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IMA 2002 Summer Program
Special Functions in the Digital Age
July 22 - August 2, 2002


Organizers:
 

George Andrews Mathematics, Penn State University andrews@math.psu.edu
Richard Askey Mathematics, University of Wisconsin, Madison askey@math.wisc.edu
Carl de Boor  Computer Science, University of Wisconsin, Madison deboor@cs.wisc.edu
Arieh Iserles Applied Math & Theoretical Physics,University of Cambridge  A.Iserles@damtp.cam.ac.uk
Daniel W. Lozier Mathematics & Computational Sciences, National Institute of Standards and Technology lozier@nist.gov
Willard Miller  Mathematics, University of Minnesota miller@ima.umn.edu
Frank W.J. Olver Institute for Physical Science & Technology, University of
Maryland and Mathematics & Computational Sciences, National Institute of Standards and Technology
olver@ipst.umd.edu
Peter Olver  Mathematics, University of Minnesota olver@ima.umn.edu
Peter Paule Research Institute for Symbolic Computation, University of Linz  peter.paule@risc.uni-linz.ac.at

Introduction:

Mathematical tables and handbooks have played a pivotal role in applications and also the development of mathematics itself over the centuries.  Now, with the advent of the digital age, the traditional handbook format has become obsolete, and a complete rethinking of the nature and role of mathematical handbooks must be undertaken.  The purpose of this program is to formulate, though concrete examples and experiences, the role and character of digital libraries in mathematics, and the mathematical and applied fields that would benefit from such a library.  The first serious attempt to address these issues is the ongoing Digital Library of Mathematical Functions (DLMF) project at the National Institute of Standards and Technology (NIST).  This workshop will take the DLMF project as a basis for assessing both the state of the art in special function theory, what aspects are of importance in applications, particularly to chemistry and physics, and the experiences gained in this project to formulate recommendations for how digitial libraries of mathematics should be organized, utilized, and developed.  We also anticipate the experiences of the DLMF project to provide insight and recomendations for how mathematics should be stored and disseminated over the internet.

Of the currently used handbooks, the most well-developed have been those devoted to special functions and their applications.  The principal handbooks on special functions, "Higher Transcendental Functions" (the Bateman Project) and the NIST (formerly National Bureau of Standards) "Handbook of Mathematical Functions," are among the most useful, widely consulted technical volumes ever published, but they are now out of date, due to rapid research progress and revolutionary changes in technology.  (See http://www.siam.org/siamnews/03-98/function.htm for additional information.) Using these as concrete examples of a mathematical digital library, the program will assess recent progress in updating these handbooks and recent advances in the theory and use of special functions, and to point out the areas of research in special functions that hold the most promise and importance for future development, both for theorists and users.  In the broader arena, the workshop will aim to use the experience in this particular subject to generate recommendations for further digital library projects in the mathematical sciences and their applications, including, but not limited to, numerical analysis, group theory, signal processing, statistics, linear algebra, partial differential equations, and so on.

See an article by Peter Paule on the DLMF project.


Description:

The  IMA workshop will use the DLMF project as a foundation and discuss what more should be done, what areas are incomplete or unrepresented, what are the resulting mathematical, symbolic, numerical and web issues, applications in physics, chemistry, etc., relationships with the Bateman project, and potential for other digital libraries in other mathematical areas. The workshop is to have a very broad outlook, encompassing a wide range of subjects connected with special functions, as well as issues concerning digital libraries and the delivery of mathematics over the internet.

A major portion of this program (7 days) will be assessments of  research progress and promising vistas for future research by distinguished experts in the areas of a symptotics,  combinatorial functions, statistics, computer algebra, algebraic and group theoretic methods, applications to the physical sciences,  orthogonal polynomials, numerical methods, zeta functions   &  random matrices,  Painlevé functions, elliptic functions,  elliptic hypergeometric functions and the Heun function group, with the aim of pointing out what is of greatest importance in the theory and applications, and what should be included in digital library projects.

The remainder of the program (3 days) will be devoted to Digital Libraries generally and, specifically, Digital Libraries and the Mathematical Sciences, including the delivery of mathematics over the Internet. It will conclude with a panel  on  the "Future of Mathematical Digital Libraries," with panelists from the special functions research and users communities, as well as representatives from mathematics societies and government funding agencies.

There will be several discussion sessions to develop specific recommendations for special function topics to be included in future Digital Libraries in Mathematics.  Also there will be poster sessions, and several software demonstrations (particularly of computer algebra and numerical packages for special functions), and much of the software will be available during the program for informal use by participants. This program will link with special function related sessions at the Foundations of Computational Mathematics (FoCM'02) meeting that will be hosted by the IMA, August 5-15, 2002.

