Explore cutting-edge cryptographic concepts in this lecture from the Quantum and Lattices Joint Reunion Workshop, focusing on Batch Arguments for NP and Succinct Non-interactive Arguments (SNARGs) for P derived from the Learning With Errors (LWE) problem. Delve into the intricate world of cryptography as Abhishek Jain from Johns Hopkins University presents groundbreaking research on these advanced topics, offering insights into their applications and implications for secure computation and verification systems.