# Mathematical Sciences Research Institute

Home » Commutative Algebra and Algebraic Geometry Seminar: The nef cone of a Coxeter complex: $\Phi$-submodular functions and deformations of $\Phi$-permutahedra

# Seminar

Commutative Algebra and Algebraic Geometry Seminar: The nef cone of a Coxeter complex: $\Phi$-submodular functions and deformations of $\Phi$-permutahedra March 05, 2019 (03:45 PM PST - 06:00 PM PST)
Parent Program: -- UC Berkeley Math (Evans Hall 939)
Speaker(s) Federico Ardila (San Francisco State University)
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Abstract/Media

We describe the nef cone of the toric variety corresponding to a Coxeter complex. Equivalently, this is the cone of deformations of a Coxeter permutahedron. This family contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra and submodular functions to any finite reflection group. This is joint work with Federico Castillo, Chris Eur, and Alex Postnikov.