Etera is a permanent researcher (Directeur de Recherche CNRS) at the Laboratoire de Physique of the Ecole Normale Supérieure de Lyon in France (, since 2005. He completed his PhD in 2003 on the spin foam path integral formalism for quantum gravity under the supervision of Carlo Rovelli  at the Centre de Physique Théorique in Marseille, France. He was later awarded the Bronze Medal of the CNRS in 2008 for his research work on quantum gravity, and more precisely on the loop quantum gravity approach. For instance, he introduced with Carlo Rovelli and collaborators the EPRL spinfoam model defining the transition amplitudes for quantum states of geometry in loop quantum gravity. He now goes on working on quantum gravity, mostly from a mathematical physics perspective, and its interfaces with quantum information, statistical physics and non-commutative geometry.

Talks by Etera Livine

3d Quantum Gravity: from tetrahedra to holography

Etera Livine École Normale Supérieure de Lyon (ENS Lyon)

3d quantum gravity is a beautiful toy-model for 4d quantum gravity: it is much simpler, it does not have local degrees of freedom, yet retains enough complexity and subtlety to provide a non-trivial example of dynamical quantum geometry and open new directions of research in physics and mathematics. I will present the Ponzano-Regge model, introduced in 1968, built from tetrahedra “quantized" as 6j-symbols from the theory of recoupling of spins.

How fundamental is the Immirzi parameter in Loop Quantum Gravity?

Etera Livine École Normale Supérieure de Lyon (ENS Lyon)

I will discuss the role(s) of the Immirzi parameter in Loop Quantum Gravity, insisting on the Poisson algebra formed by Thiemann's complexifier, the volume and the Hamiltonian constraint. In particular, we will see how loop quantum cosmology is a direct quantization of this CVH Poisson algebra and how cosmological evolution amounts to a flow in the Immirzi parameter.

Spinor and Twistor Networks in Loop Gravity

Etera Livine École Normale Supérieure de Lyon (ENS Lyon)
I will review the reformulation of the loop gravity phase space in terms of spinor networks and twistor networks, and present how these techniques can be used to write spinfoam amplitudes as discretized path integrals and to study the dynamics that they define (recursion, Hamiltonian constraints as differential equations).

A review of Spinfoams and Group Field Theory

Etera Livine École Normale Supérieure de Lyon (ENS Lyon)
We will review the definitions of spin foam models for quantum gravity and the recent advances in this field, such as the "graviton propagator", the definition of coherent states of geometry and the derivation of non-commutative field theories as describing the effective dynamics of matter coupled to quantum gravity. I will insist on the role of group field theories as providing a non-perturbative definition of spinfoams and their intricate relation with non-commutative geometry and matrix models.

The U(N) structure of Loop Quantum Gravity

Etera Livine École Normale Supérieure de Lyon (ENS Lyon)
It has recently uncovered that the intertwiner space for LQG carries a natural representation of the U(N) unitary group. I will describe this U(N) action in details and show how it can be used to compute the LQG black hole entropy, to define coherent intertwiner states and to reformulate the LQG dynamics in new terms.