Day 1 (Freiburg)

Europe/Paris
Freiburg

Freiburg

    • 09:30 10:30
      Welcome coffee 1h
    • 10:30 11:15
      Diophantine properties of Thue-Morse expansions 45m

      The Thue-Morse word over the alphabet {a, b} is the fixed point starting with a of the morphism sending a to ab and b to ba, that is, it is the limit of the sequence of finite words a, ab, abba, abbabaab, abbabaabbaababba, … We survey the Diophantine properties of real numbers whose expansion in some integer base or whose continued fraction expansion is given by a Thue-Morse word (here, a and b are distinct positive integers). We also discuss the Diophantine properties of p-adic numbers whose Hensel expansion is a Thue-Morse word and of power series over a finite field F whose continued fraction expansion is a Thue-Morse word (here, a and b are distinct nonconstant polynomials with coefficients in F).

      Orateur: Yann Bugeaud
    • 11:30 12:00
      Discussion of future plans 30m
    • 12:00 14:00
      Lunch 2h
    • 14:00 14:45
      On the distribution of algebraic numbers and its generalization in Arakelov geometry 45m

      I will talk about a new equidistribution result for the roots of polynomials with bounded Bombieri norm. This can be formulated and proven in a much broader setting for the zero sets of small sections of hermitian line bundles on arithmetic varieties in any dimension. I will discuss the main ingredients of the proof coming from geometry of numbers and from complex analysis. This is work in progress.

      Orateur: Robert Wilms
    • 14:45 15:30
      Coffee break 45m
    • 15:30 15:50
      $C^1$-triangulations of semi-algebraic sets 20m

      If one wants to treat integration of differential forms over semi-algebraic sets analogous to the case of smooth manifolds, it is desirable to have triangulations of semi-algebraic sets that are globally of class $C^1$. We will present a proof of the existence of such triangulations using the 'panel beating' method introduced by Ohmoto-Shiota (2017) and discuss possible generalizations.

      Orateur: Christoph Brackenhofer