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 Credit: D. Bailey and J. Borwein

Workshop Organizers Report

Confirmed Speakers & Participants

Workshop Schedule

Monday, July 21, 2014
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 10:00Experimental Computation and Visual Theorems - Jonathan Borwein, CARMA, University of Newcastle11th Floor Lecture Hall
10:00 - 10:15Coffee/Tea Break11th Floor Collaborative Space 
10:15 - 10:50Some Experimentation in Counting Questions - Neil Calkin, Clemson University11th Floor Lecture Hall
11:00 - 11:40The numerical reproducibility fair trade: Facing concurrency challenges at extreme scale - Michela Taufer, University of Delaware11th Floor Lecture Hall
11:50 - 12:30Reliable computing in geometry processing and CAGD - Konrad Polthier, Freie Universität Berlin11th Floor Lecture Hall
12:30 - 1:45Break for Lunch  
1:45 - 2:25Computational challenges for experimental mathematics - David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall
2:35 - 3:15Reliable numerical evaluation of special functions- algorithms and experiments - Bruno Salvy, INRIA11th Floor Lecture Hall
3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:15Outgrowths of the Digital Library of Mathematical Functions Project - Howard Cohl and Daniel Lozier, National Institute of Standards and Technology11th Floor Lecture Hall
4:15 - 5:00TBA - TBA  
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, July 22, 2014
TimeEventLocationMaterials
8:55 - 9:00Intro to numerical computing for experimental math - David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall 
9:00 - 9:40Numerical reproducibility of high-performance computations using floating-point or interval arithmetic - Nathalie Revol, INRIA11th Floor Lecture Hall
9:50 - 10:30Nonlinear Preconditioning for the Parallel Solution of Systems Algebraic Equations - Matt Knepley, University of Chicago11th Floor Lecture Hall
10:30 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:25Bugs- Black Ice on the Road to Exascale - Ganesh Gopalakrishnan and Alexey Solovyev, University of Utah11th Floor Lecture Hall
11:35 - 12:15Very Special Functions: Numerical Explorations of Random Matrix Distributions - Folkmar Bornemann, TU München11th Floor Lecture Hall
12:15 - 1:45Break for Lunch  
1:45 - 2:25Apery numbers and their experimental siblings - Armin Straub, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
2:35 - 3:15Toward HPC Runtimes that Self-adapt to your Math - Dorian Arnold, University of New Mexico11th Floor Lecture Hall
3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:10Large-scale, data-intensive physics computing - Amber Boehnlein, Stanford University11th Floor Lecture Hall
4:20 - 5:00Computational and analytics challenges in biology - Silvia Crivelli, University of California, Davis11th Floor Lecture Hall
Wednesday, July 23, 2014
TimeEventLocationMaterials
8:55 - 9:00Intro to symbolic computing for experimental math - Bruno Salvy, INRIA11th Floor Lecture Hall 
9:00 - 9:40Approximating the Fisher Information for a Partially-Observable Growing Population - Ali Eshragh, CARMA, University of Newcastle11th Floor Lecture Hall
9:50 - 10:30Mathematical practice, crowdsourcing, and social machines - Ursula Martin, University of Oxford11th Floor Lecture Hall
10:30 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:25Congruences and relations for the Fishburn numbers - Frank Garvan, University of Florida11th Floor Lecture Hall
11:30 - 12:15Moments of zeta functions associated to hyper-elliptic curves over finite fields - Michael Rubinstein, University of Waterloo11th Floor Lecture Hall
12:15 - 12:25Group Photo11th Floor Lecture Hall 
12:25 - 1:45Break for Lunch  
1:45 - 2:25Efficient Experimental Mathematics for Lattice Path Combinatorics - Alin Bostan, SpecFun, INRIA Saclay11th Floor Lecture Hall
2:35 - 3:15Symbolic local Fourier analysis - Veronika Pillwein, Johannes Kepler Universität Linz11th Floor Lecture Hall
3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:10Visualizing Projection Algorithms with Application to Protein Reconstruction - Matthew K. Tam, University of Newcastle11th Floor Lecture Hall
4:20 - 5:00Operator Orderings: from sequences to polynomials - Christophe Vignat, Tulane University11th Floor Lecture Hall
7:00 - 8:30Poster Session and Dessert Reception11th Floor Lecture Hall 
Thursday, July 24, 2014
TimeEventLocationMaterials
8:55 - 9:00Intro to connections between symbolic and numerical math - Ursula Martin, University of Oxford11th Floor Lecture Hall 
9:00 - 9:40Sparse factorizations- Towards optimal complexity and resilience at exascale - Xiaoye S. Li, Lawrence Berkeley National Laboratory11th Floor Lecture Hall
9:50 - 10:30Computational challenges arising from the theory of Orthogonal Polynomials - Diego Dominici, SUNY at New Paltz11th Floor Lecture Hall
10:30 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:25Parallel Paradigms for Experimental Mathematics - Elise DeDoncker, Western Michigan University11th Floor Lecture Hall
11:35 - 12:15Challenges and Successes in Coastal Ocean Modeling - Clint Dawson, University of Texas at Austin11th Floor Lecture Hall
12:15 - 1:45Break for Lunch  
1:45 - 2:25Equality of Dedekind sums: experimental data, and theory - Sinai Robins, Nanyang Technological University and ICERM11th Floor Lecture Hall
2:35 - 3:15Polynomials, number theory, and experimental mathematics - Michael Mossinghoff, Davidson College and ICERM11th Floor Lecture Hall
3:15 - 3:30Please take a moment to complete the survey that was distributed by email.  
3:30 - 3:45Coffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:30TBA - TBA  
4:30 - 5:00Discussion: 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 - 10:15Group meetings - All  
10:15 - 10:30Coffee/Tea Break11th Floor Lecture Hall 
10:30 - 11:00Report from Group #1 - Group #1 leader11th Floor Lecture Hall 
11:00 - 11:30Report from Group #2 - Group #2 leader11th Floor Lecture Hall 
11:30 - 12:00Report from Group #3 - Group #3 leader11th Floor Lecture Hall 
12:00 - 12:30Construct outline for report - All; led by David H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall 
12:30 - 2:00Break for Lunch  
2:00 - 3:15Draft workshop report - Group leaders and organizers  
3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
3:30 - 4:00Draft workshop report - Group leaders and organizers  

Lecture Videos

Symbolic local Fourier analysis

Veronika Pillwein
Johannes Kepler Universität Linz
July 23, 2014

Outgrowths of the Digital Library of Mathematical Functions Project

Howard Cohl
National Institute of Standards and Technology
Daniel Lozier
National Institute of Standards and Technology
July 21, 2014

Computational challenges for experimental mathematics

David H. Bailey
Lawrence Berkeley National Laboratory and UC Davis
July 21, 2014