Abstracts
for the Seminar

Spring 2015

**Speaker: **Ivan Izmestiev, Freie Universität Berlin

**Title: **Geometric Pachner moves, rigidity of non-convex polyhedra, and polytopality of simplicial spheres

**Time:** 2:30 PM, Monday, February 2, 2015

**Place:** Malott 206

**Abstract:** Morelli and Wlodarczyk solved independently in 1996/97 the "weak Oda conjecture" for toric varieties. Stated geometrically, it says that any two triangulations of a convex polytope are related by geometric bistellar moves.
In this talk I will give a version of a proof of the Morelli-Wlodarczyk theorem and discuss two applications. The first application is the rigidity of a certain class of non-convex polyhedra (joint work with Jean-Marc Schlenker). The second is is a proof of Billera's conjecture: any simplicial PL sphere becomes polytopal after several derived subdivisions (joint work with Karim Adiprasito).

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