Geometric Structures seminar - Armin Rainer - Tuesday February 27th, 2024 , 14:00 (Rome time) - room 133 at SISSA

[Samuel Borza]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker: Armin Rainer (Wien)

Title: On the semialgebraic Whitney extension problem
Time: Tuesday February 27th, 2024 , 14:00 (Rome time)
Venue: room 133 - SISSA main building

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Abstract:
In 1934, Whitney raised the question of how one can decide whether a function $f$ defined on a closed subset $X$ of $\mathbb R^n$ is the restriction of a $C^m$ function on $\mathbb R^n$. He gave a characterization in dimension $n=1$. The problem was fully solved by Fefferman in 2006. In this talk, I will discuss a related conjecture: if a semialgebraic function $f : X \to \mathbb R$ has a $C^m$ extension to $\mathbb R^n$, then it has a semialgebraic $C^m$ extension. In particular, I will show that the $C^{1,\omega}$ case of the conjecture is true (in a uniformly bounded way), for each semialgebraic modulus of continuity $\omega$. The proof is based on the existence of semialgebraic Lipschitz selections for certain affine-set valued maps. This is joint work with Adam Parusinski.
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More information can be found here: https://sites.google.com/view/geometric-structures/

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Samuël Borza