Geometric Structures - Paolo Antonini - July 6 - 2:00 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All, 

This is a reminder of today's seminar from the series "Geometric
Structures".

Speaker:  PAOLO ANTONINI ( [1]Università del Salento [1]) [1]

Title:       Infinite dimensional grassmannians, quantum states and
optimal transport 

Time:      July 6th, 2021, 2:00 pm (Rome Time)   ---------- PLEASE NOTE
THE EXCEPTIONAL CHANGE OF SCHEDULE. THIS IS A JOINT SEMINAR BETWEEN
"ANALYSIS AND MATHEMATICAL PHYSICS" AND "GEOMETRIC STRUCTURES" SEMINARS.


Venue:    from remote only, on zoom at this link 
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[2]
Passcode: geometry

Abstract:  
In this seminar we report on a recent work in collaboration with F.
Cavalletti where we develop the basic theory of optimal transport for
the quantum states of the C*-algebra of the compact operators on a
(separable) Hilbert space. 

As usual, states are interpreted as the noncommutative replacement of
probability measures; via the spectral theorem applied to their density
matrices, we associate to states discrete measures on the grassmannian
of the finite dimensional subspaces. In this way we can treat them as
ordinary probability measures and develop the theory of optimal
transport. 

The metric geometry of the grassmannian, as an infinite dimensional
manifold plays a decisive role and part of the talk will be devoted to
describing its rich structure. Notably the grassmannian is an Alexandrov
space with non negative curvature. 

Finally we will interpret pure normal states of the tensor product
$H\otimes H$ as families of transport maps. This idea leads to the
possibility of giving a definition of the Wasserstein cost for such
objects. 

More information can be found here:
https://sites.google.com/view/geometric-structures/ [3] 

Everyone is welcome! 

-- 
_Miruna-Stefana Sorea_
_Postdoctoral Researcher_
_Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste,
Italy_
_HTTPS://SITES.GOOGLE.COM/VIEW/MIRUNASTEFANASOREA/_ 

Links:
------
[1]
https://www.google.com/url?q=https%3A%2F%2Fpaoloanto.wordpress.com%2F&sa=D&sntz=1&usg=AFQjCNFyvsR52R8szwQyM2e67tWzyi1zhQ
[2]
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[3] https://sites.google.com/view/geometric-structures/