ICMS 2016

1. Univalent Foundations and Proof Assistants
Organizer:
Vladimir Voevodsky, IAS, Princeton
vladimir@ias.edu

The goal of the session is to bring together people in the proof assistant community working on the ideas inspired by the current activity surrounding the Univalence Axiom and, more generally, univalent foundations of mathematics and homotopy type theory. We expect to have representatives from several existent proof assistants as well as people working on the development of new type theories that will or may become the basis of proof assistants in the future. We consider the problem of developing the infrastructure that will allow formal specification and eventually verification of new proof assistants to be an important and possibly the most important one that is facing the community as the complexity of the type theories underlying the proof assistants grows and hope to also have talks from people and teams working in this direction.

2. Software for Mathematical Reasoning and Applications
Organizers:
Bruno Buchberger, Tudor Jebelean, Temur Kutsia, Wolfgang Windsteiger (session manager)
all: Research Instute for Symbolic Computation
Johannes Kepler University, Linz / Schloss Hagebnerg, 4232 Hagenberg, Austria
Wolfgang.Windsteiger@jku.at

In addition to traditional software for numerics and symbolics (in algebra, analysis, combinatorics, etc.), more and more software for automated reasoning based on sophisticated general and special reasoning techniques with nice user interfaces enriches the possibilities of working mathematicians, computer scientists and engineers. For this session we welcome reports on

• new versions of automated reasoning software
• user interfaces for automated reasoning software
• new implementations of general and special reasoning techniques
• interaction of automated reasoning software with numerical and algebraic software
• applications of automated reasoning in mathematics, computer science, natural sciences, engineering, education,
• the use of automated reasoning in the build-up of formal mathematical knowledge bases
• and related subjects.

3. Computational Number Theory meets computational Algebraic Geometry
Organizers:
Wolfram Decker, University of Kaiserslautern, Department of Mathematics
decker@mathematik.uni-kl.de
Claus Fieker, Univesity of Kaiserslautern, Department of Mathematics
fieker@mathematik.uni-kl.de

Both number theory and geometry have a lot of common algorithmic tasks, albeit hidden behind different languages. For example, while geometers compute normalizations, number theorists are interested in integral closures or maximal orders. As diverse as the languages are the techniques that are traditionally applied—although recently the algorithms seem to converge. In this workshop we aim to bring together experts in computational algebraic geometry and algorithmic number theory in order to facilitate a strong exchange of ideas. We expect synergy effects for the design of algorithms by bringing both worlds together.

4. Algebraic Geometry in Applications
Organizer:
Gerhard Pfister, University of Kaiserslautern
pfister@mathematik.uni-kl.de

The aim of the section is to show how algebraic geometry can be applied outside algebraic geometry in many different areas, using the basic tools such as factorization, Gröbner bases techniques, symbolic-numeric techniques and others. We want to present applications in

• Kinematics,
• Cryptology,
• Algebraic Statistics including applications in Biology,
• Electronics,
• Computer Vision

5. Computational aspects of homological algebra, group, and representation theory
Organizers:
Mohamed Barakat, University of Siegen
mohamed.barakat@uni-siegen.de
Max Horn, University of Giessen
max.horn@math.uni-giessen.de

Homological algebra is a universal language with an established presence in many fields of mathematics. The session will focus on modern applications of computational homological methods to the representation theory of groups and algebras. These methods range from the computability of group, Lie algebra, and Hochschild cohomology to the constructivity of Morita, tilting, and various other equivalences of derived and differentially enriched categories. Such equivalences also connect the representation theory to equivariant coherent sheaves on varieties admitting a tilting object and hence to algebraic geometry.

6. Software of Polynomial Systems
Organizers:
Chenqi Mou, School of Mathematics and Systems Science
Beihang University, Beijing 100191, China
chenqi.mou@buaa.edu.cn
Dongming Wang School of Mathematics and Systems Science
Beihang University, Beijing 100191, China
and
Centre National de la Recherche Scientifique
75794 Paris cedex 16, France
dongming.wang@lip6.fr

Polynomial systems appear in commutative algebra, algebraic geometry, geometric reasoning, cryptography, coding theory, biology, and many other areas of science and engineering. The study of structures, properties, and representations of mathematical objects defined by polynomial systems may involve heavy computations, for which advanced software need be developed and used. This session aims at bringing together interested researchers, software developers, and software users to present and to discuss recent work and progress on the design, implementation, analysis, and application of software for computations with polynomial systems. Specific topics for the session include, but are not limited to:

