The pr oblem of Optimal Transport is easily stated: how should one transfer mass from given initial locations to prescribed target locations\, in such a wa y that the total transport cost is minimised?

This venerable optimis ation problem plays an important role in recent development in mathematics \, at the interface of areas as metric geometry\, probability theory\, and partial differential equations.

Moreover\, optimal transport receiv es renewed interest due to applications in data analysis and machine learn ing.

In this talk we give a short introduction to the topic and pres ent some recent contributions to the area: firstly\, we discuss the discre te-to-continuous limit of dynamical optimal transport and show a homogenis ation result in this context\; secondly\, we present a non-commutative ext ension of optimal transport that yields a variational structure in dissipa tive quantum systems.

LOCATION:Raiffeisen Lecture Hall\, IST Austria ORGANIZER:arinya.eller@ist.ac.at SUMMARY:Optimal Transport: continuous\, discrete\, and quantum URL:https://talks-calendar.app.ist.ac.at/events/1677 END:VEVENT END:VCALENDAR