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Explore theoretical developments in levitated optomechanics with nanoparticles through this colloquium talk delivered by Professor Mishkat Bhattacharya at the Raman Research Institute. Delve into the principles of cooling and regenerative center-of-mass motion (phonon lasing) theory, examining their applications in experiments conducted at the University of Rochester under A. N. Vamivakas. Learn from the insights of an NSF Career award recipient (2015) and contributor to one of the Breakthroughs of the Year by Optics and Photonics magazine (2019), as he shares his expertise in theoretical quantum optics developed at the Rochester Institute of Technology.