We relate the cohomology of open positroid varieties and their point counts over finite fields to knot homology. In particular, we show that the bigraded Poincaré polynomials of top-dimensional open positroid varieties are given by rational q,t-Catalan numbers. As a consequence of the curious Lefschetz property, we obtain q,t-symmetry and unimodality statements for rational q,t-Catalan numbers. Joint work with Thomas Lam. No special background on the above objects will be assumed.