Correlation functions for the Schur process with free boundaries

Using free fermionic techniques we write down the n-point pfaffian correlation functions for the Schur process with one and two free boundaries. In the one free boundary case, we rederive asymptotic results first obtained by Baik--Rains on symmetry classes of last passage percolation problems, as well as analyze new models for old structures: symmetric plane partitions and plane over--partitions (symmetric pyramid partitions). The two free boundaries case is similar to the periodic Schur process of Borodin and we hope to exploit these similarities in a follow-up. We connect the results to the KPZ universality class, the Tracy--Widom distributions and kernels conjecturally interpolating between Airy and Gumbel/Gaussian. Based on joint work in progress with Jeremie Bouttier, Peter Nejjar and Mirjana Vuletic.