DAYLIGHT
BEGIN:STANDARD
TZNAME:EST
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
DTSTART:20221106T060000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:6a223295b8812
DTSTART;TZID=America/Toronto:20231024T143000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20231024T153000
URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-87
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:AMANDA PETCU\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY OF W
 ATERLOO\n\n\"PARTIAL PROGRESS ON A CONJECTURE OF DONALDSON BY FINE AND YAO
  (PART\n2)\"\n\nGiven a compact hypersymplectic manifold $X^4$\, Donaldson
  conjectured\nthat the hypersymplectic structure can be deformed through\n
 cohomologous hypersymplectic structures to a hyperk\\\"{a}hler\nstructure.
  Fine and Yao consider a manifold with closed\n$G_2$-structure that is set
  up as $\\mathbb{T}^3 \\times X^4$. They\nexamine the $G_2$-Laplacian flow
  under in this setting and give a flow\nof hypersymplectic structures whic
 h evolve according to the equation\n\\[\\partial_t \\underline{\\omega} = 
 d(Q d^*(Q^{-1}\n\\underline{\\omega}))\\]\nwhere $\\underline{\\omega}$ is
  the triple that gives the\nhypersymplectic structure and $Q$ is a $3 \\ti
 mes 3$ symmetric matrix\nthat relates the symplectic forms $\\omega_i$ to 
 one another. Lotay-Wei\nhave established long time existence of the $G_2$-
 Laplacian flow\nprovided the velocity of the flow remains bounded. Fine-Ya
 o use this\nextension theorem in their setup and manage to improve it by p
 roving\nlong time existence of the hypersymplectic flow provided the torsi
 on\ntensor $T$ remains bounded. Furthermore\, one can relate the scalar\nc
 urvature and torsion tensor of manifold with closed $G_2$-structure\nand t
 hus they conclude long time existence for the hypersymplectic\nflow provid
 ed the scalar curvature remains bounded. In this talk we\nwill go over som
 e details from this paper by Fine-Yao.\n\nMC 5403
DTSTAMP:20260605T022109Z
END:VEVENT
END:VCALENDAR