Andrew Marks

I'm an assistant 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

BOX 951555
Los Angeles, CA 90095-1555

Publications and preprints:

1. Folner tilings for actions of amenable groups (with Clinton Conley, Steve Jackson, David Kerr, Brandon Seward, and Robin Tucker-Drob). [ arXiv | pdf ]. Submitted.
2. Borel circle squaring (with Spencer Unger). Submitted. [ arXiv | pdf ].
3. Descriptive graph combinatorics (with Alekos Kechris). Preprint [ pdf ].
4. Hyperfiniteness and Borel combinatorics (with Clinton Conley, Steve Jackson, Brandon Seward, and Robin Tucker-Drob). Submitted. [ arXiv | pdf ]
5. Topological generators for full groups of hyperfinite pmp equivalence relations. Submitted. [ arXiv | pdf ]
6. Uniformity, universality, and computability theory. To appear in J. Math. Logic. [ arXiv | pdf ].
7. Jump operations for Borel graphs (with Adam Day). Submitted. [ arXiv | pdf ].
8. The universality of poly-time Turing equivalence. Mathematical Structures in Computer Science (2016) [ arXiv | pdf | doi ].
9. Brooks's theorem for measurable colorings (with Clinton Conley and Robin Tucker-Drob). Forum of Math. Sigma 4 (2016) [ arXiv | pdf | doi ].
10. Baire measurable paradoxical decompositions via matchings (with Spencer Unger). Advances in Mathematics 289 (2016), 397-410. [ arXiv | pdf | doi ].
11. A determinacy approach to Borel combinatorics. J. Amer. Math. Soc. 29 (2016), 579-600. [ arXiv | pdf | doi ]
12. 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 ]
13. 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):

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

Slides:

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