New paper on arXiv: Together with Prateek Dwivedi and Benedikt Pago, we study in Lower Bounds in Algebraic Complexity via Symmetry and Homomorphism Polynomials the power of symmetric algebraic computation. We introduce symmetric analogoues of the complexity classes VF, VBP, and VP called symVF, symVBP, and symVP and show unconditionally that symVF ⊊ symVBP ⊊ symVP. Key to understanding these complexity classes are homomorphism polynomials. Moreover, we give general criteria for such polynomials to be VBP-, VP-, or VNP-complete.