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A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies. 

Abstract The crystal structure, electron energy-loss spectroscopy (EELS), heat capacity, and anisotropic magnetic and resistivity measurements are reported for Sn flux grown single crystals of orthorhombic Pr₂Co₃Ge₅(U₂Co₃Si₅-type,Ibam). Our findings show thato-Pr₂Co₃Ge₅hosts nearly trivalent Pr ions, as evidenced by EELS and fits to temperature dependent magnetic susceptibility measurements. Complex magnetic ordering with a partially spin-polarized state emerges nearT_sp= 32 K, with a spin reconfiguration transition nearT_M= 15 K. Heat capacity measurements show that the phase transitions appear as broad peaks in the vicinity ofT_spandT_M. The magnetic entropy further reveals that crystal electric field splitting lifts the Hund’s rule degeneracy at low temperatures. Taken together, these measurements show that Pr₂Co₃Ge₅is an environment for complexfstate magnetism with potential strongly correlated electron states.