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SUMMARY:Conformal Yang-Mills renormalisation and higher Yang-Mills energie
 s - Rod Gover (University of Auckland)
DTSTART:20240911T103000Z
DTEND:20240911T113000Z
UID:TALK219568@talks.cam.ac.uk
DESCRIPTION:Given a gauge connection on a Riemannian 4-manifold\, the norm
  squared of its curvature gives a Lagrangian density whose integral is the
 &nbsp\;Yang-Mills action/energy -- the variation of which gives the&nbsp\;
 celebrated Yang-Mills equations. An important feature of both this&nbsp\;e
 nergy and the equations is their conformal invariance in dimension&nbsp\;f
 our.\nA natural question is whether there are analogous objects in higher 
 dimensions. We prove that there are such conformally invariant objects&nbs
 p\;on even dimensional manifolds equipped with a connection. The proof&nbs
 p\;uses a Poincare-Einstein manifold in one higher dimension and a&nbsp\;s
 uitable Dirichlet problem for the interior Yang-Mills equations on&nbsp\;t
 his structure. The higher Yang-Mills equations arise from an obstruction t
 o smoothly solving the asymptotic problem\, while the&nbsp\;higher energy 
 is a log term (the so-called anomaly term) in the&nbsp\;asymptotic expansi
 on of the divergent interior energy. More arises including links to a conn
 ection Q-curvature\, the non-local&nbsp\;renormalised Yang-Mills energy\, 
 and a related higher non-linear Dirichlet-Neumann operator.\nThis is joint
  work with Emanuele Latini\, Andrew Waldron\, and Yongbing Zhang.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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