11th polymake conference and developer meeting

Abstracts for the talks

Dominic Bunnett
TU Berlin
Polymake Introduction
Beginners introduction to polymake. Overview over functionality, polymake's rule system and data types.

Claus Fieker
TU Kaiserslautern
Class Field Theory and Applications
Class Field theory deals with the classification of abelian extensions (ie. field extensions with an abelian Galois group). Based on the type of the field we have global CFT (for number field and plane curves over finite fields) as well as local CFT (for p-adic fields and Laurent series over finite fields). Given an extension of number fields K∕k a norm equation is trying to find α K s.th. N(α) = 𝜃 for a given 𝜃 k. Classically norm equations are linked to for exmple sums-of-squares: 𝜃 is a sum of two squares iff 𝜃 is a norm for (i). Norm equations, apart from being classical objects have many applications in algebra. Classically, the solvability of norm equations is of course investigated locally: if there is a solution, there will ba one modulo every prime. CFT now classfies abelian extensions through suitable norm groups. This can and is used algorithmically, an obstacle being that local solubility is neccessary, but not sufficient, in general. In this talk I will present some of the core ideas of CFT and their links to norm equations. The corresponding algorithms are practical and available (mostly) through Hecke (hence in Oscar) and also in Magma.

Michael Joswig
TU Berlin / MPI MiS Leipzig
We will also show a first few use cases of the new computer algebra system OSCAR, which combines the features of ANTIC, GAP, Singular, polymake and other ingredients in Julia.

Marek Kaluba
TU Berlin / Adam Mickiewicz University in Poznań
, Benjamin Lorenz TU Berlin
Building Polymake (C++, Toolchain) and polymake.jl
Details on how to compile polymake from source and overview of the functionality of polymake.jl

Davide Lofano
TU Berlin
Recognizing Spaces with TOPAZ
One of the most important task in Topology is the recognition of a given space. In this talk we will explore various algorithms and heuristics implemented in polymake that will help us in this regard. We will look at classical methods like homology computations and less known ones like random approaches to discrete morse theory, bistellar flips and simple homotopy theory.

Andreas Paffenholz
TU Darmstadt
Polymake's JSON File Format and the polyDB Database
Introduction to polymake's new data format in JSON and the polyDB database for objects in discrete geometry and related areas.

Paul Vater
, Lars Kastner
Patchworking and Tropical Compactifications
We present an implementation of Viro's patchworking using tropical hypersurfaces, as well as an efficient way to compute the Z_2 homology of the resulting algebraic hypersurface. We will describe how to construct cellular sheaves in polymake, in order to compute tropical homology.


Date and Location

January 24, 2020
MPI für Mathematik in den Naturwissenschaften Leipzig
Inselstr. 22
04103 Leipzig

Scientific Organizers

Michael Joswig
MPI for Mathematics in the Sciences

Administrative Contact

Saskia Gutzschebauch
MPI für Mathematik in den Naturwissenschaften
27.01.2020, 01:27