Realization Spaces of Polytopes

Winter Semester 2020/2021, VL 2

Marta Panizzut, Institut für Mathematik, TU Berlin

Registration via email is mandatory in order to participate. In the email please give your name, your affiliation, and indicate whether you wish to receive credits.

Vorlesung:Tuesday, 14:00-16:00

The course will be held online. The zoom link for the lectures will be shared with the registered participants.
The first lecture will take place on Tuesday, November 3rd.

Prerequisites: Diskrete Geometrie I and Algebra I.

Content

The study of realization spaces of polytopes is a classical topic in geometric combinatorics at the interface between discrete and real algebraic geometry. We will begin with classical constructions and results, and then focus on recent advances.
Topics of the course are:
  • Main definitions and constructions
  • Three-dimensional vs higher dimesional polytopes
  • Comparison of different models
  • Recent advances

References (to be completed)

  • Gouveia, Macchia, Thomas, and Wiebe: The slack realization space of a polytope. SIAM J. Discrete Math. 2019.
  • Rastanawi, Sinn, Ziegler: On the Dimensions of the Realization Spaces of Polytopes. arXiv. 2020
  • Richter-Gebert: Realization Spaces of Polytopes. Lecture Notes in Mathematics. Springer. 1996
  • Ziegler: Lectures on Polytopes. Graduate Texts in Mathematics. Springer. 2007