Urbana Campus Research Calendar (OVCRI)

The question of representability for moduli problems is a central one in algebraic geometry, and spectral algebraic geometry is no exception to this. The most significant tool we have in this regard is what I call the "spectral deformation of representability". This theory, developed by Jacob Lurie, allows us to use deformation theory to reduce spectral moduli problems to their classical analogues. I will give a general overview of the theory, then describe an application from my own research: the representability of the Hilbert functor of a spectral algebraic space.