Explore tensor decomposition algorithms through the lens of algebraic complexity in this 52-minute lecture by Vishwas Bhargava. Delve into the fundamental connections between tensors and special depth 3 arithmetic circuits. Examine both worst-case and average-case algorithms for tensor decomposition, with a focus on a worst-case algorithm for decomposing low-rank tensors and an algebraic adaptation of the classic Jennrich's algorithm. Gain insights from this presentation, part of the Workshop on Tensors: Quantum Information, Complexity and Combinatorics held at the Centre de recherches mathématiques (CRM) in November 2022.