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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20240328T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/paraboli
 c-gap-theorems-yang-mills-functional
SUMMARY:Parabolic gap theorems for the Yang-Mills functional
CLASS:PUBLIC
DESCRIPTION:ALEX WALDRON\, UNIVERSITY OF WISCONSIN-MADISON\n\nGiven a princ
 ipal bundle over a compact Riemannian 4-manifold or\nspecial-holonomy mani
 fold\, it is natural to ask whether a uniform gap\nexists between the inst
 anton energy and that of any non-minimal\nYang-Mills connection. This ques
 tion is quite open in general\,\nalthough positive results exist in the li
 terature. We'll review\nseveral of these gap theorems and strengthen them 
 to statements of the\nfollowing type: the space of all connections below a
  certain energy\ndeformation retracts (under Yang-Mills flow) onto the spa
 ce of\ninstantons. As applications\, we recover a theorem of Taubes on\npa
 th-connectedness of instanton moduli spaces on the 4-sphere\, and\nobtain 
 a method to construct instantons on quaternion-Kähler\nmanifolds with pos
 itive scalar curvature.\n\nMC 5417
DTSTAMP:20260315T083343Z
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