[Settfa] NCG&T seminar afternoon, Tuesday 28 Jan

[David Bradley-Williams]

Dear all,

Due to the significant participation at the Winter School in Abstract 
Analysis -- Section Set Theory (https://www.winterschool.eu/2025), there 
will be no talk in our seminar on Tuesday morning January 28th.

The next talk in our seminar will be on Tuesday morning February 4th by 
Spencer Unger. Details to be announced.

I am also aware that on Wednesday February 5th it is expected that Andy 
Zucker will be visiting and giving a talk in the Wednesday morning 
seminar at 11:00, which may be of interest to some participants.
https://www.math.cas.cz/index.php/events/event/3902

Meanwhile, Bhishan Jacelon has sent me advance details of next week's 
talk in the NCG&T seminar on Tuesday afternoon by David Jekel (in the 
Blue room at 16.00 on Tuesday 28.01) as some participants might be 
interested. See below for the title and abstract:

Title: Free optimal transport on the trace-state space
Abstract: I discuss the development of an optimal transport theory for 
free probability.  Biane and Voiculescu defined an analog of the 
Wasserstein distance on the space of non-commutative laws of an m-tuple, 
or equivalently, the space of tracial states on a certain universal 
$\mathrm{C}^*$-algebra: the Wasserstein distance of two laws $\mu$ and 
$\nu$ is the minimal $L^2$ distance between self-adjoint $m$-tuples $X$ 
and $Y$ in a tracial von Neumann algebra $(M,\tau)$ that realize the 
laws $\mu$ and $\nu$ respectively.  Later, motivated by properties of 
optimal couplings in the classical setting, Guionnet and Shlyakhtenko 
showed that certain non commutative laws $\mu$ can be expressed as the 
pushforward of a free semicircular family by the gradient of a convex 
function.  We present a free version of Monge Kantorovich duality which 
bridges these two results by expressing the Wasserstein distance through 
a variational problem involving convex functions.  In addition, we show 
that the Wasserstein distance in the free setting gives a much stronger 
topology than the weak-* topology (which should be contrasted with the 
classical setting as well as Rieffel's quantum compact metric spaces).  
Agreement of these two topologies at a point also relates closely with 
amenability.  We also discuss the relationship between various 
non-commutative Wasserstein metrics from the free and quantum settings.  
This talk is (mostly) based on joint work with Gangbo, Nam, and 
Shlyakhtenko.

Full details at:
https://ncgandtprague.wordpress.com/2025/01/14/28-january-20245-david-jekel-university-of-copenhagen/