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Preface by the editors of the Special Volume: Albert Cohen, Wolfgang Dahmen, Hans Munthe-Kaas, Martín Sombra, and Agnes Szanto

The Society for the Foundations of Computational Mathematics supports and promotes fundamental research in computational mathematics and its applications, interpreted in the broadest sense. It fosters interaction among mathematics, computer science and other areas of computational science through its conferences, workshops and publications. Major conferences of the Society have been held in Park City (1995), Rio de Janeiro (1997), Oxford (1999), Minneapolis (2002), Santander (2005), Hong Kong (2008), Budapest (2011), Montevideo (2014) and Barcelona (2017). The next conference will be held in Vancouver, in June 2020. More information about the FoCM Society is available in the web site

The conference in Barcelona took place between July 10 and 19, 2017, and was attended by about 600 scientists. It took a format tried and tested to a great effect in the former FoCM conferences: plenary lectures in the mornings and theme-centered parallel workshops in the afternoons. It consisted of three periods of 3 days each. Each workshop extended over a period, including two semi-plenary lectures, of interest to a more general audience, as well as (typically shorter) invited talks aimed at a more technical audience and contributed poster presentations. This structure allows for a very high standard of presentation, while affording many opportunities for cross-fertilization and communication across subjects.

Workshops at the Barcelona conference were held in the following twenty-one fields:

  • Approximation theory

  • Computational algebraic geometry

  • Computational dynamics

  • Computational geometry and topology

  • Computational harmonic analysis and compressive sensing

  • Computational mathematical biology with emphasis on the genome

  • Computational number theory

  • Continuous optimization

  • Foundations of numerical PDEs

  • Geometric integration and computational mechanics

  • Graph theory and combinatorics

  • Information-based complexity

  • Learning theory

  • Mathematical foundations of data assimilation and inverse problems

  • Multiresolution and adaptivity in numerical PDEs

  • Numerical linear algebra

  • Random matrices

  • Real-number complexity

  • Special functions and orthogonal polynomials

  • Stochastic computation

  • Symbolic analysis

In addition to these workshops, eighteen plenary lectures, covering a broad spectrum of topics connected to computational mathematics, were delivered by some of the world’s leading researchers. This volume is a collection of articles based on some of the plenary talks presented at FoCM 2017. The topics covered in the lectures and in this volume reflect the breadth of research within computational mathematics as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. The Barcelona gathering proved itself to be a stimulating meeting place of researchers in computational mathematics and of theoreticians in mathematics and computer science, with emphasis on multidisciplinary interaction across subjects and disciplines in an informal and friendly atmosphere.

We hope that this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to gain some insights into the state of the art in this active and significant field.

We wish to express our gratitude to the Faculty of Mathematics of the University of Barcelona for hosting the conference and for its logistic and technical support, and to the Centre de Recerca Matemàtica and the Institut de Matemàtica of the University of Barcelona for their administrative support. We are also grateful to the local organizing committee, with members from UB, Polytechnic University of Catalonia, Barcelona, Pompeu Fabra University and ICREA, for making FoCM 2017 such an outstanding success. Finally, we thank our international and local sponsors for their financial support, including the National Science Foundation, the Foundation Compositio Mathematica, the European Mathematical Society, the UB, and the Catalan Mathematical Society.

We thank the authors of the articles in this volume for producing such excellent contributions. Above all, however, we wish to express our gratitude to all the participants of FoCM 2017 for attending the meeting and making it such an exciting, productive and scientifically stimulating event.

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Correspondence to Hans Munthe-Kaas.

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Cohen, A., Dahmen, W., Munthe-Kaas, H. et al. Preface. Found Comput Math 19, 963–964 (2019).

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