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Resonance and Chen ranks in geometry

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If you have a question about this talk, please contact Dhruv Ranganathan .

Koszul modules and their associated resonance varieties are objects appearing in a variety of contexts in algebraic geometry, topology, and combinatorics. I will offer an introduction to this circle of ideas and discuss a recent proof of the Chen Ranks Conjecture describing the Hilbert function of any Koszul module verifying natural conditions inspired by geometry. Applications to hyperplane arrangements, describing in a uniform effective manner the Chen ranks of the fundamental group of the complement of the arrangement will be presented. This is joint work with Aprodu, Raicu and Suciu.

This talk is part of the Geometry and Topology colloquium series.

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