Talks

Tensor models appear as the higher dimensional extension of the so-called matrix models describing 2D quantum gravity through the sum over triangulations of surfaces. In the light of the recent $1/N$ expansion for these tensor models, we uncover a new class of tensor models for 4D and 3D gravity which are renormalizable at all orders of perturbation theory. An overview of two papers, [arXiv:1111.4997 [hep-th]] and [arXiv:1201.0176 [hep-th]], on the renormalization of these tensor models and their beta function will be given.

Group field theories show up as a higher dimensional generalization of matrix models in background independent approaches to quantum gravity.
Their Feynman expansion generates simplicial complexes of all topologies weighted by spin foam amplitudes.
In this talk, we will present a dual formulation of these theories as non-commutative quantum fields theories, whose variables have a clear interpretation in terms of simplicial geometry. We will show that it gives a geometrically clear ways to define spin foam models for gravity which can be cast as

Recent years have seen a renewed interest, both theoretically and experimentally, in the search for topological states of matter. On the theoretical side, while much progress has been achieved in providing a general classification of non-interacting topological states, the fate of these phases in the presence of strong interactions remains an open question. The purpose of this talk is to describe recent developments on this front. In the first part of the talk, we will consider, in a scenario with time-reversal symmetry breaking, dispersionless electronic Bloch bands (flatbands) with non-zero Chern number and show results of exact diagonalization in a small system at 1/3 filling that support the existence of a fractional quantum Hall state in the absence of an external magnetic field. In the second part of the talk, we will discuss strongly interacting electronic phases with time-reversal symmetry in two dimensions and propose a candidate topological field theory with fractionalized excitations that describes the low energy properties of a class of time-reversal symmetric states.