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The purpose of the Low-$x$ Workshop series is to stimulate discussions between experimentalists and theorists in diffractive hadronic physics, QCD dynamics at low $x$, parton saturation, and exciting problems in QCD at HERA, Tevatron, LHC, RHIC, and the future EIC. The central topics of the workshop, summarized in the current Proceedings, were: Diffraction in ep and e-ion collisions (including EIC physics); Diffraction and photon-exchange in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions; Spin Physics; Low-$x$ PDFs, forward physics, and hadronic final states. This Workshop has been the XXVIII edition in the series of the workshop., Comment: The 2021 edition of the Low-$x$ International Workshop took place from September 26 to October 1 in Elba, Italy. Contains arXiv:2202.03724, arXiv:2111.04515, arXiv:2112.07827, arXiv:2110.05081, arXiv:2112.11054, arXiv:2112.13794, arXiv:2111.13916, arXiv:2201.06948, arXiv:2201.05224, arXiv:2202.04207, arXiv:2205.08785

At LHCb, proton parton distribution functions (PDFs) can be studied in a unique phase space complementary to that accessible by ATLAS and CMS, corresponding to low and high values of Bjorken-$x$. The measurements of vector boson production in the forward region, with and without an associated jet, are presented. These measurements can be used to constrain the proton PDFs, and in particular, the production of a $Z$ boson in association with a $c$-jet can be studied to measure the intrinsic charm content of the proton., Comment: Presented at the Low-$x$ Workshop, Elba Island, Italy, September 27 $-$ October 1 2021