Explore a 43-minute conference talk by Olya Mandelshtam from the University of Waterloo, presented at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the newly discovered connections between one-dimensional interacting particle models (ASEP and TAZRP) and Macdonald polynomials. Discover a new compact tableau formula for symmetric Macdonald polynomials using queue inversion statistics on sorted non-attacking tableaux. Examine the relationship between ASEP polynomials and ASEP probabilities on a circle, and understand the bijection between the presented tableaux and Martin's multiline queues. Investigate the plethystic correspondence between classical and modified Macdonald polynomials, and its connection to integrable systems linking ASEP to TAZRP.