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We discuss novel ways in which neutrino oscillation experiments can probedark matter. In particular, we focus on interactions between neutrinos andultra-light ("fuzzy") dark matter particles with masses of order $10^{-22}$ eV.It has been shown previously that such dark matter candidates arephenomenologically successful and might help ameliorate the tension betweenpredicted and observed small scale structures in the Universe. We argue thatcoherent forward scattering of neutrinos on fuzzy dark matter particles cansignificantly alter neutrino oscillation probabilities. These effects could beobservable in current and future experiments. We set new limits on fuzzy darkmatter interacting with neutrinos using T2K and solar neutrino data, and weestimate the sensitivity of reactor neutrino experiments and of futurelong-baseline accelerator experiments. These results are based on detailedsimulations in GLoBES. We allow the dark matter particle to be either a scalaror a vector boson. In the latter case, we find potentially interestingconnections to models addressing various $B$ physics anomalies.

Fuzzy Dark Matter and Non-Standard Neutrino Interactions