Week 11, Tuesday 25th March and Thursday 27th March
Amit Kuber $K$-theory of model theoretic structures
There will be three talks:
Tuesday, 1000, MALL1: Introduction to algebraic $K$-theory
Tuesday, 1400, MALL2: Grothendieck rings of structures
Thursday, 1000, MALL2: $K$-theory of model theoretic structures
Grothendieck introduced algebraic $K$-groups for the purpose of the classification of rings, and this idea was developed further by Quillen which won him a Fields medal. In the first talk I will give a brief overview of the interplay between algebra, topology and category theory and explain some key concepts in algebraic $K$-theory.
Taking a clue from Krajicek and Scanlon's definition of the Grothendieck ring of a model-theoretic structure, I will explain how the general machinery of Quillen's $K$-theory can be applied to classify model-theoretic structures. Direct computations in the case of modules will be shown with an emphasis on the role that (partial) elimination of quantifiers plays in the analysis.