In algebraic geometry, one often encounters the question of infinitesimally deforming an object of interest such as varieties and coherent sheaves, and classical deformation theory offers one framework to answer such questions.
In this talk, I will introduce a more modern perspective of deformation theory via derived algebraic geometry and give some motivations for taking this alternative perspective as well as applications without delving into technical details. The knowledge of derived algebraic geometry will not be assumed, and I also plan to review classical deformation theory in the talk as well.