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IMA Annual Program Year Workshop

Software for Algebraic Geometry

October 23-27, 2006
Organizers:
Michael E. Stillman Mathematics, Cornell University
Nobuki Takayama Mathematics, Kobe University
Jan Verschelde Mathematics, Statistics & Computer Science, University of Illinois - Chicago

Schedule Participants Program Application Feedback
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Abstracts and Talk Materials Dining Guide
Software Project Links
Photo Gallery Challenge Problems

Description:

Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms.

Surrounding the general packages, a host of specialized packages for dedicated and focused computations have created a platform for the interaction of algebraic geometry with numerous other areas of mathematics including optimization, combinatorics, polyhedral geometry, numerical analysis and computer science. We hope to bring together a wide array of theoreticians and practitioners interested in the development of algorithms and software in algebraic geometry at this workshop. Such interactions are essential for dramatic increases in the power and applicability of algorithms in the field.

Schedule
Monday, October 23
8:30a-9:15a Registration and coffee   EE/CS 3-176
9:15a-9:30a Welcome to IMA Douglas N. Arnold (University of Minnesota Twin Cities) EE/CS 3-180
9:30a-10:20a Macaulay 2, a software system for algebraic geometry Daniel R. Grayson (University of Illinois at Urbana-Champaign) EE/CS 3-180
10:20a-10:50a Coffee   EE/CS 3-176
10:50a-11:40a SAGE — software for algebra and geometry experimentation William Stein (University of Washington) EE/CS 3-180
11:40a-1:40p Lunch    
1:40p-2:30p What should a software package for numerical algebraic geometry be? Charles W. Wampler (General Motors Corporation) EE/CS 3-180
2:30p-3:00p Coffee   EE/CS 3-176
3:00p-3:50p APAtools: A Maple/Matlab toolbox for approximate polynomial algebra Zhonggang Zeng (Northeastern Illinois University) EE/CS 3-180
4:00p-6:00p Software installation/poster session/reception
Lind Hall 400
PHClab: A MATLAB/Octave interface to PHCpack Yun Guan (University of Illinois)
Jan Verschelde (University of Illinois)
KNOPPIX/Math Tatsuyoshi Hamada (Fukuoka University)
D-modules for Macaulay2 Anton Leykin (University of Minnesota Twin Cities)
PHCmaple Anton Leykin (University of Minnesota Twin Cities)
Computer Algebra System Singular 3-0 Hans Schöenemann (Universität Kaiserslautern)
Approximate Groebner bases - a backwards approach Robin Scott (University of Western Ontario)
Some useful functions in Risa/Asir Nobuki Takayama (Kobe University)
Parallel implementation of the polyhedral homotopy method Jan Verschelde (University of Illinois)
Yan Zhuang (University of Illinois)
The package CRACK for solving large overdetermined systems Thomas Wolf (Brock University)
Symbolic and numerical methods for partial differential equations Wenyuan Wu (University of Western Ontario)
Tuesday, October 24
9:00a-9:30a Coffee   EE/CS 3-176
9:30a-10:20a Algebra & algorithms for differential elimination & completion Evelyne Hubert (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
10:20a-10:50a Coffee   EE/CS 3-176
10:50a-11:40a Towards a black-box solver for finite games: The Gambit system Theodore L. Turocy (Texas A & M University) EE/CS 3-180
11:40a-1:40p Lunch    
1:40p-2:30p PHCpack: a software platform for numerical algebraic geometry Jan Verschelde (University of Illinois) EE/CS 3-180
