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### Homology classes in algebraic varieties: nef, effective, and prime

**Special Events**

Speaker: | June Huh, University of Michigan |

Location: | 2112 MSB |

Start time: | Mon, Apr 28 2014, 4:10PM |

The homology group of an algebraic variety is an abelian group equipped with several additional structures. It contains the set of primes, the homology classes of subvarieties. It contains the semigroup of effective classes, the nonnegative linear combinations of primes. It contains the semigroup of nef classes, the classes which intersect all primes of complementary dimension nonnegatively. We will see how these subsets look like in a particular algebraic variety, the one associated to the polytope `permutahedron'. The semigroups in this case have tractable structures, while the distribution of primes is more mysterious and related to some deep combinatorial conjectures on matroids.