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\\ ==== Next talks ====
[[en:seminaires:numeration:index|One world numeration seminar]]\\
Tuesday May 7, 2024, 2PM, Online\\
**Tom Kempton** (University of Manchester) //The Dynamics of the Fibonacci Partition Function//
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The Fibonacci partition function $R(n)$ counts the number of ways of representing a natural number $n$ as the sum of distinct Fibonacci numbers. For example, $R(6)=2$ since $6=5+1$ and $6=3+2+1$. An explicit formula for $R(n)$ was recently given by Chow and Slattery. In this talk we express $R(n)$ in terms of ergodic sums over an irrational rotation, which allows us to prove lots of statements about the local structure of $R(n)$.
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[[en:seminaires:numeration:index|One world numeration seminar]]\\
Tuesday May 21, 2024, 2PM, Online\\
**Gaétan Guillot** (Université Paris-Saclay) //Approximation of linear subspaces by rational linear subspaces//
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We elaborate on a problem raised by Schmidt in 1967: rational approximation of linear subspaces of $\mathbb{R}^n$. In order to study the quality approximation of irrational numbers by rational ones, one can introduce the exponent of irrationality of a number. We can then generalize this notion in the framework of vector subspaces for the approximation of a subspace by so-called rational subspaces.
After briefly introducing the tools for constructing this generalization, I will present the different possible studies of this object. Finally I will explain how we can construct spaces with prescribed exponents.
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[[en:seminaires:numeration:index|One world numeration seminar]]\\
Tuesday June 18, 2024, 2PM, Online\\
**Noy Soffer Aranov** (Technion) //Escape of Mass of the Thue Morse Sequence//
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One way to study the distribution of quadratic number fields is through the evolution of continued fraction expansions. In the function field setting, it was shown by de Mathan and Teullie that given a quadratic irrational $\Theta$, the degrees of the periodic part of the continued fraction of $t^n\Theta$ are unbounded. Paulin and Shapira improved this by proving that quadratic irrationals exhibit partial escape of mass. Moreover, they conjectured that they must exhibit full escape of mass. We show that the Thue Morse sequence is a counterexample to their conjecture. In this talk we shall discuss the technique of proof as well as the connection between escape of mass in continued fractions, Hecke trees, and number walls. This is part of ongoing work joint with Erez Nesharim.
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\\ ==== Previous talks ====
\\ === Year 2024 ===

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\\ === Year 2023 ===

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\\ === Year 2022 ===

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\\ === Year 2021 ===

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\\ === Year 2020 ===

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