Increasingly, scholars seek to integrate legal and technological insights to combat bias in AI systems. In recent years, many different definitions for ensuring non-discrimination in algorithmic decision systems have been put forward. In this paper,
we first briefly describe the EU law framework covering cases of algorithmic discrimination. Second, we present an algorithm that harnesses optimal transport to provide a flexible framework to interpolate between different fairness definitions. Third, we show that important normative and legal challenges remain for the implementation of algorithmic fairness interventions in real-world scenarios. Overall, the paper seeks to contribute to the quest for flexible technical frameworks that can be adapted to varying legal and normative fairness constraints.
Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstat
e geometries. This question is complicated by the fact that Lyapunov growth of OTOCs requires nonzero temperature, whereas constructions of microstate geometries have been mostly restricted to extremal black holes. In this paper, we compute OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display slow scrambling, characterized by cubic (rather than exponential) growth. Superposed on this average power-law growth is a sawtooth pattern, whose steep parts correspond to brief periods of Lyapunov growth associated to the nonzero temperature of the right-moving degrees of freedom in a dual conformal field theory. Next we study the extent to which these OTOCs are modified in certain superstrata, horizonless microstate geometries corresponding to these black holes. Rather than an infinite throat ending on a horizon, these geometries have a very deep but finite throat ending in a cap. We find that the superstrata display the same slow scrambling as maximally rotating BTZ black holes, except that for large enough time intervals the growth of the OTOC is cut off by effects related to the cap region, some of which we evaluate explicitly.
We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute a
symptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u(1) current algebras and recover the surprisingly simple entropy formula $S=2pi (J_0^+ + J_0^-)$, where $J_0^pm$ are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.
