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CATEGORIES:Kuwait Foundation Lectures
SUMMARY:The shape of an algebraic variety - Professor Carl
os Simpson (Nice)
DTSTART;TZID=Europe/London:20071101T170000
DTEND;TZID=Europe/London:20071101T180000
UID:TALK8781AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/8781
DESCRIPTION:An algebraic variety X over the complex numbers ha
s\, as one of its main facets\, a topological spac
e $X^{\\rm top}$. The study of $X^{\\rm top}$ has
played an important role in the history of algebr
aic geometry. We will present a way of measuring t
he “shape” of $X^{\\rm top}$ by considering maps f
rom it into different targets. The targets T\, wh
ich are like spaces\, are also profitably viewed a
s n-stacks\, a notion from higher category theory.
The complex algebraic structure of X leads to a
number of different structures on $Hom(X^{\\rm top
}\,T)$. For example when $T=BG$\, the mapping sta
ck $Hom(X^{\\rm top}\,BG)$ may be viewed as the mo
duli space of G-bundles with integrable connection
\, or principal G-Higgs bundles. These fit toget
her into Hitchin’s twistor space. Consideration
of these structures is a good way of organizing th
e investigation of the topology of complex algebra
ic varieties.
LOCATION:Wolfson Room (MR 2) Centre for Mathematical Scienc
es\, Wilberforce Road\, Cambridge
CONTACT:Helen Innes
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