conference
24/01/2020 24/01/2020

# 11th polymake conference and developer meeting

On Friday there will be one invited talk by Claus Fieker and several tutorial, demo and helpdesk sessions for polymake users.

Participants are encouraged to bring their own laptop and use them in the tutorials, preferably with an installed version of polymake. If you have any polymake problem you want to get help during the workshop please describe your problem during the sign up process.

### Program

 24.01.2020 09:30 - 10:30 Claus Fieker (TU Kaiserslautern, Germany) 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 $\alpha\in K$ s.th. $N(\alpha) = \theta$ for a given $\theta\in k$. Classically norm equations are linked to for exmple sums-of-squares: $\theta\in\mathbb Z$ is a sum of two squares if $\theta$ is a norm for $\mathbb Q(i)$. 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. 10:30 - 11:00 11:00 - 12:00 Andreas Paffenholz (TU Darmstadt, Darmstadt, Germany) 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. 11:00 - 12:00 Dominic Bunnett (TU Berlin, Berlin, Germany) Polymake Introduction Beginners introduction to polymake. Overview over functionality, polymake's rule system and data types. 12:00 - 13:00 Michael Joswig (TU Berlin / MPI MiS Leipzig, Leipzig, Germany) OSCAR 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. 13:00 - 14:00 14:00 - 15:00 Paul Vater (MPI MiS, Leipzig, Germany), 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. 14:00 - 15:00 Marek Kaluba (TU Berlin / Adam Mickiewicz University in Poznań, Berlin, Germany), 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 15:00 - 15:30 15:30 - 16:30 Davide Lofano (TU Berlin, Berlin, Germany) 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. 16:30 - 17:30 18:00 - 23:00

FU Berlin

TU Berlin

### Turku Ozlum Celik

Max Planck Institute for Mathematics in the Sciences

MPI MiS

TU Berlin

### Eliana Duarte

Otto-Von-Guericke Universität Magdeburg

Georgia Tech

TU Berlin

MPI MIS Leipzig

### Sophia Elia

Freie Univeristät Berlin

### Claus Fieker

TU Kaiserslautern

### Paul Görlach

Max Planck Institute MiS Leipzig

### Benedikt Gräßle

Humboldt Universität zu Berlin

TU Berlin

MPI MiS

MPI MiS

MiS MPI Leipzig

TU Berlin

### Michael Joswig

TU Berlin / MPI MiS Leipzig

### Marek Kaluba

TU Berlin / Adam Mickiewicz University in Poznań

TU Berlin

MPI MiS Leipzig

TU Berlin

TU Berlin

TU Berlin

MPI MiS

UCLA / MPI MIS

TU Berlin

TU Berlin

TU Berlin

TU Berlin

TU Berlin

### Laith Rastanawi

Freie Universität Berlin

### Yue Ren

Swansea University

OVGU Magdeburg

MPI-MIS

MPI MiS

MPI MIS

### Peter Schenzel

Universität Halle

MPI MiS

MPI MIS Leipzig

### Miruna-Stefana Sorea

Max-Planck-Institut für Mathematik in den Naturwissenschaften

TU Berlin

MPI MiS

KU Leuven

TU Berlin

TU Berlin

MPI MiS

### Lorenzo Venturello

Max Planck Institute for Mathematics in the Sciences

### Elise Walker

Texas A&M University

### Thomas Yahl

Texas A&M University

TU Braunschweig

### Michael Joswig

Max Planck Institute for Mathematics in the Sciences