Extensions of target space T-duality to non-Abelian isometry groups and even to spaces without isometry have found recent utility within the AdS/CFT correspondence and have played a central role in the development of new classes of integrable string backgrounds called $\eta$ and $\lambda$-models. After a pedagogical introduction to the topic I will outline some recent results concerning the open sector of $\lambda$-models and the interpretation of these theories within the formalism of double field theory.

In this talk I shall give a review of two classes of integrable non-linear sigma models called \eta and \lambda deformations. Three reasons to be interested are 1) these are interesting examples of relatively rare integrable QFT displaying quantum group symmetries; 2) viewed as string theory sigma models they may have application to N=4 SYM via holography and 3) they provide concrete examples for generalised notions of T-duality. This talk will describe a variety of classical and quantum properties of these theories and their multi-parameter extensions drawing in part on arXiv:1711.00084; arXiv:1706.05322

I will explain how the notion of T-duality can be generalised to the case of a non-abelian isometry group and applied as a solution generating symmetry to type II supergravity backgrounds involving RR flux. I will show some novel mappings between IIB and (massive) IIA supergravity and apply the technique to backgrounds of importance in the context of the gauge/gravity correspondence. In particular we will find some surprising connections between $AdS_5\times S^5$ and the geometry proposed by Gaiotto and Maldacena as dual to certain N=2 SCFT's and between the Klebanov-Witten background ($AdS_5 \times T^{1,1}$) and the geometries discussed already in this seminar series by Wecht as dual to certain N=1 SCFT's. Time permitting I will describe some recent developments relating to the gravity duals of cascading gauge theories.