Topology of Algebraic Varieties | |

Topic: | Toric chordality and applications |

Speaker: | Karim Adiprasito |

Affiliation: | Hebrew University of Jerusalem; Member, School of Mathematics |

Date: | Wednesday, January 28 |

Time/Room: | 11:15am - 12:30pm/S-101 |

Video Link: | http://video.ias.edu/tav/2015/0128-Adiprasito |

Inspired by the elementary notion of graph chordality, we introduce the notion of toric chordality, which naturally gives a tool to to study the geometry and combinatorics of cohomology classes of toric varieties and the weight algebras of polytopes. Moreover, I will sketch some interesting applications:

-- The notion of toric chordality naturally provides new proofs and generalizations of a variety of crystallization theorems arising in commutative algebra.

-- Moreover, I will discuss a quite unprecedented relation between primitive Betti numbers of toric varieties and the shape of a convex polytope, and finally

-- I will discuss some applications to the study of deformation spaces of polytopes.