Lurie, Jacob A.Brantner, David Lukas Benjamin2019-08-092017-052017-05-132017Brantner, David Lukas Benjamin. 2017. The Lubin-Tate Theory of Spectral Lie Algebras. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.http://nrs.harvard.edu/urn-3:HUL.InstRepos:41140243We use equivariant discrete Morse theory to establish a general technique in poset topology and demonstrate its applicability by computing various equivariant properties of the partition complex and related posets in a uniform manner. Our technique gives new and purely combinatorial proofs of results on algebraic and topological Andr\'{e}-Quillen homology. We then carry out a general study of the relation between monadic Koszul duality and unstable power operations. Finally, we combine our techniques to compute the operations which act on the homotopy groups K(n)-local Lie algebras over Lubin-Tate space.application/pdfenMorava E-theory, Lubin-Tate space, spectral Lie algebras, poset topology, discrete Morse theory, Andre-Quillen homology, monoids, Koszul dualityThesis or Dissertation2019-08-09