Spectral Lie algebras and unstable homotopy theory

In this talk I will review spectral Lie algebras, an adaptation of the theory of Lie algebras to the category of spectra. These generalize differential graded Lie algebras over the rational numbers and admit similar applications in derived algebraic geometry and homotopy theory. As an example of this, I will discuss their role as algebraic models for spaces, generalizing Quillen's rational homotopy theory.

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