The shape of an algebraic variety

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• Professor Carlos Simpson (Nice)
• Thursday 01 November 2007, 17:00-18:00
• Wolfson Room (MR 2) Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Helen Innes.

An algebraic variety X over the complex numbers has, as one of its main facets, a topological space $X^{$. The study of $X}{\rm top}$ has played an important role in the history of algebraic geometry. We will present a way of measuring the “shape” of $X^{$ by considering maps from it into different targets. The targets T, which are like spaces, are also profitably viewed as 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 stack $Hom(X^{\rm top},BG)$ may be viewed as the moduli space of G-bundles with integrable connection, or principal G-Higgs bundles. These fit together into Hitchin’s twistor space. Consideration of these structures is a good way of organizing the investigation of the topology of complex algebraic varieties.

This talk is part of the Kuwait Foundation Lectures series.

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