Abstract
Classical applications of Galois theory concern algebraic numbers and algebraic functions. Still, the night before his duel, Galois wrote that his last mathematical thoughts had been directed toward applying his “theory of ambiguity to transcendental functions and transcendental quantities”. In this talk, we will outline some more or less recent ideas and results in this direction.
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References
See e.g. M. van der Put, M. Singer, Galois theory of linear differential equations, Springer Grundlehren der Math. Wiss. 328, 2003.
B. Malgrange “On nonlinear differential Galois theory”. Frontiers in mathematical analysis and numerical methods, 185–196, World Sci. Publ., 2004.
“Mixed Tate Motives over Spec(Z)”, in Annals of Math., volume 175, no. 1 (2012).
Cf. M. Kontsevich, D. Zagier: Periods. Mathematics unlimited—2001 and beyond, 771–808, Springer.
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André, Y. (2013). Galois theory beyond algebraic numbers and algebraic functions. In: Zannier, U. (eds) Colloquium De Giorgi 2010–2012. Publications of the Scuola Normale Superiore, vol 4. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-457-1_1
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DOI: https://doi.org/10.1007/978-88-7642-457-1_1
Publisher Name: Edizioni della Normale, Pisa
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