Recorded 28 March 2024. Eveliina Peltola of Aalto University presents "On variants of Specht polynomials and random geometry" at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Abstract: Certain classes of polynomials associated with column-strict, rectangular Young tableaux, that we call (fused) Specht polynomials, give explicit formulas for conformal blocks (partition functions) describing a general class of conformally invariant boundary conditions and crossing probabilities for models building on the Gaussian free field (GFF): e.g. double-dimers contours and multi-dimer webs of higher degree. Also, analogous determinantal formulas describe the geometry of uniform spanning tree (UST) branches (loop-erased walks). These objects also display rich algebraic content: they carry irreducible representations of certain diagram algebras: e.g., the (fused) Hecke algebra, Temperley-Lieb algebra, or the Kuperberg algebra defined from sln webs. I shall discuss the general framework and results towards the connection to random geometry. While the precise connection is partly conjectural, it has been verified in special cases. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-statistical-mechanics-and-discrete-geometry/