Topics in relational Hrushovski constructions
Omer Mermelstein, Fall 2018
The spine of the course will consist of an exposition of the original constructions and their background, an exploration of their associated geometries (finitary matroids), and reduction relations (in the sense of 'reduct') between variations on the constructions. Other isolated topics/results (within the course) we may touch upon include: gammoids and flatness, fusion, coefficients in (0,1), aleph-zero categorical construction, specific counter-examples constructed using Fraïssé-Hrushovski amalgamation, ampleness.
Presentation and choice of topics will be heavily biased towards combinatorics. The lion's share of proofs will be elementary and hands-on, at the cost of getting our hands dirty with technical complexity. One should expect to emerge a resourceful engineer rather than a visionary geometer.
Time permitting, during the final weeks of the course, the instructor may indulge in getting everyone's hands even dirtier with some results in ordinal Ramsey theory
Familiarity with mathematical logic will be helpful. However, in our setting, abstract model-theoretic notions will have a concrete manifestation, making the course fairly self-contained.