Model Theoretic Tameness in Multiplicative Combinatorics

Explore model theoretic tameness in multiplicative combinatorics through this 50-minute Association for Symbolic Logic Invited Address given by Gabriel Conant from Cambridge University at the Joint Mathematics Meetings. Delve into topics such as products of subsets of groups, Freiman-Ruzsa structure theorems, stable subsets of finite and infinite groups, stability and tripling in arbitrary groups, descending stabilizers of stable sets, and the relationship between stability and discreteness. Examine the quantitative structure of stable sets and the NIP case, gaining insights into how model theory intersects with combinatorial number theory and group theory.

Intro
Products of subsets of groups
Freiman-Ruzsa structure theorems
Other groups
Stable subsets of finite groups
Finite stable subsets of infinite groups
Stability and tripling in arbitrary groups
Descending stabilizers of stable sets
Stability and discreteness
Putting it all together
Quantitative structure of stable sets
The NIP case