<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal>INSTITUTE FOR ADVANCED STUDY<o:p></o:p></p><p class=MsoNormal>School of Mathematics<o:p></o:p></p><p class=MsoNormal>Princeton, NJ 08540<o:p></o:p></p><p class=MsoNormal><b><o:p> </o:p></b></p><p class=MsoNormal><b>Analysis Seminar<o:p></o:p></b></p><p class=MsoNormal><b>Friday, December 7<o:p></o:p></b></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Topic: Morrey Saces and Regularity for Yang-Mills Higgs Equations<o:p></o:p></p><p class=MsoNormal>Speaker: Karen Uhlenbeck, School of Mathematics<o:p></o:p></p><p class=MsoNormal>Time/Room: 4:30pm - 5:30pm/Simonyi Hall 101<o:p></o:p></p><p class=MsoNormal><span lang=FR>Abstract Link: </span><a href="http://www.math.ias.edu/seminars/abstract?event=140127"><span lang=FR>http://www.math.ias.edu/seminars/abstract?event=140127</span></a><span lang=FR><o:p></o:p></span></p><p class=MsoNormal><span lang=FR><o:p> </o:p></span></p><p class=MsoNormal>We start with background on regularity theory for the equations of gauge theory. Morrey spaces arise naturally from monotinicity theorems in dimensions greater than 4. Our main technical result is that functions in a Morrey space which satisfy an elliptic inequality off a singular set of Hausdorf codimension 4 can be bounded in a much better Morrey space in the interior. This can be used to show that when the curvature is small in the relevant Morrey space, solutions of a Yang-Mills-Higgs equation off a singular set of codimensions 4 are in interior domains gauge equation to a connection which is smooth. This simplifies a classic paper of Tao-Tian.<span lang=FR><o:p></o:p></span></p></div></body></html>