VL: Discrete Geometry III, Summer 21

This is a BMS Advanced Course, which will thus be given in English (online). To participate registration via email is mandatory. In that email please give your name, your affiliation, and indicate whether you wish to receive credits (the latter is only possible for students of FU, HU and TU Berlin and BMS students).

VL: Monday 10-12 zoom
Wednesday 10-12 zoom
UE: tba    

Teaching assistant: Lars Kastner

The course will be organized as a reading course, on zoom. Zoom link will be sent upon request.

Contents

We will study a class of convex polytopes, known as generalized permutahedra.

The prerequisites are a course Discrete Geometry II or equivalent. For instance, see my own course in the winter term.

References (to be extendeded)

  1. Postnikov: Permutohedra, associahedra and beyond. Int. Res. Math. Res. Not. 6 (2009), 1026-1106.
  2. Chapoton, Fomin & Zelevinsky: Polytopal realizations of generalized associahedra, Canad. Math. Bull. 45 (2002), 537-566.
  3. Hohlweg & Lange; Realizations of the associahedron and cyclohedron, Discrete Comput. Geom. 37 (2007), 517-543.
  4. Ardila, Benedetti & Doker: Matroid polytopes and their volumes. Discrete Comput. Geom. 43 (2010), 841-854.
  5. Jochemko & Ravichandran: Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity, arXiv:1909.08448.
  6. Murota: Discrete convex analysis. Springer 2003.

References are given in the intended order of reading.


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Last modified: Mi Jun 30 07:57:35 UTC 2021 by mic