2:30p-3:00p Coffee   EE/CS 3-176
3:00p-3:50p On computing using FGb/RS software Fabrice Rouillier (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
4:00p-4:10p Group picture    
4:20p-6:00p Challenge problems   EE/CS 3-180
6:30p-8:30p Workshop dinner   Shuang Cheng Restaurant in Dinkytown, 1320 4th Street SE, 612-378-0208  
Wednesday, October 25
9:00a-9:30a Coffee   EE/CS 3-176
9:30a-10:20a CoCoALib, a C++ library for computations in commutative algebra Anna M. Bigatti (Università di Genova) EE/CS 3-180
10:20a-10:50a Coffee   EE/CS 3-176
10:50a-11:40a 4ti2 -- A software package for algebraic, geometric and combinatorial problems on linear spaces Raymond Hemmecke (Otto-von-Guericke-Universität Magdeburg) EE/CS 3-180
11:40a-1:40p Lunch    
1:40p-2:30p Parallel implementation of the polyhedral homotopy method for polynomial systems Masakazu Kojima (Tokyo Institute of Technology) EE/CS 3-180
2:30p-3:00p Coffee   EE/CS 3-176
3:00p-3:50p SYNAPS, a library for symbolic-numeric computation Bernard Mourrain (Institut National de Recherche en Informatique Automatique (INRIA)) EE/CS 3-180
4:00p-7:00p Tutorial/demonstration session
Lind Hall 400
PHClab Yun Guan (University of Illinois)
KNOPPIX/Math Tatsuyoshi Hamada (Fukuoka University)
DEMiCs, software for dynamic enumeration of all mixed cells Akiko Takeda (Tokyo Institute of Technology)
The Gambit system for computing in finite games Theodore L. Turocy (Texas A & M University)
Algorithms for algebraic geometry in Magma John Voight (University of Minnesota Twin Cities)
Thursday, October 26
9:00a-9:30a Coffee   EE/CS 3-176
9:30a-10:20a D-modules for Macaulay 2 Anton Leykin (University of Illinois) EE/CS 3-180
10:20a-10:50a Coffee   EE/CS 3-176
10:50a-11:40a New recombination techniques for polynomial factorization algorithms based on Hensel lifting Grégoire Lecerf (Université Versailles/Saint Quentin-en-Yvelines) EE/CS 3-180
11:40a-1:40p Lunch    
1:40p-2:30p Sums of squares of polynomials and SOSTOOLS Pablo A. Parrilo (Massachusetts Institute of Technology) EE/CS 3-180
2:30p-3:00p Coffee   EE/CS 3-176
3:00p-3:50p Computing tropical varieties in Gfan Anders Nedergaard Jensen (Aarhus University) EE/CS 3-180
4:00p-7:00p Tutorial/demonstration session
Lind Hall 400
Computing tropical varieties in Gfan Anders Nedergaard Jensen (Aarhus University)
4ti2 – Computing with lattices, cones, and subspaces Peter Nicholas Malkin (Université Catholique de Louvain)
Software for partial differential equations Gregory J. Reid (University of Western Ontario)
SINGULAR – a tool for algebraic geometry Hans Schöenemann (Universität Kaiserslautern)
Demonstration of HomLab Charles W. Wampler (General Motors Corporation)
Solving large overdetermined systems with CRACK Thomas Wolf (Brock University)
Friday, October 27
9:00a-9:30a Coffee   EE/CS 3-176
9:30a-10:20a Gauss-Manin systems for isolated singularities in singular Mathias Schulze (Oklahoma State University) EE/CS 3-180
10:20a-10:50a Coffee   EE/CS 3-176
10:50a-11:40a Application of numerical algebraic geometry to partial differential equations Gregory J. Reid (University of Western Ontario) EE/CS 3-180
11:40a-1:40p Lunch    
1:40p-2:30p Introduction to Bertini: a software package for numerical algebraic geometry Daniel J. Bates (University of Notre Dame) EE/CS 3-180
2:30p-3:00p Coffee   EE/CS 3-176
3:00p-3:50p Maple 11 preview Jürgen Gerhard (Maplesoft) EE/CS 3-180
4:00p-5:20p Answers to challenges   EE/CS 3-180
5:20p-5:30p Closing discussion   EE/CS 3-180

