# Model Theory Seminar

### School of Mathematics, University of Leeds

There are three seminars this week. We will meet about twenty minutes before each seminar in the common room for tea and coffee.

The seminar is organised by Will Anscombe.

### Spring Term 2014

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.