My research is in set theory, operator algebras, and combinatorics.

Preprints

Forcing axioms and coronas of nuclear C*-algebras (with Alessandro Vignati). arXiv:1806.09676.

Reduced products of UHF algebras under forcing axioms. arXiv:1303.5037.

Publications

Density of monochromatic infinite subgraphs (with Louis DeBiasio). arXiv:1611.05423.
To appear in Combinatorica.

Finite decomposition rank for virtually nilpotent groups (with Caleb Eckhardt and Elizabeth Gillaspy). arXiv:1706.04142.
To appear in Transactions of the American Mathematical Society.

Ulam stability for some classes of C*-algebras (with Alessandro Vignati). arXiv:1601.05445.
To appear in Proceedings of the Royal Society of Edinburgh Section A.

Finitely-generated nilpotent group C*-algebras have finite nuclear dimension (with Caleb Eckhardt). arXiv:1409.4056.
Journal für die reine und angewandte Mathematik 738 (2018), 281-298.

Homeomorphisms of Cech-Stone remainders: the zero-dimensional case (with Ilijas Farah). arXiv:1211.4765.
Proceedings of the American Mathematical Society 146 (2018), 2253-2262.

Classification of C*-algebras generated by representations of the unitriangular group UT(4,Z) (with Caleb Eckhardt and Craig Kleski). arXiv:1506.01272.
Journal of Functional Analysis, 271 (2016), no. 4, 1022–1042.

Automorphisms of P(lambda)/I_kappa (with Paul Larson). arXiv:1506.03433.
Fundamenta Mathematicae 233 (2016), no. 3, 271-291.

Some Calkin algebras have outer automorphisms (with Ilijas Farah and Ernest Schimmerling). arXiv:1211.4134.
Archive for Mathematical Logic 52 (2013) 517-524.

Recent talks

Asymptotic density of monochromatic subgraphs, 30th Cumberland conference on combinatorics, graph theory, and computing. (May 2018)

The Katowice problem and automorphisms of omega_1^*, University of Pittsburgh topology mini-meeting. (May 2018)

Rigidity of corona algebras, OHIO (Operators on Hilbert spaces In Ohio) meeting. (April 2018)

Automorphisms of corona algebras, Logic and operator algebras session, Winter CMS meeting. (December 2017)

Asymptotic density of monochromatic subgraphs, Discrete mathematics seminar, Notre Dame University. (November 2017)

Set theory and automorphisms of corona algebras, colloquium, University of Dayton. (November 2017)

Asymptotic density of monochromatic subgraphs, MIGHTY LVIII, Grand Valley State University. (October 2017)

Set theory and automorphisms of corona algebras, Operator algebra seminar, Purdue University. (September 2017)

Rigidity and nonrigidity of corona algebras, 6th European set theory conference, Alfred Renyi Institute. (July 2017)

Rigidity and nonrigidity of corona algebras, SUMTOPO, University of Dayton. (June 2017)

Rigidity and nonrigidity of corona algebras, NCGOA, Vanderbilt University. (May 2017)

Automorphisms of P(lambda)/I_kappa, TOPOSYM, Prague. (July 2016)

Automorphisms of P(lambda)/I_kappa, Boise Extravaganza in Set Theory, San Diego University. (June 2016)

Automorphisms of P(lambda)/I_kappa, 50th Spring Topology and Dynamics Conference, Baylor University. (March 2016)