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SUMMARY:Alex Waldron (University of Wisconsin - Madison)
DTSTART:20230606T150000Z
DTEND:20230606T160000Z
DTSTAMP:20260423T022743Z
UID:Geolis/124
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/124/"
 >Strong gap theorems via Yang-Mills flow</a>\nby Alex Waldron (University 
 of Wisconsin - Madison) as part of Geometria em Lisboa (IST)\n\n\nAbstract
 \nGiven a principal bundle over a compact Riemannian 4-manifold or special
 -holonomy manifold\, it is natural to ask whether a uniform gap exists bet
 ween the instanton energy and that of any non-minimal Yang-Mills connectio
 n. This question is quite open in general\, although positive results exis
 t in the literature. We'll review several of these gap theorems and streng
 then them to statements of the following type: the space of all connection
 s below a certain energy deformation retracts (under Yang-Mills flow) onto
  the space of instantons. As applications\, we recover a theorem of Taubes
  on path-connectedness of instanton moduli spaces on the 4-sphere\, and ob
 tain a method to construct instantons on quaternion-Kähler manifolds with
  positive scalar curvature.\n\nThe talk is based on joint work in progress
  with Anuk Dayaprema (UW-Madison).\n
LOCATION:https://researchseminars.org/talk/Geolis/124/
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