Recorded 16 April 2024. Arvind Ayyer of the Indian Institute of Science presents "The inhomogeneous multispecies PushTASEP" at IPAM's Integrability and Algebraic Combinatorics Workshop. Abstract: We introduce and study a natural multispecies variant of the inhomogeneous PushTASEP with site-dependent rates on the finite ring. We show that the stationary distribution of this process is proportional to the ASEP polynomials at q = 1 and t = 0. We do so by constructing a multiline process which projects to the multispecies PushTASEP, and identifying its stationary distribution using time-reversal arguments. We also study symmetry properties of the process under interchange of the rates associated to the sites out of equilibrium. Lastly, we give explicit formulas for nearest-neighbour two-point correlations in terms of Schur functions. This is joint work with James Martin (arXiv:2310.09740). Work on a generalized model we call the inhomogeneous multispecies t-PushTASEP will be presented by Lauren Williams. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-integrability-and-algebraic-combinatorics/