Recent Advances on the Two-Dimensional Hubbard Model

The Hubbard model is a paradigm of the `strong correlation problem', with relevance to high-T_c superconductors and ultra-cold atoms in optical lattices. Key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods working in synergy (such as quantum embedding, tensor networks, various flavors of quantum Monte Carlo and, recently, neural quantum states). I will review some of these recent developments in this presentation and highlight open questions.