• Software for fast arithmetic with polynomials
• Software for polynomial root finding
• Software for polynomial system solving
• Software for parametric polynomial systems
• Software for polynomial systems over the reals
• Databases related to polynomial systems
• Special-purpose software for applications
• Software development paradigms and methodologies
• Case studies, experiments, and comparisons

7. Software for the Symbolic Study of Functional Equations
Organizers:
Moulay A. Barkatou,
Thomas Cluzeau,
University of Limoges ; CNRS ; XLIM UMR 7252
123, Avenue Albert Thomas, 87060 Limoges, France
moulay.barkatou@unilim.fr,
thomas.cluzeau@unilim.fr
Suzy S. Maddah,
Fields Institute
222 College St, Toronto, ON M5T 3J1 Ontario, Canada
suzy.maddah@inria.fr

The aim of this session is to present softwares or packages dedicated to the symbolic or symbolic-numeric treatment of (systems of) functional equations such as ordinary or partial differential equations, (q-)difference equations, differential time-delay equa¬tions, discrete-time equations, . . . . The presentations are expected to enhance inter¬actions between developers and potential users on the one hand, and amongst developers/ researchers on the other hand. Survey talks of research groups, reviews of the state of the art, works which make substantial use of such existing softwares for mis¬cellaneous applications, and demonstrations of softwares under development are also welcomed.
The topics include but are not limited to:

• Symbolic resolution of linear or nonlinear functional equations or systems,
• Symbolic manipulation of functional operators,
• Qualitative study of functional systems,
• Applications.

8. Symbolic Integration
Organizer:
Christoph Koutschan
RICAM, Austrian Academy of Sciences, Altenberger Strasse 69
4040 Linz, AUSTRIA
christoph.koutschan@ricam.oeaw.ac.at

The symbolic evaluation of integrals is a classic topic in computer algebra. This refers to indefinite integrals, i.e., finding the antiderivative of a given function, as well as to definite integrals. In the past decades tremendous progress has been made in this field, and the capabilities of today's computer algebra systems are truly impressive. As these capabilities are particularly based on table-lookup, there is still a considerable interest in algorithmic approaches to symbolic integration, which also nowadays is a very active field of research. In this session we want to discuss recent developments concerning the algorithmic evaluation of integrals, either in closed form or using some implicit representation, e.g., in terms of a differential equation satisfied by a given parametric integral.

9. Symbolic computation and elementary particle physics
Organizers:
Carsten Schneider
Research Institute for Symbolic Computation (RISC)
Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz, Austria
Carsten.Schneider@risc.jku.at
Johannes Bluemlein
Deutsches Elektronen--Synchrotron, DESY
Platanenallee 6, D--15738 Zeuthen, Germany
johannes.bluemlein@desy.de

In the research area of elementary particle physics and in the research areas of symbolic computation and of computer algebra in particular, there is the following very strong common interest: How can one simplify expressions represented in terms of multiple-sums and multiple-integrals or in terms coupled difference/differential equations, and how can one extract analytic properties of these expressions by symbolic manipulations?
In the last decades very efficient algorithms and tools have been developed that address these problems. Especially in the last few years, new algorithms have been worked out that are inspired by the different techniques of both communities. In this session we will present the newest technologies from both research communities that can be used to evaluate complicated massive Feynman integrals coming from calculations in quantum chromodynamics (QCD). In particular, we aim at pushing forward these very promising interdisciplinary developments.

10. Software for numerically solving polynomial systems
Organizers:
Daniel Bates, Colorado State U.
Department of Mathematics, Colorado State University
bates@math.colostate.edu
Jonathan Hauenstein, U. of Notre Dame
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame
hauenstein@nd.edu
Daniel Brake, U. of Notre Dame
Department of Applied and Computational Mathematics and Statistics, University of Notre Dame dbrake@nd.edu

This session will bring together researchers and practitioners related to solving polynomial systems using numerical and hybrid symbolic-numeric methods. This session will consider new algorithmic and computational approaches as well as applications. The topics include algebraic geometry, applications of algebraic geometry, computational algebra, computer algebra systems, hybrid symbolic-numeric methods, and numerical algebraic geometry.

