Kolmogorov’s Heritage in Mathematics

1. The youth of Andrei Nikolaevich and Fourier series
Jean-Pierre Kahane

2. Kolmogorov’s contribution to intuitionistic logic
Thierry Coquand

3. Some aspects of the probabilistic work
Loïc Chaumont, Laurent Mazliak, Marc Yor

4. Infinite dimensional Kolmogorov equations
Giuseppe Da Prato

5. From Kolmogorov’s theorem on empirical distribution to number theory
Kevin Ford

6. Kolmogorov’s e-entropy and the problem of statistical estimation
Mikhail Nikouline, Valentin Solev

7. Kolmogorov and topology
Victor M. Buchstaber

8. Geometry and approximation theory in A. N. Kolmogorov’s works
Vladimir M. Tikhomirov

9. Kolmogorov and population dynamics
Karl Sigmund

10. Resonances and small divisors
Étienne Ghys

11. The KAM Theorem
John H. Hubbard

12. From Kolmogorov’s Work on entropy of dynamical systems to Non-uniformly hyperbolic dynamics
Denis V. Kosygin, Yakov G. Sinai

13. From Hilbert’s 13th Problem to the theory of neural networks: constructive aspects of Kolmogorov’s Superposition Theorem
Vasco Brattka

14. Kolmogorov Complexity
Bruno Durand, Alexander Zvonkin

15. Algorithmic Chaos and the Incompressibility Method
Paul Vitanyi

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Keywords: MATHEMATICS / General MAT000000