Talks

Studying the usefulness of resources can be formalized via the framework of a resource theory. However, the complete answer to the question whether a certain resource is more useful than another one is often hard to find in many of the numerous applications of the framework. Approximate answers can be found by identifying so-called monotones—measures of "resourcefulness". I will present several generic constructions of monotones, of which many monotones known in the literature are concrete examples of. These constructions provide a way to relate monotones in different resource theories, thus enabling for the translation of results between them.

 One of the most important discoveries of the 20th century has been the finding of neutrino oscillations. That phenomena implies that neutrinos are massive and shows the existence of physics beyond the standard model. Fundamental questions associated to this discovery are: what are the absolute neutrino masses? and what is their hierarchy? In this talk I will discuss how to use cosmological observables to answer these questions. I will first show one of the predictions of the Big Bang theory: the existence of a cosmic neutrino background. I will then present the effects that it introduces on several cosmological observables such as the matter power spectrum, halo/galaxy properties, cluster counts, halo/galaxy clustering and cosmic voids. I will show how to use these effects to weigh neutrinos. I will emphasize the importance of having accurate theory predictions, and to search for new observables, in order to achieve a 5-sigma detection of the minimum sum of the neutrino masses.

Simplicial complexes naturally describe discrete topological spaces. When their links are assigned a length they describe discrete geometries. As such simplicial complexes have been widely used in quantum gravity approaches that involve a discretization of spacetime. Recently they are becoming increasingly popular to describe complex interacting systems such a brain networks or social networks. In this talk we present non-equilibrium statistical mechanics approaches to model large simplicial complexes. We propose the simplicial complex model of Network Geometry with Flavor (NGF), we explore the hyperbolic nature of its emergent geometry and their relation with Tree Tensor Networks. Finally we reveal the rich interplay between Network Geometry with Flavor and dynamics. We investigate the percolation properties of NGF using the renormalization group finding KTP and discontinuous phase transitions depending on the dimensionality simplex. We also comment on the synchronization properties of NGF and the emergence of frustrated synchronization.

In quanum physics, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by smoothed min- or max-entropies. In this talk, I will discuss new results that give single-shot interpretations to the von Neumann entropy under appropriate conditions. I first present new results that give a single-shot interpretation to the Area Law of entanglement entropy in many-body physics in terms of compression of quantum information on the boundary of a region of space. Then I show that the von Neumann entropy governs single-shot transitions whenever one has access to arbitrary auxiliary systems, which have to remain invariant in a state-transition ("catalysts"), as well as a decohering environment. Getting rid of the decohering environment yields the "catalytic entropy conjecture", for which I present some supporting arguments.

If time permits, I also discuss some applications of these result to thermodynamics and speculate about consequences for quantum information theory and holography.

I will present recent results (with Zhen Bi) on novel quantum criticality and a possible field theory duality in 3+1 spacetime dimensions. We describe several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D.   We present situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility - which we dub “unnecessary quantum critical points” - of stable generic continuous phase transitions within the same phase. We present examples of interaction driven band-theory- forbidden continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3 + 1-D field theory duality between SU(2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.