*Note day of the week and location*

The area law is a key property of quantum many-body systems, stating that entanglement entropy increases proportionally to the surface area of a region. A central question is: Which states satisfy the area law? Hastings (2007) initially proved that gapped ground states obey the area law in 1-dimensional quantum spin systems, with a property known as Hastings factorization playing a pivotal role in the proof. Recently, I presented an extended proof for the infinite volume setting and for fermion systems (arXiv:2407.12324). This seminar will be based on that work.