11. High-precision arithmetic, effective analysis and special functions
Organizer:
Fredrik Johansson
INRIA Bordeaux-Sud-Ouest and Institut de Mathématiques de Bordeaux
fredrik.johansson@gmail.com

High-precision methods have become an important tool to get reliable results when solving numerical problems of increased size and complexity. The goal of this session is to present advances in software for high-precision or certified numerical methods, particularly in the context of effective complex analysis and computation of transcendental functions. Possible subjects include but are not limited to:

• Arbitrary-precision and mixed-precision arithmetic
• Interval arithmetic and Taylor methods
• High-precision or rigorous computation of D-finite functions, L-functions and modular forms
• Certified numerical integration and solution of ODEs
• Applications, for instance in number theory, combinatorics, and mathematical physics

12. Mathematical Optimization
Organizers:
Ambros M. Gleixner, Zuse Institute Berlin
gleixner@zib.de
Christian Kirches, IWR Heidelberg/TU Braunschweig
christian.kirches@iwr.uni-heidelberg.de
John Mitchell, Rensselaer Polytechnic Institute
mitchj@rpi.edu
Ted Ralphs, Lehigh University
ted@lehigh.edu

One out of four mathematical software packages listed in the database swMATH.org is categorized under the search term "optimization". This indicates the prominent role of computational research in the field of optimization, and vice versa. This session aims at spanning the broad range of mathematical optimization software from algorithms for continuous, convex optimization that exploit strong duality theory to solver software for nonconvex problem classes, including packages that support the modeling process.

Recent developments that deserve special, though not exclusive attention are the integrated handling of nonconvex constraints from discrete and continuous optimization, the exploitation of increasingly available parallel hardware architecture, and arithmetically exact methods that render optimization a tool for mathematical theory exploitation. The session shall provide a forum for discussing common and distinct challenges and future trends. An overview talk will provide an introduction to a general audience in mathematical computation.

13. Interactive operation to scientific artwork and mathematical reasoning
Organizers:
Setsuo Takato, Toho University, Japan, takato@phar.toho-u.ac.jp
Mastaka Kaneko, Toho University, Japan, masataka.kaneko@phar.toho-u.ac.jp
Ulrich Kortenkamp, University of Potsdam, Germany, ulrich.kortenkamp@uni-potsdam.de

Because of the spectacular innovations in interactive computer tools, we are shocked by the paradigm shift in mathematical reasoning in a way we have never experienced. Among the innovations, the development of tools for interactively generating and visualizing mathematical artwork, including dynamic geometry software and computer algebra systems, has had a great influence especially on education. These tools help educators to make simulations, to formulate conjectures, to verify mathematical facts, and to observe mathematical mechanisms. Despite the capabilities of such software, a more efficient linkage to other technology, including scientific and graphical editors, word processors, high-performance computing tools, and mathematical utilities for the web, is needed if the tools are to fully support mathematical reasoning in both research and education.
The aim of this session is to bring together researchers, developers and users of mathematical web/mobile interfaces, mathematical computing and editing facilities, and scientific visualization tools, and help them focus on all the exciting developments in these fields. The session accepts papers that address related research and development and present new technologies. Papers exploring educational experiences by using these technologies in an original way are also welcome.

14. Information services for mathematics: software, services, models, and data
Organizers:
Wolfram Sperber, FIZ Karlsruhe, Wolfram.Sperber@fiz-karlsruhe.de
Michael Kohlhase, Jacobs University Bremen, m.kohlhase@jacobs-university.de

Math Inside – this could be a slogan for much of research and technology today. Indeed, it is hard to imagine any that is not driven by Mathematics at its core. But mathematical knowledge is not enough, it must be made useful by mathematical software, services, models, and data (MathSSMD). As a consequence MathSSMD are under dynamic development, widely distributed, and dependent on hard- and software. This makes access, verification, and reuse of MathSSMD difficult, especially as standards and policies for the presentation and description of mathematical MathSSMD are missing.

Fortunately the mathematical community is actively engaged to design and establish powerful information services for MathSSMD, especially

• repositories of MathSSMD, e.g., Netlib or the R Project for Statistical Computing,
• portals and bibliographic databases for MathSSMD, e.g., swMATH or Plato
• services, e.g., OEIS or DMLF
• standards for the content analysis of MathSSMD, e.g., a citation standard and metadata schemes for MathSSMD
• evaluation and quality control of MathSSMD, e.g., peer reviewing in journals with focus on mathematical software

15. SemDML: Towards a Semantic Layer of a World Digital Mathematical Library
Organizers:
Michael Kohlhase, Jacobs University Bremen, m.kohlhase@jacobs-university.de
Olaf Teschke, FIZ Karlsruhe, olaf.teschke@fiz-karlsruhe.de
Stephen Watt, University of Waterloo, smwatt@uwaterloo.ca

The dream of a comprehensive digital mathematical library is almost as old as the practice of distributing documents electronically. Recently, the International Mathematical Union has chartered a working group for establishing World Digital Mathematical Library (WDML) with a semantic layer, i.e. a layer where mathematical knowledge is represented in a way that supports semantic services like computation, proof-checking, or search.

