Current Understanding and Open Questions in Hot and Dense QCD Theory*

This talk aims to discuss the current knowledge and open queries in hot and dense Quantum Chromodynamics (QCD). Understanding QCD under extreme conditions is essential to reveal the early universe and the nature of dense cosmic objects like neutron stars. We will delve into the QCD phase diagram, addressing the interplay between confinement and deconfinement phases, as well as the phenomena of Quark-Gluon Plasma (QGP) and color superconductivity. We will introduce approaches to QCD phase diagrams using generalized global symmetries and discuss the current understanding of quark-hadron continuity at finite density. A significant theoretical challenge is understanding high-density and nonequilibrium QCD. This is largely due to the difficulties in analyzing Lattice QCD using Monte Carlo simulations, stemming from the so-called sign problem. We will present various innovative methods to overcome this problem, such as tensor network methods and quantum computation.