Neutrino physics underwent a dramatic transformation over the past two decades. As recently as 1996, the Particle Data Group summary on neutrinos still read: "no direct, uncontested evidence for massive neutrinos or lepton mixing has been obtained". Yet, only four years later, the summary was quite different: "there is now rather convincing evidence that neutrinos have nonzero mass". The change was precipitated by the remarkable atmospheric neutrino data from SuperKamiokande released in the interim. During the following two years, the long-standing solar "problem" was also solved, in a spectacular and conclusive fashion. The flux deficit that had confounded physicists since the late sixties was shown to be caused by neutrino flavor oscillations. In the last ten years, 3-flavor oscillation effects were also observed and measured with reactor and beam neutrinos. By now, the mass-square splittings and the mixing parameters have been established with impressive accuracy and the subject has entered a high-precision era.
Neutrino masses represent one of the very few experimental clues regarding the physics that lies beyond the standard model. What they are telling us is still an open mystery. At the minimum, they indicate the presence of new particle states (right-handed neutrinos), the existence of the first dimension-5 operators in the Lagrangian (Majorana mass terms), or both. The ongoing neutrinoless double-beta decay searches may be able to shine light on the matter. But the neutrino sector could also contain additional surprises. Examples extensively discussed in the literature include additional light states or novel ("nonstandard") interactions. Such new physics can manifest itself in a variety of ways. For example, neutrino magnetic moments could provide additional channels of energy drain from stellar interiors, thus modifying the evolution of stars. Sterile neutrinos could manifest themselves as additional species in the CMB signals, or as missing flux at precision oscillation experiments. They can also cause "unexpected" transitions between active flavors in short-baseline experiments. New neutrino interactions could manifest themselves in distortions of the solar neutrino spectra, in precision long-baseline experiments, or at the LHC.
An especially rich problem is to understand what happens to neutrinos in a supernova environment. Here, neutrinos oscillate in a time-evolving background, with shocks and turbulent density fluctuations. They are also so dense that their mutual coherent forward scattering becomes physically important. The goal is to understand this rich physics, quantify its impact on the astrophysics and nucleosynthesis of the explosion, and identify the best signals for current and future neutrino detectors, include the far detector of the planned LBNE experiment.
Examples of our recent work include understanding the roles three-flavor instabilities  and geometric (multiangle) effects  play in collective oscillations of supernova neutrinos. We have also studied how nonstandard neutrino interactions could modify the signal at the NOvA and LBNE experiments , building on our earlier work in this area [4,5,6]. An example of this effect is shown in Fig. 1. On the collider front, we have derived constraints  on nonstandard interactions from the monojet and multi-lepton data collected at the Tevatron and the LHC.
Some of the ongoing work includes studies of the collective dynamics of supernova neutrinos, modeling of the supernova signal at LBNE and other detectors, and the physics of PeV astrophysical neutrinos recently detected at the IceCUBE experiment.
With the neutrino program poised to take a central role in the US HEP effort, there are great many theoretical issues that need urgent attention. For a sample set, see Ref. .
- A. Friedland, Self-refraction of supernova neutrinos: mixed spectra and three-flavor instabilities, Phys.Rev.Lett. 104 (2010) 191102.
- H. Duan and A. Friedland, Self-induced suppression of collective neutrino oscillations in a supernova, Phys.Rev.Lett. 106 (2011) 091101.
- A. Friedland and I. M. Shoemaker, Searching for Novel Neutrino Interactions at NOvA and Beyond in Light of Large theta13, arXiv:1207.6642 [hep-ph].
- A. Friedland, C. Lunardini and C. Pena-Garay, Solar neutrinos as probes of neutrino matter interactions, Phys.Lett. B 594, 347 (2004).
- A. Friedland and C. Lunardini, A Test of tau neutrino interactions with atmospheric neutrinos and K2K, Phys.Rev. D 72, 053009 (2005).
- A. Friedland and C. Lunardini, Two modes of searching for new neutrino interactions at MINOS, Phys.Rev. D 74, 033012 (2006).
- A. Friedland, M. L. Graesser, I. M. Shoemaker and L. Vecchi, Probing Nonstandard Standard Model Backgrounds with LHC Monojets, Phys.Lett. B 714, 267 (2012).
- A. de Gouvea, A. Friedland, P. Huber and I. Mocioiu, Opportunities in Neutrino Theory -- a Snowmass White Paper, arXiv:1309.7338 [hep-ph].