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SUMMARY:The shape of an algebraic variety - Professor Carlos Simpson (Nice
 )
DTSTART:20071101T170000Z
DTEND:20071101T180000Z
UID:TALK8781@talks.cam.ac.uk
CONTACT:Helen Innes
DESCRIPTION:An algebraic variety X over the complex numbers has\, as one o
 f its main facets\, a topological space $X^{\\rm top}$.  The study of $X^{
 \\rm top}$ has played an important role in the history of algebraic geomet
 ry. We will present a way of measuring the “shape” of $X^{\\rm top}$ b
 y considering maps from it into different targets.  The targets T\, which 
 are like spaces\, are also profitably viewed as n-stacks\, a notion from h
 igher category theory.  The complex algebraic structure of X leads to a nu
 mber of different structures on $Hom(X^{\\rm top}\,T)$.  For example when 
 $T=BG$\, the mapping stack $Hom(X^{\\rm top}\,BG)$ may be viewed as the mo
 duli space of G-bundles with integrable connection\, or principal G-Higgs 
 bundles.   These fit together into Hitchin’s twistor space.   Considerat
 ion of these structures is a good way of organizing the investigation of t
 he topology of complex algebraic varieties.  
LOCATION:Wolfson Room (MR 2) Centre for Mathematical Sciences\, Wilberforc
 e Road\, Cambridge
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