Organizing Committee
Abstract

Over the past 25 years, experimental mathematics has developed as an important additional arrow in the mathematical quiver. Many mathematical scientists now use powerful symbolic, numeric and graphic (sometimes abbreviated "SNAG") computing environments in their research, in a remarkable departure from tradition. While these tools collectively are quite effective, challenges remain in numerous areas, including: (a) rapid, high-precision computation of special functions and their derivatives; (b) user-customizable symbolic computing; (c) graphical computing; (d) data-intensive computing; and (e) large-scale computing on parallel and GPU architectures (including algorithm and software design for such systems).

This workshop will convene mathematical and computer scientists who create or exploit these tools, together with computational tool developers and commercial vendors of mathematical software, to exchange approaches and extend the state of the art in the field, both in the design of software and in the usage of this software for serious mathematical research.

Image for "Challenges in 21st Century Experimental Mathematical Computation"
Image Credit: D. Bailey and J. Borwein

Workshop Organizers Report

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, July 21, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:00am EDTExperimental Computation and Visual Theorems - Jonathan Borwein, CARMA, University of Newcastle11th Floor Lecture Hall
10:00 - 10:15am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:15 - 10:50am EDTSome Experimentation in Counting Questions - Neil Calkin, Clemson University11th Floor Lecture Hall
11:00 - 11:40am EDTThe numerical reproducibility fair trade: Facing concurrency challenges at extreme scale - Michela Taufer, University of Delaware11th Floor Lecture Hall
11:50 - 12:30pm EDTReliable computing in geometry processing and CAGD - Konrad Polthier, Freie Universität Berlin11th Floor Lecture Hall
12:30 - 1:45pm EDTBreak for Lunch  
1:45 - 2:25pm EDTComputational challenges for experimental mathematics - David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall
2:35 - 3:15pm EDTReliable numerical evaluation of special functions- algorithms and experiments - Bruno Salvy, INRIA11th Floor Lecture Hall
3:15 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:15pm EDTOutgrowths of the Digital Library of Mathematical Functions Project - Howard Cohl and Daniel Lozier, National Institute of Standards and Technology11th Floor Lecture Hall
4:15 - 5:00pm EDTTBA - TBA  
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, July 22, 2014
TimeEventLocationMaterials
8:55 - 9:00am EDTIntro to numerical computing for experimental math - David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall 
9:00 - 9:40am EDTNumerical reproducibility of high-performance computations using floating-point or interval arithmetic - Nathalie Revol, INRIA11th Floor Lecture Hall
9:50 - 10:30am EDTNonlinear Preconditioning for the Parallel Solution of Systems Algebraic Equations - Matt Knepley, University of Chicago11th Floor Lecture Hall
10:30 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:25am EDTBugs- Black Ice on the Road to Exascale - Ganesh Gopalakrishnan and Alexey Solovyev, University of Utah11th Floor Lecture Hall
11:35 - 12:15pm EDTVery Special Functions: Numerical Explorations of Random Matrix Distributions - Folkmar Bornemann, TU München11th Floor Lecture Hall
12:15 - 1:45pm EDTBreak for Lunch  
1:45 - 2:25pm EDTApery numbers and their experimental siblings - Armin Straub, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
2:35 - 3:15pm EDTToward HPC Runtimes that Self-adapt to your Math - Dorian Arnold, University of New Mexico11th Floor Lecture Hall
3:15 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:10pm EDTLarge-scale, data-intensive physics computing - Amber Boehnlein, Stanford University11th Floor Lecture Hall
4:20 - 5:00pm EDTComputational and analytics challenges in biology - Silvia Crivelli, University of California, Davis11th Floor Lecture Hall
Wednesday, July 23, 2014
TimeEventLocationMaterials
8:55 - 9:00am EDTIntro to symbolic computing for experimental math - Bruno Salvy, INRIA11th Floor Lecture Hall 
9:00 - 9:40am EDTApproximating the Fisher Information for a Partially-Observable Growing Population - Ali Eshragh, CARMA, University of Newcastle11th Floor Lecture Hall
9:50 - 10:30am EDTMathematical practice, crowdsourcing, and social machines - Ursula Martin, University of Oxford11th Floor Lecture Hall
10:30 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:25am EDTCongruences and relations for the Fishburn numbers - Frank Garvan, University of Florida11th Floor Lecture Hall
11:30 - 12:15pm EDTMoments of zeta functions associated to hyper-elliptic curves over finite fields - Michael Rubinstein, University of Waterloo11th Floor Lecture Hall
12:15 - 12:25pm EDTGroup Photo11th Floor Lecture Hall 
12:25 - 1:45pm EDTBreak for Lunch  
1:45 - 2:25pm EDTEfficient Experimental Mathematics for Lattice Path Combinatorics - Alin Bostan, SpecFun, INRIA Saclay11th Floor Lecture Hall
2:35 - 3:15pm EDTSymbolic local Fourier analysis - Veronika Pillwein, Johannes Kepler Universität Linz11th Floor Lecture Hall
3:15 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:10pm EDTVisualizing Projection Algorithms with Application to Protein Reconstruction - Matthew K. Tam, University of Newcastle11th Floor Lecture Hall
4:20 - 5:00pm EDTOperator Orderings: from sequences to polynomials - Christophe Vignat, Tulane University11th Floor Lecture Hall
7:00 - 8:30pm EDTPoster Session and Dessert Reception11th Floor Lecture Hall 
Thursday, July 24, 2014
TimeEventLocationMaterials
8:55 - 9:00am EDTIntro to connections between symbolic and numerical math - Ursula Martin, University of Oxford11th Floor Lecture Hall 
9:00 - 9:40am EDTSparse factorizations- Towards optimal complexity and resilience at exascale - Xiaoye S. Li, Lawrence Berkeley National Laboratory11th Floor Lecture Hall
9:50 - 10:30am EDTComputational challenges arising from the theory of Orthogonal Polynomials - Diego Dominici, SUNY at New Paltz11th Floor Lecture Hall
10:30 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:25am EDTParallel Paradigms for Experimental Mathematics - Elise DeDoncker, Western Michigan University11th Floor Lecture Hall
11:35 - 12:15pm EDTChallenges and Successes in Coastal Ocean Modeling - Clint Dawson, University of Texas at Austin11th Floor Lecture Hall
12:15 - 1:45pm EDTBreak for Lunch  
1:45 - 2:25pm EDTEquality of Dedekind sums: experimental data, and theory - Sinai Robins, Nanyang Technological University and ICERM11th Floor Lecture Hall
2:35 - 3:15pm EDTPolynomials, number theory, and experimental mathematics - Michael Mossinghoff, Davidson College and ICERM11th Floor Lecture Hall
3:15 - 3:30pm EDTPlease take a moment to complete the survey that was distributed by email.  
3:30 - 3:45pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:30pm EDTTBA - TBA  
4:30 - 5:00pm EDTDiscussion: What have we learned; organize groups - David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis or Jonathan Borwein, CARMA, University of Newcastle11th Floor Lecture Hall 
Friday, July 25, 2014
TimeEventLocationMaterials
9:00 - 10:15am EDTGroup meetings - All  
10:15 - 10:30am EDTCoffee/Tea Break11th Floor Lecture Hall 
10:30 - 11:00am EDTReport from Group #1 - Group #1 leader11th Floor Lecture Hall 
11:00 - 11:30am EDTReport from Group #2 - Group #2 leader11th Floor Lecture Hall 
11:30 - 12:00pm EDTReport from Group #3 - Group #3 leader11th Floor Lecture Hall 
12:00 - 12:30pm EDTConstruct outline for report - All; led by David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall 
12:30 - 2:00pm EDTBreak for Lunch  
2:00 - 3:15pm EDTDraft workshop report - Group leaders and organizers  
3:15 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:00pm EDTDraft workshop report - Group leaders and organizers  

