國立清華大學 數學系

Abstract:
In this talk, I will begin by introducing the language of \infty-categories, which generalizes classical category theory by endowing higher morphisms. For instance, a homotopy between continuous maps can be viewed as a 2-morphism—that is, a morphism between morphisms. I will then define the K-theory of an \infty-category, which captures the behavior of these higher morphisms. Toward the end of the talk, I will briefly discuss the Grothendieck–Riemann–Roch theorem and its generalization to higher K-theory and derived schemes.