Chirantan Chowdhury (TU Darmstadt)

The six functor formalism was formulated by Grothendieck to give a framework for the basic operations and duality statements for cohomology theories. In this talk, I shall give an overview of abstract six-functor formalisms in the language of $\infty$-categories followed by its applications in the setting of Motivic Homotopy Theory. After introducing the setup, we shall show how one can extend such formalism from smaller to larger categories (for e.g. : schemes to algebraic stacks). If time permits, I would like to explain further extensions of such results to non-representable situations (joint work with Alessandro D’Angelo).