Learn about fundamental concepts in derived algebraic geometry through a seminar talk that explores prestacks, tangent complexes, and their key properties. Delve into specialized topics including quasi-smooth derived schemes and examine the singular support of ind-coherent sheaves. During this 2-hour lecture delivered by Akhil Mathew on April 3rd, 2024, gain insights into these advanced mathematical constructions and their interconnections within the field of algebraic geometry.