Explore a lecture on the inhomogeneous multispecies PushTASEP presented by Arvind Ayyer from the Indian Institute of Science at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the introduction and study of a natural multispecies variant of the inhomogeneous PushTASEP with site-dependent rates on the finite ring. Discover how the stationary distribution of this process relates to ASEP polynomials and learn about the construction of a multiline process that projects to the multispecies PushTASEP. Examine symmetry properties of the process under rate interchange and gain insights into explicit formulas for nearest-neighbor two-point correlations using Schur functions. The lecture also touches on ongoing work regarding a generalized model called the inhomogeneous multispecies t-PushTASEP.