But a semantic layer for a WDML needs the solution of some fundamental problems, including:

1. There are many possible choices of representation formats optimized towards different goals,
2. there are multiple foundations of mathematics (basic theories like ZFC on which all meaning is based), and
3. full formalization in a specific logic/foundation is prohibitively expensive and forces choices that are foreign to mathematical practice.

The SemDML Workshop wants to address these - and related - questions from foundational and technical perspectives and create a forum for advancing the scientific and technological basis for a World Digital Mathematical Library with a Semantic Layer.

16. Polyhedral methods in geometry and optimization
Organizers:
Michael Joswig , TU Berlin, joswig@math.tu-berlin.de
Marc Pfetsch , TU Darmstadt, pfetsch@mathematik.tu-darmstadt.de

Convex polyhedra occur in optimization as the feasible regions of linear programs. Moreover, integer linear programming is the same as linear programming over the convex hull of the lattice points in a polyhedron. In algebraic geometry and its applications piecewise-linear shapes occur in the guise of polyhedral fans. Examples include secondary and Gröobner fans. This session wants to bring together people working on algorithms and software dealing with any of the above.

Specific topics include, but are not restricted to, the following:

• convex hull computations
• mixed integer linear programming
• explicit methods for triangulating point configurations
• computations in toric or tropical geometry
• parallelization of polyhedral computations
• polyhedral methods in algebraic statistics
• algorithms exploiting symmetry in any of the above

17. General
Organizers:
Gert-Martin Greuel, greuel@mathematik.uni-kl.de
Peter Paule, Peter.Paule@risc.uni-linz.ac.at
Andrew Sommese, sommese@nd.edu

This session addresses aspects of mathematical software that are not covered by the previous sessions.

18. Tutorials
Organizers:
Gert-Martin Greuel, greuel@mathematik.uni-kl.de
Peter Paule, Peter.Paule@risc.uni-linz.ac.at
Andrew Sommese, sommese@nd.edu

In this tutorial I will demonstrate how to:

• create a Docker image containing software, which can then be downloaded
• and executed on the mentioned OSs;
uploading the image to DockerHub making it accessible to all users;
• using GitHub/BitBucket, Dockerfiles and DockerHub to automatically create images and make them accessible to users.

This tutorial is intended for software developers which might consider using Docker as a stress- and maintenance-free way of shipping their software.

19. Demos
Organizers:
Gert-Martin Greuel, greuel@mathematik.uni-kl.de
Peter Paule, Peter.Paule@risc.uni-linz.ac.at
Andrew Sommese, sommese@nd.edu

Abstract:
GNU TeXmacs is a free scientific office suite. Its core consists of a structured mathematical text editor with a professional typesetting quality, together with a user friendly, wysiwyg interface. The software also integrates various other tools, such as a graphical picture editor, a presentation mode, a bibliography manager, interfaces for many computer algebra systems, etc.

DEMO 2
Proposer: Simon Hampe, simon.hampe@googlemail.com
Title: Polymake 3.0

Abstract:
Description: We showcase the new and improved features of the recent polymake release 3.0, such as polytopes over the Puiseux fractions, Johnson solids, planar nets, the completely refactored application tropical, functions for computing with transversal matroids and many more.

DEMO 3 (also accepted as tutorial and poster)
Proposer: Abbott John, abbott@dima.unige.it and Anna Maria Bigatti (contact person), bigatti@dima.unige.it
Title: CoCoALib and CoCoA-5

Abstract:
CoCoA-5 is a Computer Algebra System for Computations in Commutative Algebra, and specifically for Gröbner bases. It offers a dedicated mathematician-friendly programming language and functions in many aspects of Commutative Algebra.
It is free and open source (C++) and its mathematical core, called CoCoALib, has been designed to be used as a user-friendly C++ library, in order to facilitate integration with other software. Moreover, other software libraries can be integrated with CoCoALib, and be made accessible via the interactive CoCoA-5 system.
After a brief overview of the library and interactive system, we illustrate the latest developments.

Short description:
We will show some samples of drawings in TeX documents generated with KeTCindy, which is a plug-in to excellent dynamic geometry software Cinderella. It enables us to easily synchronize the interactive operation to mathematical artwork on Cinderella and high-quality graphical output in TeX documents.
Efficient linkage to some symbolic computation software has also been established.
Remark:
I would like to apply for software demo at the ICMS 2016. I have a presentation on Tuesday, July 12 in the session 13. Because of its preparation, I cannot do my demo on Tuesday, July 12. So please set the time of my demo on Wednesday, July 13.

20. Posters
Organizers:
Gert-Martin Greuel, greuel@mathematik.uni-kl.de
Peter Paule, Peter.Paule@risc.uni-linz.ac.at
Andrew Sommese, sommese@nd.edu