Recorded 23 May 2025. Therese Landry of the University of California, Santa Barbara, presents "Quantum Wasserstein Distance on the Quantum Permutation Group" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Abstract: We investigate quantum compact groups which support quantum metric space structure. In our core example, we define an analog of the Hamming metric on the quantum permutation group S+n . The construction of our quantum metric relies on the work of Biane and Voiculescu. We also obtain an associated quantum 1 -Wasserstein distance on the tracial state space of C(S+n) . This is joint work with David Jekel and Anshu Nirbay. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-and-numerical-methods-for-non-commutative-optimal-transport/