I am a Professor in the Mathematics Department at the University of California, Irvine and am a member of the group in Logic and Foundations.
I also hold a courtesy appointment in the Department of Logic and Philosophy of Science.
I currently have a NSF grant on Model theory, quantum complexity, and embedding problems in operator algebras.
Books
- Nonstandard methods in Ramsey theory and combinatorial number theory (joint with Mauro Di Nasso and Martino Lupini)
- Ultrafilters throughout mathematics, published in the American Mathematical Society's Graduate Studies in Mathematics series.
- I edited the volume Model theory of operator algebras, which appeared in De Gruyter's Logic and its applications this year.
Editorial work
I am the Editor-in-Chief of the Journal of Logic and Analysis.
Upcoming events
- I am co-organizing (with Jim Freitag and Alf Onshuus) a special session in Pure and Applied Model Theory at the Mathematical Congress of the Americas, to be held in Miami, Florida July 21-25, 2025.
Recent events
- I gave a minicourse at the conference Groups in Logic, held at Vanderbilt University, May 28-June 1, 2025.
- I gave the 2025 Minicourse in the Noncommutative geometry in NYC seminar (by Zoom) in May 2025.
- I spoke in the special session on Logic and Analysis as well as in the special session on Model Theory and Interactions at the 2025 Spring Western Sectional Meeting of the American Mathematical Society, held at Cal Poly San Luis Obispo on May 3 and 4, 2025.
- I spoke in the University of Iowa Math Department Colloquium on April 24, 2025.
- I spoke in the UCSD Functional Analysis seminar on February 4, 2025.
- I spoke in the UCLA Functional Analysis seminar on January 22, 2025.
- I spoke in the Berkeley Logic Colloquium on December 6, 2024.
- I spoke in the special session on Structural Features in Mathematical Physics at the 2024 Fall Western Sectional Meeting of the American Mathematical Society, held at UC Riverside on October 26 and 27, 2024.
- I spoke in the seminar Noncommutative geometry in NYC (by Zoom) on October 16, 2024.
- I taught a mini-course on Nonstandard methods in Ramsey theory at Beijing Jiaotong University July 15-18, 2024. Course webpage Class photo
- I spoke in the Beijing Model Theory Conference on July 8-12, 2024. Conference photo
- I spoke in the Paris Logic Seminar on April 2, 2024.
- I led (with Michael Hehmann) the UCI Math Circle on February 27, 2024. Here is the worksheet and the solutions.
- I spoke in the UCLA Logic Colloquium on January 31, 2024.
- I spoke in the UCI Physics Colloquium on January 11, 2024. Slides
- I spoke at the workshop MIP*=RE and the Connes' Embedding Problem held at MSRI on October 16-20, 2023.
- I spoke at the Workshop on Operator Algebras and Applications: Connections with Logic, held at the Fields Institute from August 28-September 1, 2023.
- I spoke in the University of Hawaii Math Department Colloquium on August 3, 2023.
- I spoke at the Great Plains Operator Theory Symposium (GPOTS), held at the Ohio State University, May 15-19, 2023.
- I was the chair of the local organizing committee for the 2023 North American Annual Meeting of the Association for Symbolic Logic, held at UC Irvine on March 25-29, 2023. Poster
- I spoke in the workshop A Convergence of Computable Structure Theory, Analysis, and Randomness held at the Banff International Research Station March 19-24, 2023.
- I spoke at a workshop on Von Neumann Algebras and Geometric Group Theory held at UC San Diego, February 10-12, 2023.
- I spoke in the Chinese Academy of Science Logic Seminar on January 12, 2023.
- I spoke in the special session on Topological Methods in Model Theory at the Winter Meeting of the Canadian Math Society, held in Toronto, Canada, December 2-5, 2022.
- I gave the model theory course in the IMS Graduate Summer School in Logic, held in Singapore July 4-20, 2022. The topic was Model theory of tracial von Neumann algebras. Here is the webpage for the course.
- I spoke at the conference Ultramath 2022 held in Pisa, Italy on June 6-June 12, 2022. (Video)
- I was invited to speak at the conference Combinatorics meets model theory, to be held at the Clay Mathematical Institute at the University of Cambridge on June 20-24, 2022, but cancelled due to COVID-related reasons.
- I spoke in the 19th International Conference on Computability and Complexity in Analysis, held at Arcadia University (but via Zoom) on May 23-26, 2022. (Slides) (Video)
- I spoke in the University of Illinois Operator Algebras and Quantum Information Seminar on April 25th, 2022.
- I spoke in the University of Maryland Logic Seminar on April 19th, 2022.
- I gave a three-part tutorial at the 2022 North American Annual Meeting of the Association for Symbolic Logic at Cornell University on April 7-10, 2022. Here are the slides: Part 1 Part 2 Part 3
- I gave a plenary talk in the 38th Southeastern Analysis Meeting, held at the University of Florida on March 5-7, 2022.
