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The Story of Hodge Theory

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If you have a question about this talk, please contact Alexander Shannon.

This talk will start with an explanation of the celebrated theorem that the cohomology of a smooth projective complex algebraic variety breaks up in a canonical way – the so-called Hodge decomposition. I shall then go on to mention some of the ways this phenomenon generalises, including Deligne’s notion of a mixed Hodge structure, which is carried by the cohomology of any complex algebraic variety and Griffiths’ notion of a variation of Hodge structure, describing how the Hodge decomposition varies in families. Time-permitting, I shall also explain some ways in which Hodge structures appear in the more general setting of non-commutative algebraic geometry, and the efforts currently being made to study them.

This talk is part of the Directions in Research Talks series.

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