### Math 223D - Fall 2017 "Borel Graph combinatorics"

**Instructor:** Andrew Marks

**Meetings:** MWF from 12-12:50pm in MS 5117.

We'll survey the theory of Borel graph combinatorics. Topics will include:

- The G_0 dichotomy, and applications to
proving other dichotomy theorems.
- The Galvin-Prikry theorem, the Ramsey property, and infinite Borel chromatic
numbers.
- Bounded degree Borel graphs and connections with graph limits, ergodic theory, probability, and geometrical paradoxes.

We will partially follow the survey paper
"Descriptive graph
combinatorics" by Kechris and Marks: http://math.ucla.edu/~marks/papers/combinatorics16.pdf

**Prerequisites:**
Basic analysis/descriptive set theory: standard Borel spaces/standard probability spaces, Borel sets and functions, and Baire category. A good reference for these topics is Kechris's book: Classical Descriptive Set Theory