The program is meant for researchers in the theory and computation of special functions (definitely including people new to the field who are looking for the most promising areas for future research), for users of special functions, and for persons interested in the delivery of mathematics over the Internet.

WORKSHOP SCHEDULE
Week 1 July 22-26 Monday Tuesday
Week 2 July 29-August 2 Monday Tuesday
MONDAY, JULY 22
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:00 am Coffee and Registration

Reception Room EE/CS 3-176

8:50 am Douglas N. Arnold
IMA Director
Welcome and Introduction
Theme: Assessment of DLMF
9:00 am Richard Askey
University of Wisconsin
Introduction: The Role of Handbooks of Special Functions
9:15 am Dan Lozier
National Institute of Standards and Technology

Development of a New Handbook and Web Site of Properties of Special Functions

Slides:   html    pdf    powerpoint

10:05 am
Discussion
10:15 am Coffee Break Reception Room EE/CS 3-176
10:45 am Ronald F. Boisvert
National Institute of Standards and Technology

Building the DLMF: Information Technology Issues

Slides:   html    pdf

11:35 am
Discussion
11:45 am
Lunch Break
Theme: Asymptotics
1:30 pm Frank W.J. Olver
National Institute of Standards and Technology

Error Bounds; Hyperasymptotics; Uniform Asymptotics

Slides

2:20 pm
Discussion
2:30 pm Coffee Break Reception Room EE/CS 3-176
3:00 pm Michael Berry
University of Bristol

Architecture of diffraction catastrophes

Slides:    pdf    ppt

3:50 pm
Discussion
4:00 pm IMA Tea/Reception
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
TUESDAY, JULY 23
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Combinatorial Functions
9:00 am Dennis Stanton
University of Minnesota

Exponential formulas

Slides

9:50 am
Discussion
10:00 am Coffee Break Reception Room EE/CS 3-176
10:30 am David M. Bressoud
Macalester College

Where does Combinatorial Analysis fit in?

Slides:   pdf    ps

11:20 am
Discussion
11:30 am
Lunch Break
1:30 pm Alexander Berkovich
University of Florida
Partitions with gap conditions: some old and new results
2:20 pm
Discussion
2:30 pm Coffee Break Reception Room EE/CS 3-176
Theme: Group Theoretic Methods
3:00 pm Willard Miller
University of Minnesota

The Lie Theory approach to special functions

Expanded version:   pdf      ps

3:50 pm
Discussion
4:00 pm

Panel Discussion

Participants have the opportunity to pose to Stanton, Bressoud, Berkovich, and Miller any questions or suggestions that may have arisen from their talks or that circle of ideas.

WEDNESDAY, JULY 24
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Computer Algebra: Identity Verification, Summation Methods, Special Packages
9:00 am George E. Andrews
Pennsylvania State University
What is needed in Computer Algebra Packages for Mathematical Research!
9:50 am
Discussion
10:00 am Peter Paule
University of Linz

Symbolic Summation: Algorithms and Missed Opportunities

Slides

10:50 am
Discussion
11:00 am Coffee Break Reception Room EE/CS 3-176
11:30 am Doron Zeilberger
Rutgers University
The General Future of Special Functions
12:20 pm
Discussion
12:30 pm
Lunch Break
2:00 pm Otmar Scherzer
University of Innsbruck
Case examples of Special Functions in Analysis and Numerics
2:50 pm Discussion
3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm Frédéric Chyzak
INRIA

Mgfun, a Maple Package for Symbolic Summation and Integration of Special Functions and Combinatorial Sequences

Slides: minneapolis02.pdf    minneapolis02.ps    sfda.pdf    sfda.ps

4:00 pm Christian Krattenthaler
Universitat Wien

HYP and HYPQ

Matematica Slides:   hyp.nb   hyp1.nb   hypq.nb
Pdf Slides:   hyp.pdf   hyp1.pdf   hypq.pdf

4:30 pm Axel Riese
J. Kepler University, Linz
Computer Proofs of Hypergeometric Summation Identities and Partition Analysis
5:00 pm
Panel Discussion
THURSDAY, JULY 25
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Algebraic Methods: Lie Groups, Quantum Groups, Quasi-exactly Solvable Methods
9:00 am Arieh Iserles
University of Cambridge
Lie group methods for highly oscillatory differential equations
9:50 am
Discussion
10:00 am Tom H. Koornwinder
Universiteit van Amsterdam

