**Andrew Marks**

I'm an associate professor at UCLA. My research interests lie in descriptive set theory and its connections to related areas such as computability theory, combinatorics, ergodic theory, probability, and operator algebras.

**Office:** MS 6228.

**Email:**
marks@math.ucla.edu

**Address:**
UCLA Mathematics

BOX 951555

Los Angeles, CA 90095-1555

**Publications and preprints:**

- Folner tilings for actions of amenable groups (with Clinton Conley, Steve Jackson, David Kerr, Brandon Seward, and Robin Tucker-Drob). [ arXiv | pdf ]. Submitted.
- Borel circle squaring (with Spencer Unger). To appear in
*Ann. of Math.*[ arXiv | pdf ]. - Descriptive graph combinatorics (with Alekos Kechris). Preprint [ pdf ].
- Hyperfiniteness and Borel combinatorics (with Clinton Conley, Steve Jackson, Brandon Seward, and Robin Tucker-Drob). Submitted. [ arXiv | pdf ]
- Topological generators for full groups of hyperfinite pmp equivalence relations. Submitted. [ arXiv | pdf ]
- Uniformity, universality, and computability theory.
*J. Math. Logic*17 (2017) no 1. [ arXiv | pdf | doi ]. - Jump operations for Borel graphs (with Adam Day). Submitted. [ arXiv | pdf ].
- The universality of poly-time Turing equivalence.
*Mathematical Structures in Computer Science*(2016) [ arXiv | pdf | doi ]. - Brooks's theorem for measurable colorings (with Clinton Conley and Robin Tucker-Drob).
*Forum of Math. Sigma*4 (2016) [ arXiv | pdf | doi ]. - Baire measurable paradoxical decompositions via matchings (with Spencer Unger).
*Advances in Mathematics*289 (2016), 397-410. [ arXiv | pdf | doi ]. - A determinacy approach to Borel combinatorics.
*J. Amer. Math. Soc.*29 (2016), 579-600. [ arXiv | pdf | doi ] - Martin's conjecture, arithmetic
equivalence, and countable Borel equivalence
relations (with Theodore Slaman and John Steel). Ordinal definability and recursion theory: The
cabal seminar volume III,
*Lecture Notes in Logic*43, Cambridge University Press, 2016, 200-219. [ arXiv | pdf ] - Minimal Betti Numbers (with Christopher Dodd, Victor Meyerson, and Ben Richert).
*Communications in Algebra*Vol 35 (3), 2007, pp 759-772. [ arXiv | doi ]

**Research notes (not intended for publication):**

- A Baire category proof of the Ackerman-Freer-Patel Theorem. May 2016. [ pdf ]
- Structure in complete sections of the shift action of a residually finite group. November 2013. [ pdf ]
- Distance from marker sequences in locally finite Borel graphs (with Clinton Conley). October 2013. [ pdf ]
- A short proof that an acyclic n-regular Borel graph may have Borel chromatic number n+1. May 2013. [ pdf ]
- Is the Turing jump unique? : Martin's conjecture and countable Borel equivalence relations. December 2011. [ pdf ]

**Slides**:

- Borel circle squaring. Slides from the Czech winter school, 2017. [ pdf ]