Why compactify?
Tamás Hausel
2.10pm-4.00 pm February 8
939 Evans Hall, Berkeley
This is the first introductory and organizing talk of this
Berkeley-Stanford working seminar, open to anyone interested. The overall
aim is to understand the asymptotics of the metric and in turn to find
the "right" compactifications of various open manifolds. "Right" means
that certain questions of global analysis on the complete, smooth but open
manifold could be understood by analysis, in nice cases topology, of the
(usually singular) compactification. Among the manifolds we will consider
are various hyparkähler manifolds like quiver varieties, moduli of
instantons, monopoles and Higgs bundles. The compactifications which may
be treated are: Borel-Satake and various other compactifications of
locally symmetric spaces, Uhlenbeck compactifications of moduli of
instantons, Tian-Yau compactifications of Ricci-flat Kähler manifolds,
Morgan-Shalen compactification of character varieties, Thurston
compactification of Teichmüller space, Martin compactifications of
Riemannian manifolds, Lerman's symplectic cutting, etc. In this
introductory talk I will address three concrete
problems arising
in string theory (S-duality) and low dimensional topology (SU(n) and
SL(2,C) Casson invariants) and indicate how compactifications of certain
hyperkähler moduli spaces could help to attack these problems.
LECTURE NOTES ARE AVAILABLE:
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