I will discuss recent results on collective behaviour of N particles repelling each other via pairwise interaction potential and confined by an external harmonic trap. I will discuss the large-N field theory for all-to-all coupling  and the finite ranged case . These family of models contain in them various well known systems of interest both in physics and mathematics such as one component plasma, Dyson's log-gas, and the integrable Calogero-Moser model to name a few. I will also present results in the presence of a barrier . I will then discuss gap statistics (analogous to the well known level spacing statistics) in these family of models . In the end, I will present some preliminary results that show how the derived large-N theory can be used to understand collective non-equilibrium dynamics of these interacting particles.
 S. Agarwal, A. Dhar, M. Kulkarni, A. Kundu, S. N. Majumdar, D. Mukamel, G. Schehr, Phys. Rev. Lett. 123, 100603 (2019), Editors' Suggestion
 A. Kumar, M. Kulkarni, A. Kundu, Phys. Rev. E 102, 032128 (2020)
 J. Kethepalli, M. Kulkarni, A. Kundu, S. N. Majumdar, D. Mukamel, G. Schehr, arXiv:2107.00524 (2021)
 S. Santra, J. Kethepalli, S. Agarwal, A. Dhar, M. Kulkarni, A. Kundu, S. N. Majumdar, and G. Schehr [in preparation]