Explore the intricacies of entanglement entropy in 2D frustration-free spin systems through this 23-minute conference talk presented at an Association for Computing Machinery (ACM) event. Delve into the central concepts of local Hamiltonians, ground states, and entanglement entropy, while examining Hastings' proof and its underlying assumptions. Learn about the upper bounding approach, robust polynomials, and the Whole Screen Directivity Lemma. Conclude by discussing future directions and open questions in this fascinating area of quantum physics and computational complexity.