[Settfa] [Set Theory]Tuesday 19 May, Yoël Perreau

[Adam Bartoš]

Dear all,

there is a *change in the room and time* for the announced lecture at 
the seminar Set Theory and Analysis! We will meet on

Tuesday, 19 May 2026, *10:15--11:45*
in the *Blue lecture room* in the *rear building*.

Best wishes,
Adam


Dne 16.05.2026 v 9:00 kubis at math.cas.cz napsal(a):
> Set Theory and Analysis
>
> Tuesday, 19 May 2026 - 10:00 to 11:30
> Place: IM, konírna
>
> Speaker: Yoël Perreau, University of Tartu, Estonia
> Title: Points of continuity in Lipschitz free-spaces
>
> Abstract
>
> In this talk, I would like present a metric characterization of points 
> of continuity among molecules in Lipschitz free-spaces. Recall that a 
> point $x$ on the unit sphere of a Banach space $X$ is said to be a 
> point of weak-to-norm continuity of $B_X$, or simply a \emph{point of 
> continuity}, if the identity mapping $Id:(B_X,w)\to 
> (B_X,\norm{\cdot})$ is continuous at $x$. Also recall that given any 
> complete metric space $M$, the \emph{Lipschitz free-space} 
> $\lipfree{M}$ of $M$ is a Banach space which contains an isometric 
> copy of $M$ in a canonical way and satisfies the following 
> linearization property: given any Lipschitz map $f:M\to\R$, there 
> exist a unique functional $g$ on $\lipfree{M}$ such that $g\circ 
> \delta=f$ and $\norm{g}=\Lip(f)$, where $\delta:M\to \lipfree{M}$ is 
> the canonical isometric embedding. A \emph{molecule} is an element of 
> $\lipfree{M}$ of the form $m_{xy}:=\frac{\delta(x)-\delta(y)}{d(x,y)}$ 
> where $x$ and $y$ are two distinct points in $M$. Molecules act on 
> Lipschitz functions by computing slopes, and are the simplest possible 
> elements that one can find in the sphere of a Lipschitz free-space. I 
> will discuss how to relate the fact that a molecule $m_{xy}$ is a 
> point of continuity to some local compactness of the metric space $M$ 
> around the metric segment between the points $x$ and $y$ as well as a 
> lack of connectability between these points. If time permits, I will 
> also explain how this characterization can be extended to finitely 
> supported elements in $\lipfree{M}$.
>
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/6
>
> Set Theory and Analysis mailing list
> settfa at math.cas.cz
> https://list.math.cas.cz/listinfo/settfa@math.cas.cz
>
>
> _______________________________________________
> Settfa mailing list
> Settfa at math.cas.cz
> https://list.math.cas.cz/listinfo/settfa
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.math.cas.cz/pipermail/settfa/attachments/20260517/5a16b5f6/attachment.html>