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Events
Open Source Computer Algebra Research (OSCAR)

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

11/12/2017 12/12/2017

Open Source Computer Algebra Research (OSCAR)

This is a workshop co-organized by the SFB TRR 195 and the MPI MIS Leipzig on open source computer algebra research and its applications. The workshop aims at promoting the work of the German open source computer algebra community and the Max Planck Institute for Mathematics in the Sciences, with special emphasis on the newly established SFB-TRR 195 and the newly established MPI working groups on Nonlinear Algebra, Combinatorial Algebraic Geometry, and Tensors and Optimization.

The topics of the talks will revolve around computational algebraic geometry and its applications, and there will be ample time and space for collaborations and discussions.

Speakers

Janko Böhm

University of Kaiserslautern

Wolfram Decker

University of Kaiserslautern

Marvin Hahn

University of Tübingen

Martin Helmer

University of Copenhagen

Thomas Kahle

Otto von Guericke University Magdeburg

Viktor Levandovskyy

RWTH Aachen

Emre Sertöz

Max Planck Institute for Mathematics in the Sciences

Andreas Steenpaß

University of Kaiserslautern

Isabel Stenger

University of Kaiserslautern

Rebecca Waldecker

Martin Luther University Halle

Program

09:45 - 10:00	Opening Remarks
10:00 - 11:00	Wolfram Decker (University of Kaiserslautern, Kaiserslautern, Germany) OSCAR — A Visionary Computer Algebra System
11:00 - 11:30	Coffee Break
11:30 - 12:00	Janko Böhm (University of Kaiserslautern, Kaiserslautern, Germany) Massive parallelization and smoothness tests of algebraic varieties
12:00 - 12:30	Andreas Steenpaß (University of Kaiserslautern, Kaiserslautern, Germany) Refined algorithms to compute syzygies Based on Schreyer’s classical algorithm, we present a refined algorithm for the computation of syzygies. The main ideas are the following: First, we may leave out certain terms of module elements during the computation which do not contribute to the result. These terms are called ``lower order terms''. Second, we do not need to order the remaining terms of these module elements during the computation. This significantly reduces the number of monomial comparisons for the arithmetic operations. Third, we may additionally cache some partial results and reuse them at the remaining steps. Altogether, these improvements allow us to tackle previously unsolvable computational problems such as the Prym-Green conjecture for curves of genus 24.
12:30 - 13:30	Lunch
13:30 - 14:00	Marvin Hahn (University of Tübingen, Tübingen, Germany) Constructing faithful tropicalisations of plane quartics using linear modifications Any abstract non-hyperelliptic curve of genus $3$ is naturally embedded as a plane quartic via its canonical embedding. In other words, the moduli space of plane quartics maps surjectively onto the non-hyperelliptic locus of the moduli space of genus $3$ curves. It was proved by Brodsky-Joswig-Morrison-Sturmfels, that this does not hold true for the naive definition of the moduli space of tropical plane quartics. In particular, they classified which abstract tropical genus $3$ curves can be realised as a tropical quartic in $\mathbb{R}^2$. We fix this defect of tropical moduli spaces by considering quartics in tropical planes, which themselves are embedded in higher dimension. More precisely, we construct plane embeddings for any abstract tropical non-hyperelliptic genus $3$ curve using modifications. This is joint work in progress with Hannah Markwig, Yue Ren and Ilya Tyomkin.
14:00 - 14:30	Isabel Stenger (University of Kaiserslautern, Kaiserslautern, Germany) Constructing numerical Godeaux surfaces
14:30 - 15:00	Coffee Break
15:00 - 18:00	Discussion/Work Session Slides
19:00 - 00:00	Dinner in town

10:00 - 10:30	Rebecca Waldecker (Martin Luther University Halle, Halle, Germany) Orbital graphs
10:30 - 11:00	Martin Helmer (University of Copenhagen, Copenhagen, Denmark) Computing in intersection theory
11:00 - 11:30	Coffee Break
11:30 - 12:00	Emre Sertöz (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) Computing images of polynomial maps
12:00 - 12:30	Thomas Kahle (Otto von Guericke University Magdeburg, Germany) SAT solvers in non-linear algebra
12:30 - 13:30	Lunch
13:30 - 14:00	Viktor Levandovskyy (RWTH Aachen, Germany) Noncommutative computations with Singular
14:00 - 14:20	Paul Breiding (MPI MIS, Leipzig, Germany), Sascha Timme (Technische Universität Berlin) Homotopy Continuation in Julia
14:20 - 16:30	Discussion/Work Session
16:30 - 17:00	Coffee Break
17:00 - 18:00	Reports on some projects
18:00 - 18:15	Closing Remarks
19:00 - 00:00	Dinner in town

Participants

Carlos Améndola

TU Berlin

Lamprini Ananiadi

Otto von Guericke Universität

Reimer Behrends

University of Kaiserslautern

Janko Böhm

University of Kaiserslautern

Paul Breiding

MPI MIS

Thomas Breuer

RWTH Aachen

Alessio D'Alì

MPI MiS Leipzig

Ferran Dachs Cadefau

MLU Halle-Wittemberg

Timo de Wolff

TU Berlin

Wolfram Decker

University of Kaiserslautern

Papri Dey

MPI MIS Leipzig

Philipp di Dio

MPI + Uni Leipzig

Eliana Duarte

Mpi Leipzig

Christian Eder

University of Kaiserslautern

Claus Fieker

University of Kaiserslautern

Anne Frühbis-Krüger

Leibniz Universität Hannover

Paul Görlach

MPI MIS Leipzig

Sebastian Gutsche

Siegen University

Marvin Hahn

University of Tübingen

Corey Harris

MPI Leipzig

Bill Hart

Technische Universität Kaiserslautern

Martin Helmer

University of Copenhagen

Tommy Hofmann

University of Kaiserslautern

Alexandru Iosif

OvGU Magdeburg

Anders Jensen

Aarhus University

Michael Joswig

Technische Universität Berlin

Thomas Kahle

Otto von Guericke University Magdeburg

Nidhi Kaihnsa

MPI MIS Leipzig

Lars Kastner

Technische Universität Berlin

Mario Kummer

MPI MIS

Viktor Levandovskyy

RWTH Aachen

Benjamin Lorenz

TU Berlin

Anthea Monod

Columbia University

Henri Mühle

TU Dresden

Marta Panizzut

TU Berlin

Yue Ren

Max Planck Institute for Mathematics in the Sciences

Mahsa Sayyary

MPI MIS

Peter Schenzel

Universität Halle

Hans Schönemann

TU Kaiserslautern

Benjamin Schröter

TU Berlin

Henning Seidler

TU Berlin

Emre Sertöz

Max Planck Institute for Mathematics in the Sciences

Tim Seynnaeve

Max Planck Institute for Mathematics in the Sciences

Jeff Sommars

University of Illinois at Chicago

Andreas Steenpaß

University of Kaiserslautern

Isabel Stenger

University of Kaiserslautern

Christian Stump

TU Berlin

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Sascha Timme

Technische Universität Berlin

Andre Uschmajew

MPI MIS

Rebecca Waldecker

Martin Luther University Halle

Oguzhan Yürük

TU Berlin

Scientific Organizers

Yue Ren

Max Planck Institute for Mathematics in the Sciences

Bill Hart

Technische Universität Kaiserslautern

Administrative Contact

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail