## Research Interests

My research interests lie in the field of model theory, a branch of mathematical logic. More specifically, I am interested in:

• Pure and applied model theory
• Nonstandard analysis
• Model theory for metric structures
• Lie theory
• Geometric group theory
• Operator algebras
• Combinatorial number theory

Here is a link to my Curriculum Vitae.

## Publications

Bezout domains and elliptic curves (with Marc Masdeu), Communications in Algebra, Volume 36 (2008) Issue 12, 4492-4499.
Nonstandard hulls of locally exponential Lie algebras, Journal of Logic and Analysis, Volume 1:5 (2009), 1-25.
Locally compact contractive local groups (with Lou van den Dries), Journal of Lie Theory, Volume 19 (2009), 685-695.
Hilbert's fifth problem for local groups, Annals of Mathematics, Volume 172 (2010), Number 2, 1269-1314.
Globalizing locally compact local groups (with Lou van den Dries), Journal of Lie Theory, Volume 20 (2010), 519-524.
Ends of groups: a nonstandard perspective, Journal of Logic and Analysis, Volume 3:7 (2011), 1-28.
Definable functions in Urysohn's metric space Illinois Journal of Mathematics, Volume 55, Number 4 (2011), 1423-1435.
Thorn-forking in continuous logic (with Clifton Ealy) Journal of Symbolic Logic, Volume 77 (2012), 63-93.
Definable operators on Hilbert spaces Notre Dame Journal of Formal Logic, Volume 53, Number 2(2012), 193-201.
An approximate Herbrand's theorem and definable functions in metric structures Mathematical Logic Quarterly, Volume 58, Issue 3 (2012), 208-216.
Nonstandard hulls of locally uniform groups Fundamenta Mathematicae, Volume 220 (2013), 93-118.
Further thoughts on definability in the Urysohn sphere Proceedings of the 12th Asian Logic Conference, World Scientific (2013), 144-154.
The theory of tracial von Neumann algebras does not have a model companion (with Bradd Hart and Thomas Sinclair) Journal of Symbolic Logic, Volume 78, Number 3 (2013), 1000-1004.
Transseries and Todorov-Vernaeve's asymptotic fields (with Matthias Aschenbrenner) Archive for Mathematical Logic, Volume 53 (2014), 65-87.
An approximate logic for measures (with Henry Towsner) Israel Journal of Mathematics, Volume 199, Number 2 (2014), 867-913.
Definable closure in randomizations (with Uri Andrews and H. Jerome Keisler) Annals of Pure and Applied Logic, Volume 166, Issue 3 (2015), 325-341.
High density piecewise syndeticity of sumsets (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg) Advances in Mathematics, Volume 278 (2015), 1-33.
On Kirchberg's embedding problem (with Thomas Sinclair) Journal of Functional Analysis, Volume 269 (2015), 155-198.
On a sumset conjecture of Erdős (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg) Canadian Journal of Mathematics, Volume 67 (2015), 795-809.
Pseudofinite and pseudocompact metric structures (with Vinicius Cifú Lopes) Notre Dame Journal of Formal Logic, Volume 56 (2015), 493-510.
Games and elementary equivalence of II_1 factors (with Thomas Sinclair) Pacific Journal of Mathematics, Volume 278 (2015), 103-118.
Dividing and weak quasi-dimensions in arbitrary theories (with Henry Towsner) Archive for Mathematical Logic, Volume 54 (2015), 915-920.
Hilbert's fifth problem (with Lou van den Dries). L'Enseignement Mathématique, Volume 61/62 (2015), 3-43.
The fundamental group of a locally finite graph with ends: a hyperfinite approach (with Alessandro Sisto) Fundamenta Mathematicae, Volume 232 (2016), 21-39.
Existentially closed II_1 factors (with Ilijas Farah, Bradd Hart, and David Sherman) Fundamenta Mathematicae, Volume 233 (2016), 173-196.

## Papers accepted for publication

High piecewise syndeticity of product sets in amenable groups (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg) To appear in Journal of Symbolic Logic.
Omitting types in operator systems (with Thomas Sinclair) To appear in the Indiana University Mathematics Journal.
A computability-theoretic reformulation of the Connes Embedding Problem (with Bradd Hart) To appear in the Bulletin of Symbolic Logic.
A monad measure space for logarithmic density (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg) To appear in Monatshefte für Mathematik
Model theory and the QWEP conjecture To appear in the Illinois Journal of Mathematics.
The pseudoarc is a co-existentially closed continuum (with Christopher Eagle and Alessandro Vignati) To appear in Topology and its applications.