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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the ADHM Seiberg&\;ndash\;Witten equations -
Thomas Walpuski (Massachusetts Institute of Techn
ology)
DTSTART;TZID=Europe/London:20170818T143000
DTEND;TZID=Europe/London:20170818T153000
UID:TALK76121AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/76121
DESCRIPTION:Co-authors: Andriy Haydys (Albert-Ludwigs-Universitä
\;t Freiburg)\, Ale
ksander Doan (Stony Brook University)
The ADHM Seiberg&ndash\;Witten equations are
a class of generalized Seiberg&ndash\;Witten equa
tions associated with \;the hyperkä\;hler
quotient appearing in the \;Atiyah\, Dri
nfeld\, Hitchin\, and \;Manin'\;s construct
ion of the framed moduli space of ASD instantons o
n \;R4.  \;Heuristically\,&n
bsp\;degenerations of solutions to the ADHM Seiber
g&ndash\;Wiitten equation are linked with Fueter s
ections of bundles of ASD instantons moduli spaces
(through the Haydys correspondence).  \;In join
t work with \;Andriy Haydys\, we studied w
hen and how this heuristic can be made rigorous (f
ollowing work of Taubes on flat \;PSL(2
\,C)&ndash\;connections.) \; This work immedia
tely leads to a number of questions.  \;In par
ticular\, whether a given Fueter section can be re
alized as a limit \;and whether singular Fuete
r sections might appear. \;In \;
joint work with \;Aleksander Doan \;(p
artially in progress)\, \;we answer the first
question and the second (assuming a conjectural im
provement of the work with Haydys).  \;Time pe
rmitting\, I will briefly discuss which role we ex
pect the ADHM Seiberg&ndash\;Witten equation to pl
ay in gauge theory on G2&ndash\;manifolds.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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