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 In the framework of ontological models, the features of quantum

theory that emerge as inherently nonclassical always involve properties that

are fine tuned, i.e.  properties that hold at the operational level but break at the

ontological level (they only hold for fine tuned values of the ontic parameters). Famous

examples of fine tuned properties are noncontextuality and locality. We here

develop a precise theory-independent mathematical framework for characterizing

operational fine tunings. These are distinct from causal fine tunings — already

introduced by Wood and Spekkens — as they do not involve any assumption

on the underlying causal structure. We show how all the already known examples of

operational fine tunings fit into our framework, we discuss possibly new fine tunings

and we use the framework to shed new light on the relation between nonlocality

and generalized contextuality. The framework is set in the language of functors in category

theory and it aims at unifying the spooky properties of quantum theory as well as

accounting for new ones.

Magnetic skyrmions are topological solitons which occur in a large class of ferromagnetic materials and which  are currently attracting much attention, not least because of their potential use for  low-energy magnetic information storage and manipulation. The talk is about an integrable model for magnetic skyrmions, introduced in a recent paper (arxiv:1812.07268) and generalised in  arxiv:1905.06285. The model is based on a geometrical interpretation of the Dzyaloshinskii-Moriya interaction in terms of a non-abelian gauge field.  In the talk will explain the model and the geometry behind its solution, and discuss solutions and their applications.

I will discuss recent developments in describing the chiral algebras associated to 4d N=2 theories introduced by Beem et al. in terms of Omega backgrounds, and give a description of the class S chiral algebras following this perspective, in terms of boundary conditions, interfaces, and junctions in 4d N=4 SYM.

Then, I will present work in progress on a general TFT-type procedure for calculating the factorization algebras describing 2d CFTs which arise as compactifications of such configurations. I will show that this method correctly computes the class S chiral algebras, matching the construction of Arakawa, and discuss potential applications to computing the vertex algebras associated to toric divisors in toric CY3s, following Gaiotto-Rapcak.

Schur-Weyl duality, arising from tensor-power representations of the unitary group, is a big useful hammer in the quantum information toolbox. This is especially the case for problems which have a full unitary invariance, say, estimating the spectrum of a quantum state from a few copies. Many problems in quantum computing have a smaller symmetry group: the Clifford group. This talk will show how to decompose tensor-power Clifford representations through a Schur-Weyl type construction. Our results are also relevant for the theory of Howe duality between symplectic and orthogonal groups.