Isaac Goldbring

Professor, Department of Mathematics

Biography

Isaac Goldbring is a Professor in the Department of Mathematics at the University of California, Irvine, a position he has held since July 2022. Goldbring completed his Ph.D. in Mathematics at the University of Illinois at Urbana-Champaign in 2009, where his dissertation focused on nonstandard methods in Lie theory under the supervision of Lou van den Dries. Prior to his current role, he was an Associate Professor at UC Irvine from 2018 to 2022 and previously held positions at the University of Illinois at Chicago and the University of California, Los Angeles.

Goldbring's research encompasses a variety of areas in mathematics, including model theory, nonstandard analysis, continuous logic, Lie theory, geometric group theory, and operator algebras. He has published extensively, contributing over 70 peer-reviewed articles to journals such as the Journal of Symbolic Logic and Advances in Mathematics. His work has been recognized with several grants from the National Science Foundation, including a CAREER grant. Goldbring received the Gerald Sacks Prize for the best dissertation in mathematical logic worldwide in 2009, an accolade that highlights his early contributions to the field.

In addition to his research, Goldbring is actively involved in teaching and mentoring at UC Irvine. He teaches a range of courses, including Model Theory, Complex Analysis, and Real Analysis, for both undergraduate and graduate students. Goldbring also serves the academic community through his editorial work as the Editor-in-Chief of the Journal of Logic and Analysis and his involvement in organizing conferences and workshops, such as the North American Annual Meeting of the Association of Symbolic Logic. His professional service extends to reviewing for various mathematics journals and participating in several mathematical societies, including the Association for Symbolic Logic and the American Mathematical Society.

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Degrees

Ph.D. in Mathematics, University of Illinois at Urbana-Champaign, 2009
B.S. in Mathematics, University of California, Los Angeles, 2004
M.A. in Mathematics, University of California, Los Angeles, 2004

Distinctions

Gerald Sacks Prize for best dissertation in mathematical logic worldwide, 2009
Robert Sorgenfrey Distinguished Teaching Award, UCLA Department of Mathematics, 2012
Invited participant of Banff International Research Station workshop 'Classification Problems in von Neumann algebras', 2019
Scott Dissertation Completion Fellowship, 2008
American Institute of Mathematics, Accepted Workshop Proposal; project title: Nonstandard methods in combinatorial number theory and Ramsey theory, 2016
Irving Reiner Memorial Award in Algebra, University of Illinois at Urbana-Champaign, 2008
National Science Foundation CAREER Grant, 2014
Arnold O. Beckman Research Award Research Assistantship, 2008
Daus Prize in Mathematics, UCLA, 2004
National Science Foundation VIGRE Fellowship, University of Illinois at Urbana-Champaign, 2004

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Areas of Expertise

Mathematical Logic
Model Theory
Nonstandard Analysis
Operator Algebras
Geometric Group Theory
Quantum Complexity
Lie Theory
Continuous Logic
Combinatorial Number Theory
Geometric Group Theory

