"Recent progress in studying Entanglement Renormalization (ER) in the context of quantum information has led to a powerful ansatz to describe wave functions of complex quantum many-body systems. Dr. Tagliacozzo intends, with this project, to apply this ansatz to study Lattice Gauge Theories (LGT).LGT are relevant to different branches of physics: a) they constitute one of the few tools available to analyze the strongly coupled regime of Quantum Chromo Dynamics b) they play a prominent role in effective models for quantum material's antiferromagnetism and high temperature superconductivity; c) their phase diagrams are related to the stability of topological phases relevant for quantum computation.Present approaches to study LGT are mostly based on Monte Carlo (MC) simulations that incur in several limitations: 1) difficulty to directly extract information about quantum states wave functions such as their entanglement entropy or the expected value of non-local observables; 2) exponentially hard simulations of fermionic and frustrated systems; 3) very limited ability to perform time evolutions. These limitations prevent our complete understanding of LGT.By applying ER directly to the LGT Hamiltonian formulation, Dr. Tagliacozzo will provide new computational tools to override these limitations and gain access to: 1) scaling of the entanglement entropy and non local observables and fidelities, 2) simulations of LGT with either bosonic or fermionic matter and of frustrated LGT at the same computational cost; 3) time evolutions.In order to succeed with his objectives the candidate will have: 1) to expand the current theoretical framework of ER so that it can be applied to a LGT following his seminal paper; 2) develop the related numerical tools, 3) deploy them in massive simulations.The information the candidate will gather with his project will complement the current understanding of LGT based on MC simulations providing better insight of LGT in 2+1 dimensions."