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Seminar

Applications of tropical geometry to complex hyperplane arrangements October 09, 2009
Location: MSRI: Simons Auditorium
Speaker(s) Michael Falk
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We demonstrate how tropical elimination theory can be used to good effect in the study of resonance varieties of Orlik-Solomon algebras (or arrangement groups) and critical loci of master functions. The Bergman existence of nontrivial syzygies among master functions, yielding conclusions concerning the dimension of critical loci and the existence of non-local resonance components. This approach reproduces the known conditions for resonance in degree one, and affords a natural generalization to degree $p$ resonance in $p$-generic arrangements. The theory of degree-one resonance varieties and multinets suggests a further potential application of tropical methods.

This is part of a collaborative project with Dan Cohen, Graham Denham, and
Alexander Varchenko.

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