LIST OF CONFIRMED PARTICIPANTS

Name Department Affiliation
Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota Twin Cities
Donald G. Aronson Institute for Mathematics and its Applications University of Minnesota Twin Cities
Daniel J. Bates Institute for Mathematics and its Applications University of Minnesota Twin Cities
Gian Mario Besana Department of Computer Science-Telecommunications DePaul University
Anna M. Bigatti Dipartimento di Matematica Università di Genova
Rachelle Bouchat Department of Mathematics University of Kentucky
Massimo Caboara Dipartimento di Matematica Università di Genova
Ionut Ciocan-Fontanine Institute for Mathematics and its Applications University of Minnesota Twin Cities
Barry H. Dayton Department of Mathematics Northeastern Illinois University
Wolfram Decker Fachrichtung Mathematik Universität des Saarlandes
Alicia Dickenstein Departamento de Matematica - FCEyN University of Buenos Aires
Kenneth R. Driessel Department of Mathematics Iowa State University
Makan Fardad Department of Electrical and Computer Engineering University of Minnesota Twin Cities
Xuhong Gao Department of Mathematical Sciences Clemson University
Jürgen Gerhard Department of Research and Development Maplesoft
Jason E. Gower Institute for Mathematics and its Applications University of Minnesota Twin Cities
Daniel R. Grayson Department of Mathematics University of Illinois at Urbana-Champaign
Genhua Guan Department of Mathematics Clemson University
Yun Guan Department of Mathematics, Statistics & Computer Science University of Illinois
Tatsuyoshi Hamada Department of Applied Mathematics Fukuoka University
Marshall Hampton Department of Mathematics and Statistics University of Minnesota
Gloria Haro Ortega Institute for Mathematics and its Applications University of Minnesota Twin Cities
Jonathan Hauenstein Department of Mathematics University of Notre Dame
Raymond Hemmecke   Otto-von-Guericke-Universität Magdeburg
Milena Hering Institute for Mathematics and its Applications University of Minnesota Twin Cities
Benjamin J. Howard Institute for Mathematics and its Applications University of Minnesota Twin Cities
Evelyne Hubert Project CAFE Institut National de Recherche en Informatique Automatique (INRIA)
Farhad Jafari Department of Mathematics University of Wyoming
Abdul Salam Jarrah Virginia Bioinformatics Institute Virginia Polytechnic Institute and State University
Anders Nedergaard Jensen Institut for Matematiske Fag Aarhus University
Gabriela Jeronimo Departamento de Matematica - FCEyN University of Buenos Aires
Masakazu Kojima Department of Mathematical and Computing Sciences Tokyo Institute of Technology
Song-Hwa Kwon Institute for Mathematics and its Applications University of Minnesota Twin Cities
Niels Lauritzen Institut for Matematiske Fag Aarhus University
Grégoire Lecerf Laboratoire de Mathematiques Université Versailles/Saint Quentin-en-Yvelines
Anton Leykin Institute for Mathematics and its Applications University of Minnesota Twin Cities
Hstau Y Liao Institute for Mathematics and its Applications University of Minnesota Twin Cities
Gennady Lyubeznik School of Mathematics University of Minnesota Twin Cities
Diane Maclagan Department of Mathematics Rutgers University
Peter Nicholas Malkin CORE, Centre for Operations Research and Econometrics Université Catholique de Louvain
Hannah Markwig Institute for Mathematics and its Applications University of Minnesota Twin Cities
Thomas Markwig Department of Mathematics Universität Kaiserslautern
Andrew A. McLennan Department of Economics University of Minnesota Twin Cities
Richard B. Moeckel School of Mathematics University of Minnesota Twin Cities
Bernard Mourrain Project GALAAD Institut National de Recherche en Informatique Automatique (INRIA)
Uwe Nagel Department of Mathematics University of Kentucky
Jiawang Nie Institute of Mathematics and its Applications University of Minnesota Twin Cities
Michael E. O'Sullivan Department of Mathematics and Statistics San Diego State University
Rohit Pandita Department of Aerospace Engineering and Mechanics University of Minnesota Twin Cities
Antonis Papachristodoulou Engineering Science University of Oxford
Pablo A. Parrilo Laboratory for Information and Decision Systems Massachusetts Institute of Technology
Chris Peterson Department of Mathematics Colorado State University
Sonja Petrovic Department of Mathematics University of Kentucky
Kathy Wei Piret Department of Mathematics, Statistics and Computer Science University of Illinois
Sorin Popescu Department of Mathematics SUNY
Jacob Quant   University of Minnesota Twin Cities
Gregory J. Reid Department of Applied Mathematics University of Western Ontario
Victor Reiner School of Mathematics University of Minnesota Twin Cities
Joel Roberts School of Mathematics University of Minnesota Twin Cities
Fabrice Rouillier Projet SALSA Institut National de Recherche en Informatique Automatique (INRIA)
Bjarke Hammersholt Roune Department of Mathematics Aarhus University
David Rusin Department of Mathematical Sciences Northern Illinois University
Arnd Scheel Institute for Mathematics and its Applications University of Minnesota Twin Cities
Hans Schöenemann Department of Mathematics Universität Kaiserslautern
Eric Schost LIX École Polytechnique
Mathias Schulze Department of Mathematics Oklahoma State University
Robin Scott Department of Applied Mathematics University of Western Ontario
Chehrzad Shakiban Institute of Mathematics and its Applications University of Minnesota Twin Cities
Donald H. Singley   3M
Andrew Sommese Department of Mathematics University of Notre Dame
Steven Sperber School of Mathematics University of Minnesota Twin Cities
Dumitru Stamate School of Mathematics University of Minnesota Twin Cities
William Stein Department of Mathematics University of Washington
Brandilyn Stigler   Mathematical Biosciences Institute
Michael E. Stillman Department of Mathematics Cornell University
Erik Stokes   University of Kentucky
Nobuki Takayama Department of Mathematics Kobe University
Akiko Takeda Department of Mathematical and Computing Sciences Tokyo Institute of Technology
Amelia Taylor   Colorado College
Enrique Augusto Tobis Computer Science and Mathematics University of Buenos Aires
Carl Toews Institute for Mathematics and its Applications University of Minnesota Twin Cities
Elias P. Tsigaridas projet VEGAS Institut National de Recherche en Informatique Automatique (INRIA)
Theodore L. Turocy Department of Economics Texas A & M University
Balint Vanek Department of Aerospace Engineering and Mechanics University of Minnesota Twin Cities
Jan Verschelde Department of Mathematics, Statistics and Computer Science University of Illinois
John Voight Institute for Mathematics and its Applications University of Minnesota Twin Cities
Charles W. Wampler General Motors Research Lab General Motors Corporation
Stephen M. Watt Department of Computer Science University of Western Ontario
Thomas Wolf Department of Mathematics Brock University
Wenyuan Wu Department of Applied Mathematics University of Western Ontario
Zhonggang Zeng Department of Mathematics Northeastern Illinois University
Ailing Zhao Department of Mathematics, Statistics and Computer Science University of Illinois
Ke Zhou Electrical and Computer Engineering Department University of Minnesota Twin Cities
Yan Zhuang Department of Mathematics, Statistics and Computer Science University of Illinois

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