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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240328T143000
SEQUENCE:0
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URL:https://uwaterloo.ca/pure-mathematics/events/geometry-topology-seminar-
 154
SUMMARY:Geometry & Topology Seminar
CLASS:PUBLIC
DESCRIPTION:ALEX WALDRON\, UNIVERSITY OF WISCONSIN-MADISON\n\n\"PARABOLIC G
 AP THEOREMS FOR THE YANG-MILLS FUNCTIONAL\"\n\nGiven a principal bundle ov
 er a compact Riemannian 4-manifold or\nspecial-holonomy manifold\, it is n
 atural to ask whether a uniform gap\nexists between the instanton energy a
 nd that of any non-minimal\nYang-Mills connection. This question is quite 
 open in general\,\nalthough positive results exist in the literature. We'l
 l review\nseveral of these gap theorems and strengthen them to statements 
 of the\nfollowing type: the space of all connections below a certain energ
 y\ndeformation retracts (under Yang-Mills flow) onto the space of\ninstant
 ons. As applications\, we recover a theorem of Taubes on\npath-connectedne
 ss of instanton moduli spaces on the 4-sphere\, and\nobtain a method to co
 nstruct instantons on quaternion-Kähler\nmanifolds with positive scalar c
 urvature.\n\nMC 5417
DTSTAMP:20260512T075710Z
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