Algebraic methods: Lie groups, quantum groups

Expanded version:   pdf    ps

10:50 am
Discussion
11:00 am Coffee Break Reception Room EE/CS 3-176
11:30 am Alexander Turbiner
National University of Mexico

Algebraic Approaches: Quasi-Exactly-Solvable Problems (Lie-algebraic theory of polynomial solutions of differential and finite-difference linear equations)    abstract.pdf    abstract.ps

Slides:   pdf    ps

12:20 pm
Discussion
12:30 pm
Lunch Break
Theme: Applications in the Physical Sciences: Quantum Mechanics, Completely Integrable Systems
2:00 pm Alexander Its
Indiana University- Purdue University Indianapolis
Integrable Systems and Integrability
2:50 pm
Discussion
3:00 pm Coffee Break Reception Room EE/CS 3-176
3:30 pm Pavel Bleher
Indiana University- Purdue University Indianapolis
Double scaling limits in random matrix models and orthogonal polynomials: Riemann-Hilbert approach
4:20 pm
Panel Discussion
6:00 pm Workshop Dinner Bangkok Thai Restaurant
425 13th Ave. SE
Minneapolis, MN
FRIDAY, JULY 26
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30am Coffee Reception Room EE/CS 3-176
Theme: Orthogonal Polynomials
9:00 am Richard Askey
University of Wisconsin

Orthogonal Polynomials in One Variable

Slides

9:50 am
Discussion
10:00 am Coffee Break Reception Room EE/CS 3-176
10:30 am Charles F. Dunkl
University of Virginia

Orthogonal Polynomials on the Sphere

Paper form of the Slides:   pdf    ps

11:20 am
Discussion
Theme: Statistics
1:30 pm Donald Richards
University of Virginia
Computers and special functions in multivariate statistical analysis
2:20 pm
Discussion
2:30 pm Coffee Break Reception Room EE/CS 3-176
3:00 pm Ingram Olkin
Stanford University
Interface Between Statistics and Special Functions
3:50 pm
Discussion
4:00 pm
Panel Discussion
MONDAY, JULY 29
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Numerical Methods: Orthogonal Polynomials
9:00 am Walter Gautschi
Purdue University

Orthogonal Polynomials (in Matlab)

Slides

9:50 am
Discussion
10:00 am Coffee Break Reception Room EE/CS 3-176
Theme: Numerical Methods: General Special Functions, Software
10:30 am Nico M. Temme
CWI

Numerics of Special Functions

Slides:  pdf

11:20 am
Discussion
11:30 pm
Lunch Break
1:30 pm Oleg Marichev
Wolfram Research, Inc.

www.functions.wolfram.com - The web's most comprehensive site about special functions

2:00 pm Edgardo S. Cheb-Terrab
Simon Fraser University
Special functions & Maple 
2:30 pm Coffee Break Reception Room EE/CS 3-176
3:00 pm Cleve Moler
The MathWorks Inc.
The MathWorks Inc. Special Functions in MATLAB What do we have and what are we missing?
3:30 pm
Panel Discussion
7:00 pm
Informal Software Presentations, 400 Lind Hall
Simultaneous presentations by
F. Chyzak Mgfun
T. Koornwinder contiguous2f1 (R. Vidunas)
C. Krattenthaler HYP & qHYP
O. Marichev Mathematica
C. Regensburger wavelets
A. Riese q-Multisum +(q-)Zeil + Omega
C. Schneider Sigma
A. Sills q-tools
TUESDAY, JULY 30
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Zeta Functions & Random Matrices
9:00 am Andrew M. Odlyzko
University of Minnesota

Zeta Functions

9:50 am
Discussion
10:00 am Coffee Break Reception Room EE/CS 3-176
10:30 am Peter A. Clarkson
University of Kent at Canterbury

The Painleve equations - nonlinear special functions

Expanded version of the talk and figures:   SF02L.pdf   SF02L.ps   plots.pdf   plots.ps

11:20 am
Discussion
11:30 pm
Lunch Break
Theme: Elliptic Functions
1:30 pm Peter L. Walker
American University of Sharjah
The elliptic functions of Jacobi and Weierstrass
2:20 pm
Discussion
2:30 pm William P. Reinhardt
University of Washington
New and old addition theorems and Landen identities for Jacobian elliptic functions: do these indeed give rise to "novel" solutions for non-linear PDEs?
3:20 pm
Discussion
3:30 pm Coffee Break Reception Room EE/CS 3-176
4:00 pm Vyacheslav P. Spiridonov
Joint Institute for Nuclear Research, Russia

