Abstract: Topological cyclic homology is a powerful tool for computing the algebraic K-theory of rings and connective ring spectra; Hahn, Raksit and Wilson extended to suitable commutative ring spectra a filtration on topological cyclic homology defined by Bhatt, Morrow and Scholze, and showed that in the example of the Adams summand at an odd prime, it provides an impressive simplification of former computations (and a new result in the case of the prime 3). In this talk, I will outline how their approach can be used to study topological cyclic homology of connective real K-theory. This is joint work with Gabriel Angelini-Knoll and John Rognes.