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For nearly 40 years, dark matter has been widely assumed to be cold andcollisionless. Cold dark matter models make fundamental predictions for thebehavior of dark matter on small (<10 kpc) scales. These predictions includecuspy density profiles at the centers of dark matter halos and a halo massfunction that increases as dN/dM ~ M^-1.9 down to very small masses. We suggesttwo observational programs relying on extremely large telescopes to criticallytest these predictions, and thus shed new light on the nature of dark matter.(1) Combining adaptive optics-enabled imaging with deep spectroscopy to measurethe three-dimensional motions of stars within a sample of Local Group dwarfgalaxies that are the cleanest dark matter laboratories known in the nearbyuniverse. From these observations the inner slope of the dark matter densityprofile can be determined with an accuracy of 0.20 dex, enabling a central cuspto be distinguished from a core at 5 sigma significance. (2)Diffraction-limited AO imaging and integral field spectroscopy ofgravitationally lensed galaxies and quasars to quantify the abundance of darksubstructures in the halos of the lens galaxies and along the line of sight.Observations of 50 lensed arcs and 50 multiply-imaged quasars will besufficient to measure the halo mass function over the range 10^7 < M < 10^10Msun at cosmological scales, independent of the baryonic and stellarcomposition of those structures. These two observational probes providecomplementary information about the small scale structure, with a jointself-consistent analysis mitigating limitations of either probe. This programwill produce the strongest existing constraints on the properties of darkmatter on small scales, allowing conclusive tests of alternative warm, fuzzy,and self-interacting dark matter models.

Testing the Nature of Dark Matter with Extremely Large Telescopes