Dr. Nam D. Trang
University of North Texas
Mathematics
(940) 565-4084
Email:

Education

PhD, University of California, Berkeley, 2013.
Major: Mathematics
Degree Specialization: Logic/Set Theory
Dissertation Title: Generalized Solovay Measures, the HOD Analysis, and the Core Model Induction
BA, University of California, Irvine, 2007.
Major: Mathematics
BS, University of California, Irvine, 2007.
Major: Compute Science

Professional Memberships

Member, Sigma Xi. (September 15, 2020September 14, 2021).

Development Activities Attended

Workshop,"Faculty First Flight December workshop," Faculty First Flight, Denton, TX, United States of America. (December 07, 2018December 07, 2018).

Workshop,"Mentor luncheon," UNT CLEAR, Denton, TX, United States of America. (October 2, 2018October 2, 2018).

Workshop,"New Faculty Orientation," University of North Texas, Denton, Texas, United States of America. (August 14, 2018August 15, 2018).

Teaching

Teaching Experience

University of North Texas
MATH 1680, Elementary Probability and Statistics, 12 courses.
MATH 2700, Linear Algebra and Vector Geometry, 4 courses.
MATH 4010, Introduction to Metamathematics, 1 course.
MATH 4910, Special Problems, 1 course.
MATH 5010, Mathematical Logic and Set Theory, 1 course.
MATH 5610, Topology., 3 courses.
MATH 5620, Topology, 1 course.
MATH 5900, Special Problems, 9 courses.
MATH 5910, Special Problems, 1 course.
MATH 6010, Topics in Logic and Foundations, 1 course.

Directed Student Learning

Directed Individual/Independent Study,"Topics in Set theory," Mathematics. (August 31, 2023 – Present).

Directed Individual/Independent Study,"Independent research on Mathematics (matrix factorization and graph theory)," Texas Academy of Mathematics and Science. (July 31, 2021May 1, 2023).

Master's Thesis Committee Chair,"Cholesky Factorization and graph structure associated with symmetric matrices," Mathematics. (January 2021May 2022).

Directed Individual/Independent Study,"Independent reading on logic," Mathematics. (January 14, 2021May 1, 2021).

Directed Individual/Independent Study,"Independent reading on logic," Mathematics. (January 14, 2021May 1, 2021).

Directed Individual/Independent Study,"Independent reading on Set Theory (textbook: T. Jech Set Theory)," Mathematics. (August 31, 2019December 12, 2019).

Directed Individual/Independent Study,"Independent Reading on Logic (textbook H. Enderton "Mathematical Logic")," Mathematics. (January 15, 2019May 10, 2019).

Directed Individual/Independent Study,"Independent Reading on Logic," Mathematics. (August 31, 2018December 12, 2018).

