An overview of derived analytic geometry

          @misc{ scivideos_PIRSA:16040071,
            doi = {10.48660/16040071},
            url = {https://pirsa.org/16040071},
            author = {Porta, Mauro},
            keywords = {Mathematical physics},
            language = {en},
            title = {An overview of derived analytic geometry},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2016},
            month = {apr},
            note = {PIRSA:16040071 see, \url{https://scivideos.org/pirsa/16040071}}
          }
          

Abstract

After the pioneering work of J. Lurie in [DAG-IX], the possibility of a derived version of analytic geometry drew the attention of several mathematicians. The goal of this talk is to provide an overview of the state of art of derived analytic geometry, addressing both the complex and the non-archimedean setting. After providing a series of motivations for derived analytic geometry, I will survey the main results obtained in my PhD thesis: derived versions of GAGA theorems, the existence of the analytic cotangent complex and an analytic version of Lurie's representability theorem. If time will permit, I will conclude the talk by discussing the possible future directions. Parts of the results I will talk about have been obtained in collaboration with T. Y. Yu.