Recent Publications

Goldbring I., Hart B., “THE UNIVERSAL THEORY of the HYPERFINITE II FACTOR IS NOT COMPUTABLE”, Bulletin of Symbolic Logic, vol. 30, pp. 181-198, 2024.
“A non-uniformly inner amenable group”, Journal of Algebra, vol. 653, pp. 102-108, 2024.
Fox A., Goldbring I., Hart B., “Locally universal C<sup>⁎</sup>-algebras with computable presentations”, Journal of Functional Analysis, vol. 287, 2024.
Arulseelan J., Goldbring I., Hart B., “THE UNDECIDABILITY OF HAVING THE QWEP”, Journal of Operator Theory, vol. 92, pp. 349-362, 2024.
Goldbring I., Jekel D., Elayavalli S.K., Pi J., “Uniformly super McDuff II1 factors”, Mathematische Annalen, 2024.
“Spectral gap and definability”, Beyond First Order Model Theory Volume 2, CRC Press, 2023.
Bradd Hart, “A survey on the model theory of tracial von Neumann algebras”, Model theory and operator algebras, De Gruyter’s Logic and its Applications series, vol. 11, 2023.
“Non-embeddable II_1 factors resembling the hyperfinite II_1 factor”, Journal of noncommutative geometry, vol. 17, pp. 233-239, 2023.
Caleb Camrud, Timothy McNicholl, “On the complexity of the theory of a computably presented metric structure”, Archive for Mathematical Logic, vol. 62, pp. 1111-1129, 2023.
Bradd Hart, “On Tsirelson pairs of C*-algebras”, Reviews in Mathematical Physics, vol. 35, pp. Article No. 2350016, 2023.
Srivatsav Kunnawalkam Elayavalli, Yash Lodha, “Generic algebraic properties in spaces of enumerated groups”, Transactions of the American Mathematical Society, vol. 376, pp. 6245-6282, 2023.
“Model theory and ultrapower embedding problems in operator algebras”, Model theory and operator algebras, De Gruyter’s Logic and its Applications series, vol. 11, 2023.
Itaï Ben Yaacov, “Unitary representations of locally compact groups as metric structures”, Notre Dame Journal of Formal Logic, vol. 64, pp. 159-172, 2023.
Ryan Burkhart, “Subsets of virtually nilpotent groups with the SBM property”, Journal of Algebraic Combinatorics, vol. 58, pp. 837-866, 2023.
“Model theory of operator algebras”, DeGruyter’s Logic and its application series, vol. 11, 2023.
Goldbring I., “Preface”, Model Theory of Operator Algebras, pp. vii-ix, 2023.
“The Connes Embedding Problem: a guided tour”, Bulletin of the American Mathematical Society, vol. 59, pp. 503-560, 2022.
H. Jerome Keisler, “Continuous sentences preserved under reduced products”, Journal of Symbolic Logic, vol. 87, pp. 649-681, 2022.
Cyril Houdayer, “Existentially closed W*-probability spaces”, Mathematische Zeitschrift, vol. 301, pp. 3787-3816, 2022.
Jeffrey Barrett, “Everettian mechanics with hyperfinitely many worlds”, Erkenntnis, 2022.
““Hilbert’s fifth problem and related topics” by Terence Tao”, Notre Dame Journal of Formal Logic, vol. 63, pp. 581-588, 2022.
“Ultrafilters thoughout mathematics”, Graduate Studies in Mathematics Series, American Mathematical Society, vol. 220, 2022.
Bradd Hart, “Operator algebras with hyperarithmetic theory”, Journal of Logic and Computation, vol. 31, pp. 612-629, 2021.
“A nonstandard proof of the spectral theorem for unbounded self-adjoint operators”, Expositiones Mathematicae, vol. 39, pp. 590-603, 2021.
“Oracle computability of conditional expectation onto subfactors”, New York Journal of Mathematics, vol. 27, pp. 1085-1095, 2021.
Bradd Hart, Alex Kruckman, “The almost sure theory of finite metric spaces”, Bulletin of the London Mathematical Society, vol. 53, pp. 1740-1748, 2021.
“Ultrafilter methods in combinatorics”, Snapshots of modern mathematics from Oberwolfach, 2021.
“A tribute to Lou van den Dries”, Celebratio Mathematica, 2021.
“On Popa’s factorial commutant embedding property”, Proceedings of the American Mathematical Society, vol. 148, pp. 5007-5012, 2020.
Bradd Hart, “Properties expressible in small fragments of the theory of the hyperfinite II_1 factor”, Confluentes Mathematici, vol. 12, pp. 37-47, 2020.
Steven Leth, “On supra-SIM sets of natural numbers”, Combinatorial and Additive Number Theory III, pp. 123-132, 2020.
Uri Andrews, Sherwood Hachtman, H. Jerome Keisler, David Marker, “Scattered sentences have few separable randomizations”, Archive for Mathematical Logic, vol. 59, pp. 743-754, 2020.
Sean Walsh, “An invitation to nonstandard analysis and its recent applications”, Notices of the American Mathematical Society, vol. 66, pp. 842-851, 2019.
Uri Andrews, Gabriel Conant, “Definable sets containing product sets in expansion of groups”, Journal of Group Theory, vol. 22, pp. 63-82, 2019.
Uri Andrews, H. Jerome Keisler, “Independence in randomizations”, Journal of Mathematical Logic, vol. 19, pp. Article 1950005, 2019.
Thomas Sinclair, “On the axiomatizability of C* algebras as operator systems”, Glasgow Journal of Mathematics, vol. 61, pp. 629-635, 2019.
Nasso M.D., Goldbring I., Lupini M., “Nonstandard analysis”, Lecture Notes in Mathematics, vol. 2239, pp. 11-43, 2019.
Stephen Avsec, “Boundary amenability of groups via ultrapowers”, Houston Journal of Mathematics, vol. 45, pp. 731-741, 2019.
Nasso M.D., Goldbring I., Lupini M., “Working in the remote realm”, Lecture Notes in Mathematics, vol. 2239, pp. 123-131, 2019.
Nasso M.D., Goldbring I., Lupini M., “Ramsey’s theorem”, Lecture Notes in Mathematics, vol. 2239, pp. 73-79, 2019.
Nasso M.D., Goldbring I., Lupini M., “The theorems of van der waerden and hales-jewett”, Lecture Notes in Mathematics, vol. 2239, pp. 81-88, 2019.
Nasso M.D., Goldbring I., Lupini M., “Densities and structural properties”, Lecture Notes in Mathematics, vol. 2239, pp. 111-122, 2019.
Nasso M.D., Goldbring I., Lupini M., “Near arithmetic progressions in sparse sets”, Lecture Notes in Mathematics, vol. 2239, pp. 153-160, 2019.
Nasso M.D., Goldbring I., Lupini M., “The interval measure property”, Lecture Notes in Mathematics, vol. 2239, pp. 161-169, 2019.