Research

Published Intellectual Contributions

Journal Article
Trang, N., Jackson, S. C., Chan, W. (2023). More definable combinatorics around the first and second uncountable cardinal. Journal of Mathematical Logic. 23(03), . World Scientific.
Trang, N. (2023). The AD+ Conjecture and the Continuum Hypothesis. Proceedings of the American Mathematical Society. 151, .
Trang, N., Jackson, S. C., Chan, W. (2021). The size of the class of countable sequences of ordinals. Transactions of the American Mathematical Society. https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2021-08573-6/
Trang, N. (2021). Supercompactness can be equiconsistent with measurability. Notre Dame Journal of Formal Logic. 62(4), 593-618. Duke University Press.
Trang, N., Sargsyan, G. (2021). Sealing of the universally Baire sets. Bulletin of Symbolic Logic. 27(3), 254-266. Cambridge University Press.
Trang, N., Wilson, T. (2021). Determinacy from Strong Compactness of \omega_1. Annals of Pure and Applied Logic. 172(6), . Elsevier.
Trang, N., Sargsyan, G. (2021). Sealing from iterability. Transactions of the American Mathematical Society. 229-248. https://www.ams.org/journals/btran/2021-08-07/S2330-0000-2021-00065-5/
Trang, N., Ikegami, D. (2020). On supercompactness of $\omega_1$. Springer.
Trang, N., Rodriguez, D. (2018). L(R,\mu) is unique. Advances in Mathematics. 324, 355--393. Elsevier.
Trang, N., Ikegami, D. (2018). On a class of maximality principles. Archive for Mathematical Logic. 57(5-6), 713--725. Springer.
Trang, N., Shi, X. (2017). I_0 and combinatorics at lambda^+. Archive for Mathematical Logic. 56(1-2), 131--154. Springer.
Trang, N. (2016). PFA and guessing models. Israel Journal of Mathematics. 216, 607-667.
Trang, N., Sargsyan, G. (2016). Tame failures of the unique branch hypothesis and models of AD_R + Theta is regular. Journal of Mathematical Logic. 16(02), 28. World Scientific.
Trang, N. (2015). Derived models and supercompact measures on P_{\omega_1}(P(R)). Mathematical Logic Quarterly. 61(1-2), 56--65. Elsevier.
Trang, N. (2015). Structure theory of L(R,\mu) and its applications. The Journal of Symbolic Logic. 80(01), 29--55.
Trang, N. (2014). Determinacy in L(R,\mu). Journal of Mathematical Logic. 14(01), . World Scientific.
Trang, N., Sargsyan, G. (2014). Non-tame mice from tame failures of the unique branch hypothesis. Canadian Journal of Mathematics. 66(4), 903--923.
Trang, N. D. (2014). HOD in Natural Models of $\sf{AD}^+$. Annals of Pure and Applied Logic. 165(10), 1533-1556. Elsevier.
Survey paper
Trang, N. (2020). A brief account of recent developments in inner model theory. This is part of the volume on Simon Thomas' birthday. 752, . American Mathematical Society.

Presentations Given

Invited Talk

Trang, N. D. (Author & Presenter), Ikegami, D. (Author), The Spring Association of Symbolic Logic meeting, Preservation of AD via forcings, UC Irvine, UC Irvine, United States of America. (20232023).

Trang, N. D. (Author & Presenter), Muenster conference on inner model theory, Condensation for mouse pairs, Muenster university, Muenster, Germany, Germany. (20222022).

Trang, N. (Author & Presenter), The Oberwolfach Set theory meeting, 2022, Ideals and Determinacy, The Mathematisches Forschungsinstitut Oberwolfach, Via Zoom, Germany. (20222022).

Trang, N. (Author & Presenter), UC Irvine logic seminar, Ideals and determinacy, UC Irvine, via Zoom, United States of America. (20212021).

Trang, N. (Author & Presenter), Carnegie Mellon University logic seminar, Ideals and determinacy, CMU, Virtual, via Zoom, United States of America. (20202020).

Trang, N. (Author & Presenter), Berkeley Logic Colloquium, Sealing the Universally Baire sets, UC Berkeley, UC Berkeley, Berkeley, CA, United States of America. (20202020).

Trang, N. (Author & Presenter), UT Dallas Dynamics, Geometry, and Topology seminar, Large cardinals, forcing axioms, and determinacy, UT Dallas Math Department, UT Dallas, United States of America. (20192019).

Trang, N. (Author & Presenter), The XV Luminy workshop in Set Theory, The consistency strength of sealing of Hom_\infty, Luminy, France, France. (20192019).

Trang, N. (Author & Presenter), Rutgers MAMLS 2018, Forcing over models of determinacy, Rutgers University, Rutgers University, New Brunswick, United States of America. (20182018).

Trang, N. D. (Author & Presenter), Berkeley Logic Colloquium, Forcing and determinacy, UC Berkeley, Berkeley, CA, United States of America. (20182018).

Trang, N. D. (Author & Presenter), Joint Math Meeting, Forcing, elementary embeddings, and determinacy, American Mathematical Society, San Diego, CA, United States of America. (20182018).

Trang, N. (Author & Presenter), UCLA Logic Colloquium, Compactness of \omega_1, UCLA, UCLA, United States of America. (20172017).

