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Cutting Cakes with Combinatorial Fixed Point Theorems

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

September 07, 2017 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Kathryn Nyman (Willamette University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Sperner's Lemma

  • Cake cutting

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

Sperner's Lemma, a combinatorial analogue to Brower's Fixed Point Theorem, guarantees a "fully-labeled cell" in any labeled triangulation of the n-simplex meeting suitable conditions. These fully-labeled cells provide crisp solutions to envy-free cake-cutting questions.  We look at equivalences between combinatorial results and topological fixed-point theorems, along with applications to fair division problems, including the division of multiple cakes and consensus halving. 

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Video/Audio Files

14-Nyman

H.264 Video 14-Nyman.mp4 106 MB video/mp4 rtsp://videos.msri.org/data/000/029/366/original/14-Nyman.mp4 Download
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