Dual of the dual for the distance in noncommutative geometry

par Dr Pierre Martinetti (Università di Genova)

vendredi 3 déc. 2021, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Braconnier)

The Wasserstein distance associated with Monge optimal-transport problem consists in minimising a cost. Kantorovich has shown there exists a dual formulation, consisting in maximising a profit.
The distance in noncommutative geometry is defined by Conner as the search for a supremum, and may be seen as a non-commutative generalisation of Kantorovich distance.  
We will see that there is no obvious noncommutative equivalent  to the Wassertein distance, although there do exist a dual formulation for Connes distance (as an infimum rather than a supremum).