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Events
Mathematical Software Day

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

conference

03/12/2019 03/12/2019

Mathematical Software Day

A special one-day workshop dedicated to mathematical software at the Max-Planck Institute for Mathematics in the Sciences, on the occasion of Michael Joswig joining as a Max-Planck Fellow in December and Yue Ren leaving for Swansea University in January.

Speakers

Ulrich Bauer

TU Munich

Folkmar Bornemann

TU Munich

Paul Breiding

TU Berlin

Anne Frühbis-Krüger

Carl von Ossietzky University of Oldenburg

Max Horn

University of Siegen

Rudi Pendavingh

TU Eindhoven

Program

08:50 - 09:00	Welcome
09:00 - 09:50	Folkmar Bornemann (TU Munich, Germany) Levels of Rigor in Numerical Computation: Mathematical Concepts and Software We review some concepts how modern mathematical software could assess the accuracy of numerical computations, short of fully rigorous methods, to answer that pending questions: How many digits are correct, really? We demonstrate the possibilities with some case studies and display a new concept, infinite dimensional numerical linear algebra, which only recently has become feasible for effective coding using Julia.
10:00 - 10:50	Max Horn (University of Siegen, Germany) On the construction and classification of ‘small’ groups In this talk, we will review how each finite group can be disassembled into a unique set of "simple" groups, similar to the unique prime factorization of natural numbers. This raises various questions; for example: which simple pieces are there? And: in which ways can one glue these pieces together to form new finite groups? The main focus of this talk will be on this last question, and we will discuss it in the context of classifying (almost) all groups of order at most 20,000.
11:00 - 11:30	Coffee Break
11:30 - 12:20	Anne Frühbis-Krüger (Carl von Ossietzky University of Oldenburg, Germany) Parallel Algorithms in Algebraic Geometry While other branches of mathematics have greatly benefitted from massively parallel computations over the last decades, common belief was that Algebraic Geometry would not be a good field for parallelism, since one of the main workhorses, the computation of Groebner Bases, poses an important obstacle. With the advent of powerful, flexible, transparent workflow management systems, on the other hand, large problems with a very coarse granularity could be tackled for the first time. In this talk, I will outline some successful applications such as e.g. a parallel smoothness test and the computation of a GIT-fan.
12:30 - 13:30	Lunch
13:30 - 14:20	Paul Breiding (TU Berlin, Germany) Solving polynomial systems in Julia In my talk I will present the software HomotopyContinuation.jl, which is a Julia package for numerically solving systems of polynomial equations. First, I will briefly introduce the homotopy continuation algorithm and how it is implemented in Julia. Then, I will go through a couple of examples that illustrate the diversity of applications, in which the package can be used. This is joint work with Sascha Timme.
14:30 - 15:20	Rudi Pendavingh (TU Eindhoven, Netherlands) The story of the Sage matroid package In 2010, Stefan van Zwam and myself started work on on a new package for computing with matroids in Sage, the open source mathematics platform. I want to tell the story of this project: the theoretical goals that motivated us spending that much time on writing software, our design principles, and our considerations when choosing Sage as a platform. Finally, I want to discuss some of the insights gained from working on this software.
15:30 - 16:00	Coffee Break
16:00 - 16:50	Ulrich Bauer (TU Munich, Germany) Ripser: Efficient computation of Vietoris–Rips persistence barcodes I will discuss the efficient computation of the Vietoris–Rips persistence barcode for a finite metric space. The implementation in the newly developed C++ code “Ripser” focuses on memory and time efficiency, outperforming previous software by a factor of more than 40 in computation time and a factor of more than 15 in memory efficiency on typical benchmark examples. The improved computational efficiency is based on a close connection between persistent homology and discrete Morse theory, together with novel algorithmic design principles, carrying out a matrix algorithm without actually storing the entire matrix in memory.
18:00 - 00:00	Dinner at Auerbachs Keller (on individual payment)

Participants

Michael Adamer

MPI MiS

Ulrich Bauer

TU Munich

Folkmar Bornemann

TU Munich

Paul Breiding

TU Berlin

Dominic Bunnett

TU Berlin

Turku Ozlum Celik

Max Planck Institute for Mathematics in the Sciences

Francisco Criado Gallart

TU Berlin

Daniel Dörfler

Friedrich Schiller University Jena

Holger Eble

TU Berlin

Anne Frühbis-Krüger

Carl von Ossietzky University of Oldenburg

Oliver Gäfvert

KTH Royal Institute of Technology

Paul Görlach

Max Planck Institute MiS Leipzig

Benedikt Gräßle

Humboldt Universität zu Berlin

Alexander Heaton

MPI MiS

Janin Heuer

TU Braunschweig

Roser Homs Pons

TU Berlin

Max Horn

University of Siegen

Alexej Jordan

TU Berlin

Michael Joswig

Max Planck Institute for Mathematics in the Sciences

Michael Jung

Universität Potsdam

Marek Kaluba

Adam Mickiewicz University& TU Berlin

Oswald Knoth

Institut für Troposphärenforschung

Stefan Kuhlmann

TU Berlin

Viktor Levandovskyy

RWTH Aachen University

Andreas Löhne

FSU Jena

Robert Löwe

TU Berlin

Andrew Newman

TU Berlin

Alessandro Oneto

Otto-von-Guericke Universität Magdeburg

Rudi Pendavingh

TU Eindhoven

Manuel Radons

TU Berlin

Yue Ren

Max Planck Institute for Mathematics in the Sciences

Anna-Laura Sattelberger

MPI MiS Leipzig

Mahsa Sayyary Namin

MPI MIS

Peter Schenzel

Martin-Luther university

Emre Sertöz

MPI MiS

Miruna-Stefana Sorea

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Sylvain Spitz

HU Berlin

Bernd Sturmfels

MPI MiS

Simon Telen

KU Leuven

Ayush Kumar Tewari

TU Berlin

Sascha Timme

TU Berlin

Paul Vater

TU Berlin

Lorenzo Venturello

Max Planck Institute for Mathematics in the Sciences

Philipp Warode

Humboldt-Universität zu Berlin

Martin Ziegler

KAIST

Scientific Organizers

Michael Joswig

Max Planck Institute for Mathematics in the Sciences and TU Berlin

Yue Ren

Max Planck Institute for Mathematics in the Sciences

Administrative Contact

Saskia Gutzschebauch

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