Online-Workshop Computational Algebra 2021
Location & registration
The workshop will take place on 21 May 2021 starting at 13:00 CET. Note that for data protection reasons, joining requires an access code. To get it, please register for the workshop by sending an email to caworkshop with subject “Workshop Computational Algebra 2021” and including your name and affiliation.
- 13:00: Words of welcome
- 13:05-13:55: Simon Brandhorst (Saarbrücken)
- 14:05-14:55: Jean Philippe Labbé (Berlin)
- 15:05-15:55: Timo de Wolff (Braunschweig)
- 16:05-16:55: Jonathan Kliem (Berlin)
Simon Brandhorst (Saarbrücken)
Jonathan Kliem (Berlin)
A new face iterator for polyhedra and other lattices
We will discuss a depth-first algorithm to iterate over the faces of polyhedra (joint work with Christian Stump). It is very memory efficient and the implementation in SageMath is much faster than implementations of other algorithms. The algorithm can be applied to other situations such as simplicial complexes, finite polyhedral complexes, subdivisions of manifolds, extended tight spans and closed sets of matroids.
Jean Philippe Labbé (Berlin)
Lineup polytopes and applications in quantum physics
The set of all possible spectra of 1-reduced density operators for systems of N particles on a d-dimensional Hilbert space is a polytope called hypersimplex. If the spectrum of the original density operators is fixed, the set of spectra (ordered decreasingly) of 1-reduced density operators is also a polytope. A theoretical description of this polytope using inequalities was provided by Klyachko in the early 2000’s.
Adapting and enhancing tools from discrete geometry and combinatorics (symmetric polytopes, sweep polytopes, and the Gale order), we obtained such necessary inequalities explicitly, that are furthermore valid for arbitrarily large N and d.
These may therefore be interpreted as generalizations of Pauli’s exclusion principle for fermions. In particular, this approach leads to a new class of polytopes called lineup polytopes.
This is joint work with physicists Julia Liebert, Christian Schilling and mathematicians Eva Philippe, Federico Castillo and Arnau Padrol.
Timo de Wolff (Braunschweig)