Lecture Videos

Polynomials, number theory, and experimental mathematics

Michael Mossinghoff
Davidson College
July 24, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Equality of Dedekind sums: experimental data, and theory

Sinai Robins
ICERM
July 24, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Challenges and Successes in Coastal Ocean Modeling

Clint Dawson
University of Texas at Austin
July 24, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Sparse factorizations- Towards optimal complexity and resilience at exascale

Xiaoye Li
Lawrence Berkeley National Laboratory
July 24, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Operator Orderings: from sequences to polynomials

christophe vignat
tulane university
July 23, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract

Visualizing Projection Algorithms with Application to Protein Reconstruction

Matthew Tam
University of Newcastle
July 23, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Symbolic local Fourier analysis

Veronika Pillwein
Johannes Kepler Universität Linz
July 23, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Efficient Experimental Mathematics for Lattice Path Combinatorics

Alin Bostan
INRIA
July 23, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Congruences and relations for the Fishburn numbers

Frank Garvan
University of Florida
July 23, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Approximating the Fisher Information for a Partially-Observable Growing Population

Ali Eshragh
University of Newcastle
July 23, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Large-scale, data-intensive physics computing

Amber Boehnlein
Stanford University
July 22, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract

Toward HPC Runtimes that Self-adapt to your Math

Dorian Arnold
University of New Mexico
July 22, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract

Apery numbers and their experimental siblings

Armin Straub
University of Illinois at Urbana-Champaign
July 22, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Very Special Functions: Numerical Explorations of Random Matrix Distributions

Folkmar Bornemann
TU München
July 22, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Nonlinear Preconditioning for the Parallel Solution of Systems Algebraic Equations

Matt Knepley
Rice University
July 22, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Numerical reproducibility of high-performance computations using floating-point or interval arithmetic

Nathalie Revol
INRIA
July 22, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Outgrowths of the Digital Library of Mathematical Functions Project

Dan Lozier
National Institute of Standards and Technology
Howard Cohl
National Institute of Standards and Technology
July 21, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Reliable numerical evaluation of special functions- algorithms and experiments

Bruno Salvy
INRIA
July 21, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Computational challenges for experimental mathematics

David Bailey
Lawrence Berkeley National Laboratory
July 21, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

The numerical reproducibility fair trade: Facing concurrency challenges at extreme scale

Michela Taufer
University of Delaware
July 21, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides

Experimental Computation and Visual Theorems

Jonathan Borwein
The University of Newcastle
July 21, 2014
Challenges in 21st Century Experimental Mathematical Computation
Play     Abstract     Slides