Title: Almost Congruence Extension Property for subgroups of free groups. Abstract. The talk essentially based on: https://arxiv.org/abs/1606.02345 Let G be a group and H

Title: The spectral method for geometric colouring problems

Title: Stability patterns in representation theory and applications Abstract: Many natural sequences of objects come equipped with group actions, e.g. the symmetric group on n letters acting on a space X_n. This leads to fundamental instability of invariants, such as homology, arising from the representation theory of the sequence of groups. Representation stability is a new and increasingly important set of ideas that describe a sense in which such sequence of representations (of different groups) stabilizes.