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Challenges in 21st Century Experimental Mathematical Computation (July 21-25, 2014)


Organizing Committee
  • David H. Bailey
    (Lawrence Berkeley Lab and UC Davis)
  • Jonathan Borwein
    (University of Newcastle, Australia)
  • Olga Caprotti
    (University of Helsinki, Finland)
  • Ursula Martin
    (Queen Mary College)
  • Michela Taufer
    (University of Delaware)
  • Bruno Salvy
    (INRIA, France)


Picture

[Image Credit: D. Bailey and J. Borwein]

Description

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.


  • Dorian Arnold*
    (University of New Mexico)
  • David Bailey *
    (Lawrence Berkeley National Laboratory)
  • Michela Becchi
    (University of Missouri)
  • Abdessamad Ben Hamza
    (Concordia University)
  • Amber Boehnlein*
    (Stanford University)
  • Folkmar Bornemann*
    (TU München)
  • Jonathan Borwein *
    (University of Newcastle)
  • Alin Bostan*
    (INRIA )
  • Brian Brennan
    (Baylor University)
  • Neil Calkin *
    (Clemson University)
  • Wei-Fan Chiang
    (University of Utah)
  • Howard Cohl *
    (National Institute of Standards and Technology)
  • Robert Corless
    (The University of Western Ontario)
  • Silvia Crivelli*
    (University of California, Davis)
  • Clint Dawson*
    (University of Texas at Austin)
  • Elise Dedoncker*
    (Western Michigan University)
  • Diego Dominici *
    (SUNY at New Paltz)
  • Ali Eshragh *
    (University of Newcastle)
  • Cyndi Garvan
    (University of Florida)
  • Frank Garvan*
    (University of Florida)
  • Venu Gopal
    (Brown University)
  • Ganesh Gopalakrishnan *
    (University of Utah)
  • Lindley Graham
    (University of Texas at Austin)
  • Matt Knepley *
    (University of Chicago)
  • Sherry Li*
    (Lawrence Berkeley National Laboratory)
  • Steve Linton
    (University of St. Andrews)
  • Dan Lozier*
    (National Institute of Standards and Technology)
  • Ursula Martin *
    (University of Oxford)
  • Michael Mossinghoff *
    (Davidson College)
  • Chunjae Park
    (Konkuk university)
  • Veronika Pillwein *
    (Johannes Kepler Universität Linz)
MondayJuly 21, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 10:00Experimental Computation and Visual TheoremsJonathan Borwein, CARMA, University of Newcastle11th Floor Lecture Hall
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10:00 - 10:15Coffee/Tea Break11th Floor Collaborative Space
10:15 - 10:50Some Experimentation in Counting QuestionsNeil Calkin, Clemson University11th Floor Lecture Hall
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11:00 - 11:40The numerical reproducibility fair trade: Facing concurrency challenges at extreme scaleMichela Taufer, University of Delaware11th Floor Lecture Hall
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11:50 - 12:30Reliable computing in geometry processing and CAGDKonrad Polthier, Freie Universität Berlin11th Floor Lecture Hall
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12:30 - 1:45Break for Lunch
1:45 - 2:25Computational challenges for experimental mathematicsDavid H. Bailey, Lawrence Berkeley National Laboratory and UC Davis11th Floor Lecture Hall
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2:35 - 3:15Reliable numerical evaluation of special functions- algorithms and experimentsBruno Salvy, INRIA11th Floor Lecture Hall
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3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:15Outgrowths of the Digital Library of Mathematical Functions ProjectHoward Cohl and Daniel Lozier, National Institute of Standards and Technology11th Floor Lecture Hall
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4:15 - 5:00TBATBA
5:00 - 6:30Welcome Reception11th Floor Collaborative Space

