Report from ARIES Muon Collider Workshop in Padua

Several novel concepts could help the muon collider become a reality. These concepts include parametric ionization cooling, low-emittance muon production by positron annihilation (LEMMA scheme), production of low-emittance muon or positron beams using the Gamma Factory concept, and strategies to upgrade large accelerator complexes, like the LHC or the FCC, into a highest-energy muon collider. The muon collider workshop organized by ARIES APEC at Padua in July 2018 gathered the international community in order to review the recent progress and to formulate a common R\&D; strategy. Several important conclusions and recommendations were drawn.