Elliptic Hypergeometric Functions

Slides

4:50 pm
Discussion
5:00 pm
Panel Discussion
WEDNESDAY, JULY 31
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Mathieu, Lamé, and Spheroidal Wave Functions
9:00 am Hans W. Volkmer
University of Wisconsin

Mathieu, Lamé, and Spheroidal Wave Functions   pdf    ps

Slides

9:50 am
Discussion
10:00 am Coffee Break Reception Room EE/CS 3-176
Theme: Digital Library Infrastructure for Mathematical DL's: Display and Manipulation, Meta Data, Searching
10:30 am Andrew M. Odlyzko
University of Minnesota

The new (and of necessity digital) libraries for mathematics

Slides:    pdf    ps

11:20 am
Discussion
11:30 pm
Lunch Break
1:30 pm Abdou Youssef
The George Washington University
Search Systems for Mathematical Equations    pdf    ps
2:20 pm
Discussion
2:30 pm Coffee Break Reception Room EE/CS 3-176
3:00 pm Patrick Ion
Math Reviews
Mathematics on the Web
3:50 pm
Discussion
4:00 pm
Panel Discussion
THURSDAY, AUGUST 1
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: Digital Library Infrastructure for Mathematical DL's: Display and Manipulation, Meta Data, Searching (continued)
9:00 am Bruce R. Miller
NIST

Representation, display and manipulation of mathematics on the Web    pdf    ps

Slides:   pdf

9:50 am
Discussion
10:00 am Coffee Break Reception Room EE/CS 3-176
10:30 am Bonita V. Saunders
National Institute of Standards and Technology
Interactive 3D Visualizations of High Level Functions in a Mathematical Digital Library
11:20 am
Discussion
11:30 pm
Lunch Break
Theme: Theorema
1:30 pm Bruno Buchberger
Johannes Kepler University

Theorema and Mathematical Knowledge Management

Slides:    pdf    ps

2:20 pm
Discussion
2:30 pm Coffee Break Reception Room EE/CS 3-176
3:00 pm Carsten Schneider
University of Linz

Sigma: A Summation Package for Discovering and Proving

Slides:    pdf    ps

3:30 pm
Panel Discussion
6:00 pm Workshop Dinner Mangia Restaurant
1501 University Ave. in Dinkytown Dome
FRIDAY, AUGUST 2
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30 am Coffee Reception Room EE/CS 3-176
Theme: What is Needed?
9:00 am Richard Askey
University of Wisconsin

Assessment of DLMF (Digital Library of Mathematical Functions)

Slides

9:30 am
Discussion
9:40 am Mourad Ismail
University of South Florida

Continued Fractions and Biorthogonal Functions

Slides

10:30 am
Discussion
10:40 am Coffee Break Reception Room EE/CS 3-176
11:10 am Dennis Stanton
University of Minnesota

Comments on Combinatorics and Special Functions

Slides

11:40 am
Discussion
11:50 am

Dan Lozier
NIST

Peter A. Clarkson
University of Kent

What can the SIAM OPSF Activity Group do for you?
12:00 pm
Discussion
12:10 pm
Lunch Break
Theme: Panel on Future of Mathematical Digital Libraries: Funding, Maintenance, Copyright, Publication
2:00 pm

Panel Discussion
Patrick Ion, Math Reviews
Arieh Iserles, University of Cambridge
Peter Paule, University of Linz
Peter Olver, University of Minnesota

3:30 pm Coffee Break Reception Room EE/CS 3-176
4:00 pm
Panel Discussion
Week 1 July 22-26 Monday Tuesday
Week 2 July 29-August 2 Monday Tuesday

LIST OF CONFIRMED PARTICIPANTS
(in addition to postdocs and long-term participants)

