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A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the d-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information-transmission. Joint work with Robert Koenig.

Single field inflation with derivative interactions provides a class of scenarios with interesting theoretical and observational properties. I will discuss properties of correlation functions in generic single field models and the implications of those relationships for inflationary observables, as well as for eternal inflation

Key notions from statistical physics, such as "phase transitions" and "critical phenomena", are providing important insights in fields ranging from computer science to probability theory to epidemiology. Underlying many of the advances is the study of phase transitions on models of networks. Starting from the classic ideas of Erdos and Renyi, recent attempts to control and manipulate the nature of the phase transition in network connectivity will be discussed. Next, the influence of self-organization on phase transitions will be presented, as well as connections between the jamming transition in models of granular materials and constraint satisfaction problems in computer science. Finally, turning to network growth, I will show that local optimization can play a fundamental role leading to the mechanism of Preferential Attachment, which previously had been assumed as a basic axiom and, furthermore, resolves a long standing controversy between Herb Simon and Benoit Mandelbrot.

We investigate the feasibility of explosive particle production via parametric resonance or tachyonic preheating in multi-field inflationary models by means of lattice simulations. We observe a strong suppression of resonances in the presence of four-leg interactions between the inflaton fields and a scalar matter field, leading to insufficient preheating when more than two inflatons couple to the same matter field. This suppression is caused by a dephasing of the inflatons that increases the effective mass of the matter field. Including three-leg interactions leads to tachyonic preheating, which is not suppressed by an increase in the number of fields. If four-leg interactions are sub-dominant, we observe a slight enhancement of tachyonic preheating. Thus, in order for preheating after multi-field inflation to be efficient, one needs to ensure that three-leg interactions are present. If no tachyonic contributions exist, we expect the old theory of reheating to be applicable.

Modifications of the initial-state of the inflaton field can induce a departure from Gaussianity and leave a testable imprint on the higher order correlations of the CMB and large scale structures in the Universe. I will discuss general vacuum state modifications in the case of a canonical single-field action, after adding a dimension 8 higher order derivative term, and DBI models of inflation. Observed bounds on local and equilateral non-Gaussianities, even though they correspond to template shapes that are far from optimal, can lead to constraints that are already competing to those derived from the power spectrum alone, due to enhancement effects. We emphasize that the construction and application of especially adapted templates could lead to significant improvements in the CMB bispectrum constraints on modified initial states.

Gauge theories with deformed products of fields in the lagrangian constitute an interesting generalization of the gauge/string duality. We review a systematic procedure to find the string duals of such theories, called the TsT transformation, and illustrate its properties by means of a few examples.

In my talk I will provide an overview of the applications of Wilson's modern renormalization group (RG) to problems in quantum gravity. I will first discuss the development of the RG for continuum gravity within the framework of Feynman's covariant path integral approach. Then I will discuss a number of issues that arise when implementing the path integral approach with an explicit lattice UV regulator, and later how non-perturbative RG flows and universal non-trivial scaling dimensions can in principle be extracted from these calculations. Towards the end I will discuss recent attempts at formulating RG flows for gravitational couplings within the framework of a set of manifestly covariant, but non-local, effective field equations suitable for quantum cosmology.

"A Hamiltonian action of a Lie group on a symplectic manifold $(M,\omega)$ gives rise to a gauge theoretic deformation of the Cauchy-Riemann equations, called the symplectic vortex equations. Counting solutions of these equations over the complex plane leads to a quantum version of the Kirwan map. In joint work with Christopher Woodward, we interpret this map as a weak morphism of cohomological field theories."