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Fitness, Apprenticeship, and Polynomials

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Combinatorial Algebraic Geometry

Part of the book series: Fields Institute Communications ((FIC,volume 80))

Abstract

This article discusses the design of the Apprenticeship Program at the Fields Institute, held 21 August–3 September 2016. Six themes from combinatorial algebraic geometry were selected for the 2 weeks: curves, surfaces, Grassmannians, convexity, abelian combinatorics, parameters and moduli. The activities were structured into fitness, research and scholarship. Combinatorics and concrete computations with polynomials (and theta functions) empowers young scholars in algebraic geometry, and it helps them to connect with the historic roots of their field. We illustrate our perspective for the threefold obtained by blowing up six points in \(\mathbb{P}^{3}\).

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Acknowledgements

This article benefited greatly from comments by Lara Bossinger, Fatemeh Mohammadi, Emre Sertöz, Mauricio Velasco, and an anonymous referee. The apprenticeship program at the Fields Institute was supported by the Clay Mathematics Institute. The author also acknowledges partial support from the Einstein Foundation Berlin, MPI Leipzig, and the US National Science Foundation (DMS-1419018).

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Bernd Sturmfels

  2. Max-Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany

    Bernd Sturmfels

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  1. Bernd Sturmfels
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Correspondence to Bernd Sturmfels .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada

    Gregory G. Smith

  2. Department of Mathematics, University of California, Berkeley, California, USA

    Bernd Sturmfels

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Sturmfels, B. (2017). Fitness, Apprenticeship, and Polynomials. In: Smith, G., Sturmfels, B. (eds) Combinatorial Algebraic Geometry. Fields Institute Communications, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7486-3_1

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