Elliptic cohomology and derived algebraic geometry
-- Jacob Lurie

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We will review the classical theory of elliptic cohomology, 
leading up to the construction of the spectrum of topological modular 
forms (tmf) by Hopkins and Miller. We will then introduce the language of 
derived algebraic geometry, and explain how it leads to a new (and easier) 
construction of tmf. If time permits, we will discuss various 
applications, such as the construction of equivariant elliptic cohomology.