Photometric Redshift Challenges: Rubin Observatory and Beyond*

Most probes of cosmology rely on determining the relationship between some observable quantity and redshift.  For many experiments such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), those redshifts must be inferred based on information from imaging.  The resulting photometric redshift estimates -- also known as photo-z's -- have substantial uncertainties and can be biased.  In this talk I will highlight some of the foremost challenges we will face in using photometric redshifts from next-generation experiments, as well as key avenues for progress.  We wish both to improve the performance of photo-z methods -- i.e., how well we can predict the redshifts of individual objects -- as well as the statistical characterization of redshift distributions, as associated uncertainties may be a dominant systematic. I will highlight new progress we have made on improving the fidelity of predictions for redshift probability distribution functions via machine learning-based methods, ensuring that they in fact fulfill the statistical definition of a PDF; these methods can be applied to PDF predictions made for any purpose.  I will also describe the role that spectroscopic campaigns with an improved DESI instrument or a Stage V Spectroscopic Facility (Spec-S5) could play in improving both the performance and characterization of photo-z's.