Recorded 08 February 2024. Carolin Wille of the University of Cambridge presents "Topological Dualities from Matchgate Tensor Networks" at IPAM's Tensor Networks Workshop. Abstract: The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly associated to different areas of physics -- that of long range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically non-local, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this work, we propose a unified approach to this duality via matchgate tensor networks. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/tensor-networks/