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In this talk, we will review recent efforts to probe spin–spin and spin–orbit entanglement at the upcoming Electron–Ion Collider (EIC). We will also discuss its connections to nucleon structure and high-energy QCD dynamics.

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In this lecture series I will give an overview of lattice QCD studies of hot nuclear matter with emphasis on heavy flavor probes. In the first lecture I will review the lattice QCD results on the deconfinement and chiral transitions, and the equation of state. In the subsequent lectures, I will discuss the nature of heavy flavor degrees of freedom across the transition temperature, the fate of heavy quark anti-quark bound states and heavy quark diffusion.

In this talk, I'll give a brief overview of the theory of probing the internal structure of the nucleon in 3D at the upcoming electron-ion collider (EIC).

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Multi-body QCD exhibits rich and complex phenomenology, notably in the Quark-Gluon Plasma (QGP) at high temperature, which is generated in nuclear collisions at RHIC and the LHC; and at high density, corresponding to low momentum fraction x in hadrons and nuclei, which can be probed by forward RHIC and LHC measurements and the future Electron-Ion Collider. These lectures will explore how we study multi-body QCD by combining experiment and theory. The focus of the first two lectures is the measurement of jet quenching, the interaction of energetic quark and gluon jets with the QGP. The third lecture discusses a comprehensive analysis of the world’s jet quenching data using Bayesian Inference enhanced by Machine Learning, to quantify the structure and dynamics of the QGP. The fourth lecture turns to many-body QCD at low x, presenting a new framework for the comprehensive analysis of Deep Inelastic Scattering and hadron collider data - likewise using ML-enhanced Bayesian Inference - to search for evidence of non-linear QCD evolution and gluon saturation.

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Multi-body QCD exhibits rich and complex phenomenology, notably in the Quark-Gluon Plasma (QGP) at high temperature, which is generated in nuclear collisions at RHIC and the LHC; and at high density, corresponding to low momentum fraction x in hadrons and nuclei, which can be probed by forward RHIC and LHC measurements and the future Electron-Ion Collider. These lectures will explore how we study multi-body QCD by combining experiment and theory. The focus of the first two lectures is the measurement of jet quenching, the interaction of energetic quark and gluon jets with the QGP. The third lecture discusses a comprehensive analysis of the world’s jet quenching data using Bayesian Inference enhanced by Machine Learning, to quantify the structure and dynamics of the QGP. The fourth lecture turns to many-body QCD at low x, presenting a new framework for the comprehensive analysis of Deep Inelastic Scattering and hadron collider data - likewise using ML-enhanced Bayesian Inference - to search for evidence of non-linear QCD evolution and gluon saturation.

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Multi-body QCD exhibits rich and complex phenomenology, notably in the Quark-Gluon Plasma (QGP) at high temperature, which is generated in nuclear collisions at RHIC and the LHC; and at high density, corresponding to low momentum fraction x in hadrons and nuclei, which can be probed by forward RHIC and LHC measurements and the future Electron-Ion Collider. These lectures will explore how we study multi-body QCD by combining experiment and theory. The focus of the first two lectures is the measurement of jet quenching, the interaction of energetic quark and gluon jets with the QGP. The third lecture discusses a comprehensive analysis of the world’s jet quenching data using Bayesian Inference enhanced by Machine Learning, to quantify the structure and dynamics of the QGP. The fourth lecture turns to many-body QCD at low x, presenting a new framework for the comprehensive analysis of Deep Inelastic Scattering and hadron collider data - likewise using ML-enhanced Bayesian Inference - to search for evidence of non-linear QCD evolution and gluon saturation.

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Heavy quarks are unique probes of the transport properties and hadronization of the quark–gluon plasma formed in ultra-relativistic heavy-ion collisions, but their strong coupling to the evolving medium requires a multi-ingredient approach for reliable descriptions of in-medium interactions. I will present a newly developed framework [1] that combines state-of-the-art ingredients for heavy-flavor transport in hot QCD matter. It couples lattice-QCD–constrained T-matrix based elastic scattering to relativistic Langevin dynamics with diffusion and medium-induced gluon radiation, embedded in a 2+1D viscous hydrodynamic evolution. Hadronization is evaluated with a four-momentum conserving recombination approach supplemented with fragmentation constrained by proton–proton data, followed by diffusion in the hadronic phase using the Ultra-relativistic-Quantum-Molecular-Dynamics (UrQMD) model. I will report our recent results for charm-hadron nuclear modification factors, elliptic flow, and charm hadro-chemistry ratios, and compare them to Pb–Pb data at 5 TeV from ALICE and CMS as well as Au–Au data at 200 GeV from STAR. Constraints on heavy-flavor diffusion coefficient in hot QCD matter are discussed. [1]: T. Krishna, R. Rapp, Y. Fu, S. A. Bass, and W. Ke, Phys. Lett. B 871,(2025)(139999)

Multi-body QCD exhibits rich and complex phenomenology, notably in the Quark-Gluon Plasma (QGP) at high temperature, which is generated in nuclear collisions at RHIC and the LHC; and at high density, corresponding to low momentum fraction x in hadrons and nuclei, which can be probed by forward RHIC and LHC measurements and the future Electron-Ion Collider. These lectures will explore how we study multi-body QCD by combining experiment and theory. The focus of the first two lectures is the measurement of jet quenching, the interaction of energetic quark and gluon jets with the QGP. The third lecture discusses a comprehensive analysis of the world’s jet quenching data using Bayesian Inference enhanced by Machine Learning, to quantify the structure and dynamics of the QGP. The fourth lecture turns to many-body QCD at low x, presenting a new framework for the comprehensive analysis of Deep Inelastic Scattering and hadron collider data - likewise using ML-enhanced Bayesian Inference - to search for evidence of non-linear QCD evolution and gluon saturation.

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We study direct photon production within a hybrid minijet-hydrodynamics framework that incorporates initial-state fluctuations and minijet-medium interactions. Using the IP-Glasma + MUSIC + UrQMD framework, and a dedicated photon emission module, we perform a comprehensive analysis of direct photon production. By including minijet effects in the hydrodynamic evolution, we examine the sensitivity of photon yields and elliptic flow to the dynamics of the quark-gluon plasma. Our results demonstrate the significant impact of hydrodynamic evolution on photon production, highlighting the essential role of minijet-medium interactions.

The main focus of the talk will be how non-equilibrium aspects of hot QCD matter (the quark–gluon plasma) produced in heavy-ion collisions affect the properties of heavy quarks.