Explore the construction of efficient Probabilistically Checkable Proofs (PCPs) using High-Dimensional Expanders (HDX) in this 53-minute conference talk. Delve into advanced theoretical computer science concepts as the speaker presents cutting-edge research on how high-dimensional expanders can be leveraged to create more efficient PCP constructions. Learn about the mathematical foundations underlying these proof systems and their applications in computational complexity theory. Discover the geometric and algebraic properties of high-dimensional expanders that make them particularly suitable for PCP constructions, and understand how this approach contributes to the broader field of probabilistic proof verification. This presentation is part of a discussion meeting focused on the intersection of geometry, probability, and algorithms, offering insights into one of the most active areas of research in theoretical computer science.