TuesdayJuly 22, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:55 - 9:00Intro to numerical computing for experimental mathDavid 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 arithmeticNathalie Revol, INRIA11th Floor Lecture Hall
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9:50 - 10:30Nonlinear Preconditioning for the Parallel Solution of Systems Algebraic EquationsMatt Knepley, University of Chicago11th Floor Lecture Hall
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10:30 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 11:25Bugs- Black Ice on the Road to ExascaleGanesh Gopalakrishnan and Alexey Solovyev, University of Utah11th Floor Lecture Hall
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11:35 - 12:15Very Special Functions: Numerical Explorations of Random Matrix DistributionsFolkmar Bornemann, TU München11th Floor Lecture Hall
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12:15 - 1:45Break for Lunch
1:45 - 2:25Apery numbers and their experimental siblingsArmin Straub, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
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2:35 - 3:15Toward HPC Runtimes that Self-adapt to your MathDorian Arnold, University of New Mexico11th Floor Lecture Hall
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3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:10Large-scale, data-intensive physics computingAmber Boehnlein, Stanford University11th Floor Lecture Hall
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4:20 - 5:00Computational and analytics challenges in biologySilvia Crivelli, University of California, Davis11th Floor Lecture Hall
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WednesdayJuly 23, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:55 - 9:00Intro to symbolic computing for experimental mathBruno Salvy, INRIA11th Floor Lecture Hall
9:00 - 9:40Approximating the Fisher Information for a Partially-Observable Growing PopulationAli Eshragh, CARMA, University of Newcastle11th Floor Lecture Hall
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9:50 - 10:30Mathematical practice, crowdsourcing, and social machinesUrsula Martin, University of Oxford11th Floor Lecture Hall
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10:30 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 11:25Congruences and relations for the Fishburn numbersFrank Garvan, University of Florida11th Floor Lecture Hall
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11:30 - 12:15Moments of zeta functions associated to hyper-elliptic curves over finite fieldsMichael Rubinstein, University of Waterloo11th Floor Lecture Hall
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12:15 - 12:25Group Photo11th Floor Lecture Hall
12:25 - 1:45Break for Lunch
1:45 - 2:25Efficient Experimental Mathematics for Lattice Path CombinatoricsAlin Bostan, SpecFun, INRIA Saclay11th Floor Lecture Hall
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2:35 - 3:15Symbolic local Fourier analysisVeronika Pillwein, Johannes Kepler Universität Linz11th Floor Lecture Hall
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3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:10Visualizing Projection Algorithms with Application to Protein ReconstructionMatthew K. Tam, University of Newcastle11th Floor Lecture Hall
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4:20 - 5:00Operator Orderings: from sequences to polynomialsChristophe Vignat, Tulane University11th Floor Lecture Hall
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7:00 - 8:30Poster Session and Dessert Reception11th Floor Lecture Hall

ThursdayJuly 24, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:55 - 9:00Intro to connections between symbolic and numerical mathUrsula Martin, University of Oxford11th Floor Lecture Hall
9:00 - 9:40Sparse factorizations- Towards optimal complexity and resilience at exascaleXiaoye S. Li, Lawrence Berkeley National Laboratory11th Floor Lecture Hall
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9:50 - 10:30Computational challenges arising from the theory of Orthogonal PolynomialsDiego Dominici, SUNY at New Paltz11th Floor Lecture Hall
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10:30 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 11:25Parallel Paradigms for Experimental MathematicsElise DeDoncker, Western Michigan University11th Floor Lecture Hall
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11:35 - 12:15Challenges and Successes in Coastal Ocean ModelingClint Dawson, University of Texas at Austin11th Floor Lecture Hall
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12:15 - 1:45Break for Lunch
1:45 - 2:25Equality of Dedekind sums: experimental data, and theorySinai Robins, Nanyang Technological University and ICERM11th Floor Lecture Hall
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2:35 - 3:15Polynomials, number theory, and experimental mathematicsMichael Mossinghoff, Davidson College and ICERM11th Floor Lecture Hall
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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 - 4:30TBATBA
4:30 - 5:00Discussion: What have we learned; organize groupsDavid H. Bailey, Lawrence Berkeley National Laboratory and UC Davis or Jonathan Borwein, CARMA, University of Newcastle11th Floor Lecture Hall

FridayJuly 25, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:15Group meetingsAll
10:15 - 10:30Coffee/Tea Break11th Floor Lecture Hall
10:30 - 11:00Report from Group #1Group #1 leader11th Floor Lecture Hall
11:00 - 11:30Report from Group #2Group #2 leader11th Floor Lecture Hall
11:30 - 12:00Report from Group #3Group #3 leader11th Floor Lecture Hall
12:00 - 12:30Construct outline for reportAll; 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 reportGroup leaders and organizers
3:15 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 4:00Draft workshop reportGroup leaders and organizers

      Workshop Organizer's Report