- I spoke in the University of Oxford Logic Seminar on March 3rd, 2022.
- I delivered a 8 part Lecture Series in the Yonsei University Logic Seminar. The talks were from January 4 through February 22, 2022.
- I spoke in the Iowa State University Math Department Colloquium on November 16, 2021.
- I spoke in the UCSD Functional Analysis Seminar on September 28, 2021.
- I spoke in the Geometry and Analysis on Groups Research Seminar at the University of Vienna (via Zoom) on May 18, 2021.
- I gave a plenary lecture (via Zoom) in the 2020 Chinese Mathematical Logic Annual Meeting during the weekend of November 13-14, 2020.
- I spoke (via Zoom) in the University of Colorado, Colorado Springs Math Department Colloquium on November 4, 2020.
- I gave an expository lecture on model theory and von Neumann algebras at the Groundwork for Operator Algebra Lecture Series held at Michigan State University during the week of July 6-10, 2020.
- I was supposed to speak at the workshop A Convergence of Computable Structure Theory, Computable Analysis, and Randomness to be held at the Banff International Research Station during the week of May 17-22, 2020. (Cancelled)
- I was supposed to attend the Nanjing Logic Workshop in Nanjing, China on May 11-15, 2020. (Cancelled)
- I was supposed to deliver the University of Texas, San Antonio Math Department Colloquium on April 17, 2020. (Cancelled)
- I was supposed to deliver the University of Houston Math Department Colloquium on April 15, 2020. (Cancelled)
- I was the chair of the local organizing committee for the 2020 Association of Symbolic Logic North American Annual Meeting, to be held at UC Irvine on March 25-28, 2020. (Cancelled)
- I delivered the Ohio State University Math Department Colloquium on February 27, 2020.
- I spoke at the Oberwolfach Meeting Model theory: groups, geometries, and combinatorics, held during the week January 12-18, 2020.
- I spoke in the special session on Advances in Operator Algebras during the 2019 Fall Sectional Meeting of the AMS to be held at UC Riverside November 9-10, 2019.
- I spoke at the UCLA Logic Colloquium on November 15, 2019.
- I spoke at the Berkeley Logic Colloquium on November 1, 2019.
- I spoke at the workshop Classification Problems in von Neumann algebras held at the Banff International Research Station during the week of September 30-October 4, 2019.
- I spoke in the special session on Logic and Universal Algebra at the XXIII Latinamerican Algebra Colloquium held in Mexico City on August 5-9, 2019.
- I spoke at Antalya Algebra Days XXI held at the Nesin Mathematics Village in Turkey on May 15-19, 2019.
- I was a co-organizer of the special session on Applications of Ultrafilters and Nonstandard Methods at the 2019 Spring Central and Western Joint Sectional Meeting of the AMS held at the University of Hawaii on March 22-24, 2019. Here are slides from the session.
- I was a plenary speaker at the 2019 Southern Ontario Operator Algebras Seminar held at the Fields Institute in Toronto on February 16-17, 2019.
- I co-organized the workshop Model Theory and Operator Algebras at the Banff International Research Station during the week of November 25-30, 2018.
- I delivered the USC math department colloquium on November 13, 2018.
- I spoke at a one day workshop on operator algebras as part of the Nebraska-Iowa Functional Analysis Seminar on November 3, 2018.
- I attended a Trimester program in Model theory, combinatorics, and valued fields at the IHP in Paris from January through March of 2018.
- I spoke at the workshop on Finite and pseudofinite model theory at the University of Leeds on April 9-11, 2018.
- I spoke at the workshop Approximation properties in operator algebras and ergodic theory held at IPAM at UCLA on April 30-May 5, 2018.
- I was a co-organizer of the special session on Model Theory at the 2017 Fall Western Sectional Meeting of the AMS that was held at UC Riverside on November 4-5, 2017. I also spoke in the special session on Advances in Operator Algebras.
- As part of my NSF CAREER Grant, I organized a conference Model theory and operator algebras at UC Irvine that took place on September 20-24, 2017.
- I was a co-organizer of the American Institute of Mathematics workshop on "Nonstandard methods in combinatorial number theory", that took place August 14-18, 2017.
- I spoke in two special sessions at the Mathematical Congress of the Americas Meeting that took place July 24-28, 2017 in Montreal: 'Interactions between Model Theory and Analysis and Topology' and 'von Neumann algebras and their applications.'
- I spoke at the 2017 Spring Institute of Noncommutative Geometry and Operator Algebras that took place May 5-11, 2017 at Vanderbilt University.
- I spoke in the special session on Continuous Model Theory at the 2017 North American Annual Meeting of the Association of Symbolic Logic that took place March 20-23, 2017 at Boise State University.
Current students
- Ryan Burkhart
- Alec Fox
- Michael Hehmann
- Jennifer Pi (joint with Mike Cranston)
- Jessica Schirle