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f-vectors of polytopes and simplicial complexes, part I: results and problems

Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017

September 06, 2017 (10:30 AM PDT - 11:30 AM PDT)
Speaker(s): Eran Nevo (The Hebrew University of Jerusalem)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

What are the possible face numbers of d-dimensional: polytopes? simplicial polytopes (namely those whose proper faces are all simplices)? flag polytopes (namely simplicial polytopes all whose minimal nonfaces have size 2)? centrally symmetric polytopes (namely those invariant under the map x-->-x)?...

We'll survey results and open problems concerning face numbers (f-vectors) of polytopes and simplicial complexes, including subfamilies of particular interest.

As the area is vast and fast growing, this talk will cover only a portion of it, representing some of the main methods used. These methods range from algebraic to combinatorial, topological and geometric, and will form Part II given by Martina Juhnke-Kubitzke.

Supplements
29480?type=thumb Nevo Notes 1.82 MB application/pdf Download
Video/Audio Files

6-Nevo

H.264 Video 6-Nevo.mp4 419 MB video/mp4 rtsp://videos.msri.org/data/000/029/351/original/6-Nevo.mp4 Download
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