Gabriel Conant

Research Associate
C2.06, DPMMS
Centre for Mathematical Sciences
University of Cambridge

gconant@maths.cam.ac.uk
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Easter Term 2020

Applications of Pseudofinite Model Theory

Time: MWF 16:00 (Cambridge)

Dates: Friday 24 April through Wednesday 20 May (12 lectures)

Location: Online via Zoom

Description
This course will cover recent applications of pseudofinite model theory in the setting of group theory and arithmetic combinatorics. We will begin with a brief introduction to several key ingredients from model theory, including: We will then focus on the main result of arXiv 1802.04246, which gives a structural approximation of NIP sets in finite groups by Bohr neighborhoods of bounded complexity in subgroups of bounded index.

Logistics Prerequisites and Resources
I will assume prior knowledge of first-order logic and basic model theory, including the notions of first-order languages, structures, and the Compactness Theorem. In addition, the following is suggested reading: In general, Model Theory: An Introduction (by Dave Marker) is a good resource for the model theoretic prerequisites of the course. I believe this book is available online from the Cambridge university library (via Proquest). The following are some other online notes on model theory. The only other prerequisite for the course is basic topology, including topological groups. Some parts of the course will use more sophisticated results on the structure of compact groups (e.g., the Peter-Weyl Theorem), which can mostly be treated as black boxes. The following resources may also be helpful: