Abstract

In this talk, I will provide a brief introduction to algebraic K-theory.

The first part of the talk will focus on the K-theory of rings and Waldhausen categories. I will begin with K₀ and K₁, and then move on to higher K-theory, discussing their definitions, motivations, and examples. In the second part, I will introduce the language of -categories, which generalizes classical category theory by endowing higher morphisms. For example, a homotopy between continuous maps can be viewed as a 2 morphism, i.e., a morphism between morphisms.  Finally, I will briefly discuss the Grothendieck–Riemann–Roch theorem and its generalizations to higher K-theory and derived schemes.

 

Organizer: Adeel Khan (AS)