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SUMMARY:Simon K. Donaldson (Simons Center for Geometry and Physics Stony B
 rook and Imperial College London)
DTSTART:20201215T170000Z
DTEND:20201215T180000Z
DTSTAMP:20260423T022724Z
UID:Geolis/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/25/">
 Co-associative fibrations of $G_{2}$-manifolds and deformations of singula
 r sets</a>\nby Simon K. Donaldson (Simons Center for Geometry and Physics 
 Stony Brook and Imperial College London) as part of Geometria em Lisboa (I
 ST)\n\n\nAbstract\nThe first part of the talk will review background mater
 ial on the differential geometry of $7$-dimensional manifolds with the exc
 eptional holonomy group $G_{2}$. There are now many thousands of examples 
 of deformation classes of such manifolds and there are good reasons for th
 inking that many of these have fibrations with general fibre diffeomorphic
  to a $K3$ surface and some singular fibres: higher dimensional analogues 
 of Lefschetz fibrations in algebraic geometry. In the second part of the t
 alk we will discuss some questions which arise in the analysis of these fi
 brations and their "adiabatic limits". The key difficulties involve the si
 ngular fibres. This brings up a PDE problem\, analogous to a free boundary
  problem\, and similar problems have arisen in a number of areas of differ
 ential geometry over the past few years\, such as in Taubes' work on gauge
  theory. We will outline some techniques for handling these questions.\n
LOCATION:https://researchseminars.org/talk/Geolis/25/
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