Nasso M.D., Goldbring I., Lupini M., “Loeb measure”, Lecture Notes in Mathematics, vol. 2239, pp. 55-70, 2019.
Nasso M.D., Goldbring I., Lupini M., “Triangle removal and szemerédi regularity”, Lecture Notes in Mathematics, vol. 2239, pp. 173-180, 2019.
Nasso M.D., Goldbring I., Lupini M., “Sumset configurations in sets of positive density”, Lecture Notes in Mathematics, vol. 2239, pp. 145-152, 2019.
Nasso M.D., Goldbring I., Lupini M., “Many stars: Iterated nonstandard extensions”, Lecture Notes in Mathematics, vol. 2239, pp. 49-54, 2019.
Nasso M.D., Goldbring I., Lupini M., “Approximate groups”, Lecture Notes in Mathematics, vol. 2239, pp. 181-186, 2019.
Nasso M.D., Goldbring I., Lupini M., “Jin’s sumset theorem”, Lecture Notes in Mathematics, vol. 2239, pp. 133-143, 2019.
Nasso M.D., Goldbring I., Lupini M., “From hindman to gowers”, Lecture Notes in Mathematics, vol. 2239, pp. 89-98, 2019.
Nasso M.D., Goldbring I., Lupini M., “Hyperfinite generators of ultrafilters”, Lecture Notes in Mathematics, vol. 2239, pp. 45-48, 2019.
Nasso M.D., Goldbring I., Lupini M., “Partition regularity of equations”, Lecture Notes in Mathematics, vol. 2239, pp. 99-108, 2019.
Nasso M.D., Goldbring I., Lupini M., “Ultrafilters”, Lecture Notes in Mathematics, vol. 2239, pp. 3-10, 2019.
Di Nasso M., Goldbring I., Lupini M., “Preface”, Lecture Notes in Mathematics, vol. 2239, pp. vii-x, 2019.
Martino Lupini, “Model-theoretic aspects of the Gurarij operator system”, Israel Journal of Mathematics, vol. 226, pp. 87-118, 2018.
Bradd Hart, Henry Towsner, “Explicit sentences distinguishing McDuff’s II_1 factors”, Israel Journal of Mathematics, vol. 227, pp. 365-377, 2018.
Goldbring I., “Model theory of operator algebras: Workshop and conference co-sponsored by the association for symbolic logic irvine, California September 20-24, 2017”, Bulletin of Symbolic Logic, vol. 24, pp. 536, 2018.
Andrews U., Goldbring I., “Hindman’s theorem and idempotent types”, Semigroup Forum, vol. 97, pp. 471-477, 2018.
Thomas Sinclair, “Omitting types in operator systems”, Indiana University Mathematics Journal, vol. 66, pp. 821-844, 2017.
Thomas Sinclair, “Robinson forcing and the quasidiagonality problem”, International Journal of Mathematics, vol. 23, pp. Article 1750008, 2017.
Bradd Hart, “A computability-theoretic reformulation of the Connes Embedding Problem”, Bulletin of Symbolic Logic, vol. 22, pp. 238-248, 2016.
Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, Karl Mahlburg, “High density piecewise syndeticity of product sets in amenable groups”, Journal of Symbolic Logic, vol. 81, pp. 1555-1562, 2016.
Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, Karl Mahlburg, “A monad measure space for logarithmic density”, Monatshefte für Mathematik, vol. 181, pp. 577-599, 2016.
Alessandro Sisto, “The fundamental group of a locally finite graph with ends: a hyperfinite approach”, Fundamenta Mathematicae, vol. 232, pp. 21-39, 2016.
Mauro Di Nasso, Renling Jin, Steven Leth, Martino Lupini, Karl Mahlburg, “Approximate polynomial structure in addtitively large sets”, Integers, vol. 16, pp. A49, 2016.
Mauro di Nasso, Renling Jin, Steven Leth, Martino Lupini, Karl Mahlburg, “On a sumset conjecture of Erdős”, Canadian Journal of Mathematics, vol. 67, pp. 795-809, 2015.
Mauro di Nasso, Renling Jin, Steven Leth, Martino Lupini, Karl Mahlburg, “High density piecewise syndeticity of sumsets”, Advances in Mathematics, vol. 278, pp. 1-33, 2015.
Vinicius Cifú Lopes, “Pseudofinite and pseudocompact metric structures”, Notre Dame Journal of Formal Logic, vol. 56, pp. 493-510, 2015.
Uri Andrews, H. Jerome Keisler, “Definable closure in randomizations”, Annals of Pure and Applied Logic, vol. 166, pp. 325-341, 2015.
Thomas Sinclair, “Games and elementary equivalence of II_1 factors”, Pacific Journal of Mathematics, vol. 278, pp. 103-118, 2015.
“Model theory and the QWEP conjecture”, Illinois Journal of Mathematics, vol. 59, pp. 795-599, 2015.
Henry Towsner, “Dividing and weak quasi-dimensions in arbitrary theories”, Archive for Mathematical Logic, vol. 54, pp. 915-920, 2015.
Lou van den Dries, “Hilbert’s fifth problem”, L’Enseignement Mathématique, vol. 61/62, pp. 3-43, 2015.
Henry Towsner, “An approximate logic for measures”, Israel Journal of Mathematics, vol. 199, pp. 867-913, 2014.
Matthias Aschenbrenner, “Transseries and Todorov-Vernaeve’s asymptotic fields”, Archive for Mathematical Logic, vol. 53, pp. 65-87, 2014.
“Nonstandard hulls of locally uniform groups”, Fundamenta Mathematicae, vol. 220, pp. 93-118, 2013.
“Further thoughts on definability in the Urysohn sphere”, World Scientific, pp. 144-154, 2013. Presented at 12th Asian Logic Conference,
Van Den Dries L., Goldbring I., “Erratum: Globalizing locally compact local groups (Journal of Lie Theory (2010) 20 (519-524))”, Journal of Lie Theory, vol. 22, pp. 489-490, 2012.
“Definable operators on Hilbert spaces”, Notre Dame Journal of Formal Logic, vol. 53, pp. 193-201, 2012.
“An approximate Herbrand’s theorem and definable functions in metric structures”, Mathematical Logic Quarterly, vol. 58, pp. 208-216, 2012.
“Definable functions in Urysohn’s metric space”, Illinois Journal of Mathematics, vol. 55, pp. 1423-1435, 2011.
“Ends of groups: a nonstandard perspective”, Journal of Logic and Analysis, vol. 3:7, pp. 1-28, 2011.
Lou van den Dries, “Globalizing locally compact local groups”, Journal of Lie Theory, vol. 20, pp. 519-524, 2010.
Lou van den Dries, “Locally compact contractive local groups”, Journal of Lie Theory, vol. 19, pp. 685-695, 2009.
“Nonstandard hulls of locally exponential Lie algebras”, Journal of Logic and Analysis, vol. 1:5, pp. 1-25, 2009.
Marc Masdeu Sabate, “Bezout domains and elliptic curves”, Communications in Algebra, vol. 36, pp. 4492-4499, 2008.

