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The inner ear is a remarkable detector of sound waves, sensitive to signals that vary over 3 orders of magnitude in frequencies and 6 orders in pressure. This detection furthermore occurs in a noisy and highly viscous environment, as the sensory cells – the hair cells – are immersed in a fluid compartment, at room temperature or higher. It was proposed that this sensitivity is achieved by poising the system close to a critical point described by a Hopf bifurcation. I present a new model based on a different bifurcation that can likewise act as an amplifier, and compare the performance with previously suggested models as well as with experimental data, obtained both in vivo and in vitro. This new approach leads to predictions that are in agreement with experiments. In addition, I will demonstrate that ambient noise enhances the detection sensitivity of this mechanism.

Continuous phase transitions, in which the order parameter changes continuously at the transition, exhibit universal features such as critical exponents. This universality is deeply related to the divergence of a length scale. On the other hand first order transitions, in which the order parameter is discontinuous, are not associated with diverging length scales and hence they are non-universal. This dichotomy fails in quite a number of models which exhibit phase transitions of mixed nature, namely transitions which on the one hand exhibit a diverging correlation length and on the other hand display a discontinuous order parameter. Examples include models of wetting, glass and jamming transitions, DNA denaturation, rewiring networks and some one-dimensional models with long-range interactions.
An exactly soluble Ising model which provides a link between some of these rather distinct classes of systems is introduced and analyzed through exact calculations and renormalization group (RG) analysis. The RG analysis reveals an intriguing connection between Bose Einstein condensation type transitions and Kosterlitz-Thouless type transitions in one dimension.

The Renyi entropy is a generalization of entanglement entropy which can be used to further characterize the ground state of a quantum field theory. I'll present an observable, analogous to the Renyi entropy, which is defined for a 3d gauge theory preserving four supercharges, and which preserves a subset of the supersymmetry. Using localization techniques, this supersymmetric Renyi entropy can be calculated exactly for a variety of strongly coupled 3d gauge theories. I’ll present the results of this calculation and some examples from interesting 3d models.