As of 8/5/2002
Name
Department Affiliation
George E. Andrews Mathematics Penn State
Richard A. Askey Mathematics University of Wisconsin-Madison
Alex Berkovich Mathematics University of Florida
Michael Berry Physics University of Bristol
Pavel Bleher Mathematics Indiana University Purdue University
Ronald F. Boisvert Mathematical and Computational Sciences NIST
David M. Bressoud Mathematics and Computer Science Macalester College
Bruno Buchberger Research Institute for Symbolic Computation Johannes Kepler University
Bille C. Carlson Mathematics and Ames Laboratory Iowa State University
Jamylle Carter   Institute for Mathematics & its Applications
Edgardo S. Cheb-Terrab Centre for Experimental & Construct. Mathematics Simon Fraser University
Christine Cheng Institute for Mathematics & its Applications University of Minnesota
Jacob Stordal Christiansen Mathematics University of Copenhagen
Frederic Chyzak   INRIA Rocquencourt
Charles W. Clark Electron and Optical Physics NIST
Peter A. Clarkson Institute of Mathematics and Statistics University of Kent at Canterbury
Charles Conley Mathematics University of North Texas
Steven Benjamin Damelin Mathematics Georgia Southern University
Carl de Boor Computer Science and Mathematics University of Wisconsin-Madison
Charles F. Dunkl Mathematics University of Virginia
Michael Efroimsky University of Minnesota Institute for Mathematics and its Applications
Kristina Garrett   Carleton College
Walter Gautschi Computer Science Purdue University
Amparo Gil Mathematics Universidad Autonoma de Madrid
John Hall Mathematics University of Minnesota
Hazem Hamdan Mathematics Unhiversity of Minnesota
Patrick Ion Associate Editor Math Reviews
Arieh Iserles Applied Mathematics and Theoretical Physics University of Cambridge
Mourad Ismail Mathematics University of South Florida
Alexander Its Science Indiana University-Purdue University Indianapolis
Sara Jane Johnston Mathematics University of the Witwatersrand
Tom Koornwinder Korteweg-de Vries Institute for Mathematics Universiteit van Amsterdam
Christian Krattenthaler Institut fur Mathematik Universitat Wien
Arno Kuijlaars Mathematics Katholieke Universiteit Leuven/ from CWI
James Licari Digital Technology Center University of Minnesota
Jose L. Lopez Mathematics and Informatics Public University of Navarra
Jeremy Lovejoy Mathematics University of Wisconsin, Madison
Daniel W. Lozier Mathematical and Computational Sciences NIST
Robert S. Maier Mathematics and Physics University of Arizona
Elizabeth L. Mansfield Institute of Mathmematics and Statistics University of Kent at Canterbury
Oleg Marichev Information Resources Wolfram Research Inc.
Bruce R. Miller National Institute of Standards and Technology NIST
Willard Miller Mathematics University of Minnesota
Robert Miner   Design Science, Inc.
Cleve Moler Chairman and Chief Scientist The MathWorks Inc.
Mahdi Nezafat Electrical and Computer Engineering University of Minnesota
Nilima Nigam Mathematics McGill University
Andrew Odlyzko Digital Technology Center University of Minnesota
Adri Olde Daalhuis Mathematics and Statistics Edinburgh University
Ingram Olkin Statistics Stanford University
Frank W. J. Olver Institute for Physical Science & Technology University of Maryland
Peter J. Olver Mathematics University of Minnesota
Jeong-Soo Park Statistics Chonnam National University/SRCCS
Peter Paule Institute for Symbolic Computation University of Linz
Georg Regensburger Institut für Informatik Universität Innsbruck
Vic Reiner Mathematics University of Minnesota
William P. Reinhardt Chemistry Box 351700 University of Washington
Donald Richards Statistics University of Virginia
David A. Richter Mathematics Southeast Missouri State University
Axel Riese Research Institute for Symbolic Computation J. Kepler University Linz
Bonita V. Saunders Mathematical and Computational Sciences NIST
Otmar Scherzer Applied Mathematics - Dept. of Computer Science University of Innsbruck
Michael Schlosser Mathematics University of Vienna
Carsten Schneider Research Institute for Symbolic Computation University of Linz
Javier Segura Mathematics Universidad Carlos III de Madrid
Ajay Kumar Shukla Mathematics / ASHD S.V. Regional College of Engineering & Technology
Andrew V. Sills Mathematics Penn State University
Vyacheslav P. Spiridonov Bogoliubov Laboratory of Theoretical Physics Joint Institute for Nuclear Research
Dennis Stanton Mathematics University of Minnesota
Nico M. Temme Analysis CWI
Paul Terwilliger Mathematics University of Wisconsin
Alexander Turbiner Instituto de Ciencias Nucleares National University of Mexico
Hans W. Volkmer Mathematical Sciences University of Wisconsin
Peter L. Walker    
S. Ole Warnaar Mathematics and Statistics The University of Melbourne
Jim Wilson Mathematics Iowa State University
Abdou Youssef Computer Science The George Washington University
Doron Zeilberger Mathematics Rutgers, The State University of New Jersey

Foundations of Computational Mathematics 2002 (FoCM'02) August 5-14, 2002    
2002-2003 Program: Optimization

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