**Andrew Marks**

I'm a 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, operator algebras, and quantum information.

**Office:** MS 6228.

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

**Address:**
UCLA Mathematics

BOX 951555

Los Angeles, CA 90095-1555

**Publications and preprints:**

- One-ended spanning subforests and treeability of groups (with Clinton Conley, Damien Gaboriau, and Robin Tucker-Drob). Submitted [ pdf | arXiv ]
- Borel asymptotic dimension and hyperfinite equivalence relations (with Clinton Conley, Steve Jackson, Brandon Seward, and Robin Tucker-Drob). Submitted [ pdf | arXiv ]
- On a question of Slaman and Steel (with Adam Day). Submitted. [ arXiv | pdf ]
- Scott ranks of classifications of the admissibility equivalence relation (with William Chan and Matthew Harrison-Trainor). Submitted [ arXiv | pdf ]
- Descriptive graph combinatorics (with Alekos Kechris). Preprint [ pdf ].
- Distance from marker sequences in locally finite Borel graphs (with Clinton Conley) in Samuel Coskey and Grigor Sargysan eds.
*Trends in Set Theory*, Contemp. Math. 752, (2020), 89-92 [ arXiv | pdf | doi ]. - Measurable realizations of abstract systems of congruences (with Clinton Conley and Spencer Unger).
*Forum of Math, Sigma*8, (2020) e10 [ arXiv | pdf | doi ]. - Hyperfiniteness and Borel combinatorics (with Clinton Conley, Steve Jackson, Brandon Seward, and Robin Tucker-Drob).
*J. European Math. Soc.*22, No. 3 (2020), 877-892 [ arXiv | pdf | doi ] - Topological generators for full groups of hyperfinite pmp equivalence relations. Submitted. [ arXiv | pdf ]
- Folner tilings for actions of amenable groups (with Clinton Conley, Steve Jackson, David Kerr, Brandon Seward, and Robin Tucker-Drob).
*Mathematische Annalen*371 (2018), 663-683. [ arXiv | pdf | doi ] - Jump operations for Borel graphs (with Adam Day).
*J. Symb. Log*82 (2018), 13-28. [ arXiv | pdf | doi | errata ]. - Borel circle squaring (with Spencer Unger).
*Ann. of Math.*186 (2017), 581-605. [ arXiv | pdf | doi | pictures ]. - Uniformity, universality, and computability theory.
*J. Math. Logic*17 (2017) no 1. [ arXiv | pdf | doi | errata ]. - 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 | errata ]. - Baire measurable paradoxical decompositions via matchings (with Spencer Unger).
*Adv. Math.*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 | doi | errata ] - Minimal Betti Numbers (with Christopher Dodd, Victor Meyerson, and Ben Richert).
*Communications in Algebra*Vol 35 (3), 2007, pp 759-772. [ arXiv | doi ]

**Past Teaching:**

- Notes on effective desciptive set theory from a course I taught in spring 2019.
- Notes on set theory from a course I taught in spring 2020 and spring 2021.

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

- A short proof of the Connes-Feldman-Weiss theorem. November 2017. [ pdf ]
- 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 ]
- 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 ]