Explore a cutting-edge lecture on the intersection of classical topology and quantum complexity presented by Tamara Kohler from Stanford University at IPAM's Topology, Quantum Error Correction and Quantum Gravity Workshop. Delve into recent findings about the computational complexity of determining homology groups in simplicial complexes, a fundamental task in computational topology. Discover how this seemingly classical problem may have quantum mechanical implications, as evidenced by its QMA1-hardness and containment within QMA under certain conditions. Examine the extension of these results to clique complexes, which are relevant to topological data analysis. Gain insights into the proof techniques that combine Hamiltonian complexity and homological algebra, inspired by connections to supersymmetric quantum mechanics. Uncover the intuition behind the proof and explore how supersymmetry influenced this groundbreaking research in the field of computational topology and quantum complexity. Read more