[iasmath-semru] Reminder for today's Analysis Seminar--4:30pm

[Kristina Phillips]

INSTITUTE FOR ADVANCED STUDY

School of Mathematics

Princeton, NJ 08540

 

Analysis Seminar

Friday, December 7

 

Topic:                    Morrey Saces and Regularity for Yang-Mills Higgs
Equations

Speaker:              Karen Uhlenbeck, School of Mathematics

Time/Room:       4:30pm - 5:30pm/Simonyi Hall 101

Abstract Link:      <http://www.math.ias.edu/seminars/abstract?event=140127>
http://www.math.ias.edu/seminars/abstract?event=140127

 

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.

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