Trang, N. (Author & Presenter), UIC Set Theory workshop, Compactness of \omega_1, University of Illinois, Chicago, Chicago, United States of America. (20162016).

N. (Author & Presenter), Logic Colloquium, Large cardinals, determinacy, and forcing axioms, Association of Symbolic Logic, Leeds, UK, United Kingdom. (20162016).

Trang, N. (Author & Presenter), ASL Annual Meeting, Large cardinals, determinacy, and forcing axioms, Association of Symbolic Logic, University of Connecticut, Connecticut, United States of America. (20162016).

Media Contributions

Magazine
"NSF CAREER GRANTS AWARDED FOR INNOVATIVE RESEARCH," UNT Research Magazine (Vol. 28, 2020). (November 16, 2020).

Contracts, Grants and Sponsored Research

Grant - Research
Trang, N. D. (Co-Principal), "AIM SQUARE : Large cardinal axioms and left-distributive algebras," Sponsored by AIM (the American Institute of Mathematics), International, Funded. (January 1, 2023December 31, 2025).
Trang, N. D., "CAREER: CURRENT AND FUTURE DEVELOPMENTS OF THE CORE MODEL INDUCTION," Sponsored by National Science Foundation, Federal, $403716 Funded. (September 1, 2020August 31, 2025).
Trang, N. D. (Principal), "Descriptive Inner Model Theory and its Applications," Sponsored by National Science Foundation, Federal, $120591 Funded. (September 1, 2019August 31, 2022).
Trang, N., "UNT Junior Research Grant," Sponsored by UNT, University of North Texas, $5000 Funded. (June 1, 2020June 30, 2020).
Trang, N., "UNT Junior Faculty Research Grant," Sponsored by University of North Texas, University of North Texas, $5000 Funded. (June 1, 2019June 30, 2019).
Trang, N. (Principal), "NSF grant," Sponsored by The National Science Foundation, Federal, $95359 Funded. (July 1, 2016June 30, 2019).

Awards and Honors

NSF CAREER GRANT, National Science Foundation. (March 31, 2020August 31, 2025).

NSF Grant, National Science Foundation. (September 1, 2019August 31, 2022).

UNT Mathematics Department Research Award, UNT Mathematics Department. (May 15, 2020May 15, 2021).

NSF Grant, The National Science Foundation (NSF). (July 01, 2016June 30, 2019).

Service

University Service

Committee Member, Algebra/Number Theory Search Committee. (December 15, 2021 – Present).

Committee Member, Topology qualifying exam committee. (August 1, 2021 – Present).

Program Organizer, Millican Colloquium. (August 31, 2021May 1, 2022).

Chairperson, Outreach committee. (June 1, 2020May 30, 2021).

Chairperson, Topology Qualifying Exam Committee. (June 1, 2020May 30, 2021).

Committee Member, Newsletter Committee. (December 2019May 2020).

Committee Member, Topology Qual Committee. (December 2019January 2020).

Committee Member, Topology Qual Committee. (May 2019August 2019).

Committee Member, Hiring Committee for Math/Data Science Assistant Professor position. (December 2018March 2019).

Committee Member, Topology Qualifying Exam Committee. (August 2018August 2018).

Professional Service

Reviewer, Journal Article, Several Mathematics Journals. (January 1, 2020 – Present).

Reviewer, Journal Article, AMS (Mathscinet reviews). (September 2017 – Present).

Editor, Journal Editor, Bulletin of Symbolic Logic (Reviews). (January 1, 2019December 31, 2024).

Reviewer, Grant Proposal, Funding Agency. (November 18, 2020November 20, 2020).

Reviewer, Journal Article, Proceedings of the American Mathematical Society. (July 1, 2019November 1, 2020).

Reviewer, Journal Article, Journal of Symbolic Logic. (October 1, 2019July 1, 2020).

Reviewer, Journal Article, Advances in Mathematics. (September 1, 2019June 1, 2020).

Reviewer, Journal Article, Israel Journal of Mathematics. (September 1, 2019May 1, 2020).

Reviewer, Grant Proposal, Funding Agency. (November 2017November 2017).