Recorded 28 February 2025. Aldo Garcia Guinto of Michigan State University presents "Schreier's Formula for some Free Probability Invariants" at IPAM's Free Entropy Theory and Random Matrices Workshop. Abstract: Let α:G↷(M,τ) be a trace-preserving action of a finite group G on a tracial von Neumann algebra. Suppose that A⊂M is a finitely generated unital ∗ -subalgebra which is globally invariant under α . We give a formula relating the von Neumann dimension of the space of derivations on A valued on its coarse bimodule to the von Neumann dimension of the space of derivations on A⋊algαG valued on its coarse bimodule, which is reminiscent of Schreier's formula for finite index subgroups of free groups. This formula induces a formula for dimDerc(A,τ) (defined by Shlyakhtenko) and Δ (defined by Connes and Shlyakhtenko). These quantities and the free entropy dimension quantities agree on a large class of examples, and so by combining these results with known inequalities, one can expand the family of examples for which the quantities agree. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/free-entropy-theory-and-random-matrices/