## 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.
Model theory and the QWEP conjecture, Illinois Journal of Mathematics, Volume 59 (2015), 795-799.
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.
The pseudoarc is a co-existentially closed continuum (with Christopher Eagle and Alessandro Vignati), Topology and its applications, Volume 207 (2016), 1-9.
A computability-theoretic reformulation of the Connes Embedding Problem (with Bradd Hart), Bulletin of Symbolic Logic, Volume 22 (2016), 238-248.
Approximate polynomial structure in additively large sets (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg), Integers, Volume 16 (2016), Article A49.
High piecewise syndeticity of product sets in amenable groups (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg), Journal of Symbolic Logic, Volume 81 (2016), 1555-1562.
A monad measure space for logarithmic density (with Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, and Karl Mahlburg), Monatshefte für Mathematik, Volume 181 (2016), 577-599.
Robinson forcing and the quasidiagonality problem (with Thomas Sinclair), International Journal of Mathematics, Volume 28 (2017), Article 1750008.
Omitting types in operator systems (with Thomas Sinclair), Indiana University Mathematics Journal, Volume 66 (2017), 821-844.
On the theories of McDuffs II_1 factors (with Bradd Hart), to appear in International Mathematics Research Notices, Volume 27, Issue 18 (2017), 5609-5628.
Model-theoretic aspects of the Gurarij operator system (with Martino Lupini), Israel Journal of Mathematics, Volume 226 (2018), 87–118.
Explicit sentences distinguishing McDuff's II_1 factors (with Bradd Hart and Henry Towsner), Israel Journal of Mathematics, Volume 227 (2018), 365–377.

## Papers accepted for publication

Hindman's theorem and idempotent types (with Uri Andrews), to appear in Semigroup Forum.
On the axiomatizability of C* algebras as operator systems (with Thomas Sinclair), to appear in Glasgow Journal of Mathematics.
Boundary amenability of groups via ultrapowers (with Stephen Avsec), to appear in Houston Journal of Mathematics.
Definable sets containing productsets in expansions of groups (with Uri Andrews and Gabriel Conant), to appear in Journal of Group Theory.

## Papers submitted for publication

Randomizing o-minimal theories (with Uri Andrews and H. Jerome Keisler)
Scattered sentences have few separable randomizations (with Uri Andrews, Sherwood Hachtman, H. Jerome Keisler, and David Marker)
Enforceable operator algebras
Spectral gap and definability
On supra-SIM sets of natural numbers (with Steven Leth)

## Preprints

Correspondences, ultraproducts, and model theory (with Bradd Hart and Thomas Sinclair)

## Books

Nonstandard methods in Ramsey theory and combinatorial number theory (with Mauro Di Nasso and Martino Lupini). Preliminary draft.

## Research notes

Seminar notes on Hilbert's Fifth Problem (with Lou van den Dries)
An erratum to "Globalizing locally compact local groups"
A short note on Hilbert's fifth problem and Ind/Type-definable groups (with Anand Pillay).
A note on ends of groups.
Two small nonstandard group-theoretic observations.
A note on Property (T).