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Most Cited Publications

Thomas Sinclair, “On Kirchberg’s embedding problem”, Journal of Functional Analysis, vol. 269, pp. 155-198, 2015.
“Hilbert’s fifth problem for local groups”, Annals of Mathematics, vol. 172, pp. 1269-1314, 2010.
Ilijas Farah, Bradd Hart, David Sherman, “Existentially closed II_1 factors”, Fundamenta Mathematicae, vol. 233, pp. 173-196, 2016.
Bradd Hart, Thomas Sinclair, “The theory of tracial von Neumann algebras does not have a model companion”, Journal of Symbolic Logic, vol. 78, pp. 1000-1004, 2013.
Bradd Hart, “On the theories of McDuff’s II_1 factors”, International Mathematics Research Notices, vol. 27, no. 18, pp. 5609-5628, 2017.
Clifton Ealy, “Thorn-forking in continuous logic”, Journal of Symbolic Logic, vol. 77, pp. 63-93, 2012.
Christopher Eagle, Alessandro Vignati, “The pseudoarc is a co-existentially closed continuum”, Topology and its applications, vol. 207, pp. 1-9, 2016.
“Enforceable operator algebras”, Journal of the Institute of Mathematics of Jussieu, vol. 20, pp. 31-63, 2021.
Scott Atkinson, Srivatsav Kunnawalkam Elayavalli, “Factorial commutants and II_1 factors with the generalized Jung property”, Advances in Mathematics, vol. 396, pp. Paper No. 108107, 2022.
Mauro Di Nasso, Martino Lupini, “Nonstandard methods in Ramsey theory and combinatorial number theory”, Lecture Notes in Mathematics, Springer-Verlag, vol. 2239, 2019.

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Contact Information

Website: http://www.math.uci.edu/~isaac

Email: isaac@math.uci.edu

Phone: (949) 824-5500

Address: 340 Rowland Hall (Bldg. #400) Irvine, CA 92697-3875

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This profile was last updated on 2/14/2025.

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