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Mathematics Going Forward

Collected Mathematical Brushstrokes

  • Book
  • © 2023

Overview

Editors:
  1. Jean-Michel Morel

    1. CMLA, École Normale Supérieure, Cachan CX, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Bernard Teissier

    1. Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013, Paris, France

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Presents open problems, conjectures and musings on the future of mathematics
  • Collects contributions by leading mathematicians
  • Provides motivation for future research in mathematics

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2313)

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Table of contents (44 chapters)

  1. Front Matter

    Pages i-x
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  2. Letter from Jean-Pierre Eckmann

    • Jean-Pierre Eckmann
    Pages 1-3

  3. Algebraic Geometry

    1. Front Matter

      Pages 5-5
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    2. Une liste de problèmes

      • Jean-Louis Colliot-Thélène
      Pages 7-28

    3. Some Ideas in Need of Clarification in Resolution of Singularities and the Geometry of Discriminants

      • Bernard Teissier
      Pages 29-41

    4. Shifted Sheaves for Space-Time

      • Pierre Schapira
      Pages 43-46

    5. Lefschetz Fixed Point Theorems for Correspondences

      • Loring W. Tu
      Pages 47-57

  4. Dynamical Systems

    1. Front Matter

      Pages 59-60
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    2. Vous avez dit “qualitatif” ?

      • Alain Chenciner
      Pages 61-80

    3. Tale o’ pi by pilota

      • Ariel Amir, Tadashi Tokieda
      Pages 81-84

  5. Finance

    1. Front Matter

      Pages 85-85
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    2. What Next?

      • L. C. G. Rogers
      Pages 87-94

    3. Some Remarks on Enlargement of Filtration and Finance

      • Monique Jeanblanc
      Pages 95-114

    4. Modern Extreme Value Theory at the Interface of Risk Management, Bayesian Networks and Heavy-Tailed Time Series

      • Paul Embrechts, Claudia Klüppelberg, Thomas Mikosch
      Pages 115-139

    5. Limits of Limit-Order Books

      • Christopher Almost, John Lehoczky, Steven Shreve, Xiaofeng Yu
      Pages 141-155

  6. Geometry

    1. Front Matter

      Pages 157-157
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    2. Spinors in 2022

      • Jean-Pierre Bourguignon
      Pages 159-166

    3. Cohomological Localizations and Set-Theoretical Reflection

      • Carles Casacuberta
      Pages 167-181

    4. Geometry of Data

      • Parvaneh Joharinad, Jürgen Jost
      Pages 183-198

    5. A Chapter About Asymptotic Geometric Analysis: Isomorphic Position of Centrally Symmetric Convex Bodies

      • Vitali Milman
      Pages 199-207
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Keywords

About this book

This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Editors and Affiliations

  • CMLA, École Normale Supérieure, Cachan CX, France

    Jean-Michel Morel

  • Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013, Paris, France

    Bernard Teissier

About the editors

Jean-Michel Morel is professor of mathematics at Ecole Normale Supérieure Paris-Saclay.  He works on theories and algorithms for the restoration and automatic analysis of digital images and video.

Bernard Teissier is Emeritus Director of Research of CNRS at the Institut Mathématique de Jussieu-Paris Rive Gauche. His research interests center on the algebra and geometry of singularities in algebraic and analytic geometry.

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