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Dr. Nam D. Trang

Associate Professor

University of North Texas

Department of Mathematics

(940) 565-4084

Email: Nam.Trang@unt.edu

Education

  • PhD, University of California, Berkeley, 2013
    Major: Mathematics
    Specialization: Logic/Set Theory
    Dissertation: 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

  • Sigma Xi. (September 15, 2020 - September 14, 2021).

Development Activities

  • Workshop, Faculty First Flight December workshop, Faculty First Flight. Denton,TX,United States of America. (December 07, 2018 - December 07, 2018).
  • Workshop, Mentor luncheon, UNT CLEAR. Denton,TX,United States of America. (October 2, 2018 - October 2, 2018).
  • Workshop, New Faculty Orientation, University of North Texas. Denton,Texas,United States of America. (August 14, 2018 - August 15, 2018).

Teaching

Teaching Experience

    University of North Texas

  • MATH 1680 - Elementary Probability and Statistics, 12 courses.
  • MATH 2700 - Linear Algebra and Vector Geometry, 5 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, 10 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).
  • Directed Individual/Independent Study, "Independent research on Mathematics (matrix factorization and graph theory)," Texas Academy of Mathematics and Science. (July 31, 2021 - May 1, 2023).
  • Master's Thesis Committee Chair, "Cholesky Factorization and graph structure associated with symmetric matrices," Mathematics. (January 2021 - May 2022).
  • Directed Individual/Independent Study, "Independent reading on logic," Mathematics. (January 14, 2021 - May 1, 2021).
  • Directed Individual/Independent Study, "Independent reading on logic," Mathematics. (January 14, 2021 - May 1, 2021).
  • Directed Individual/Independent Study, "Independent reading on Set Theory (textbook: T. Jech Set Theory)," Mathematics. (August 31, 2019 - December 12, 2019).
  • Directed Individual/Independent Study, "Independent Reading on Logic (textbook H. Enderton "Mathematical Logic")," Mathematics. (January 15, 2019 - May 10, 2019).
  • Directed Individual/Independent Study, "Independent Reading on Logic," Mathematics. (August 31, 2018 - December 12, 2018).

Awards and Honors

  • NSF CAREER GRANT, National Science Foundation. (March 31, 2020).
  • NSF Grant, National Science Foundation. (September 1, 2019).
  • UNT Mathematics Department Research Award, UNT Mathematics Department. (May 15, 2020).
  • NSF Grant, The National Science Foundation (NSF). (July 01, 2016).

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. (2023 - 2023).
  • Trang, N.D. (Author & Presenter), Muenster conference on inner model theory, Condensation for mouse pairs, Muenster university, Muenster, Germany, Germany. (2022 - 2022).
  • Trang, N. (Author & Presenter), The Oberwolfach Set theory meeting, 2022, Ideals and Determinacy, The Mathematisches Forschungsinstitut Oberwolfach, Via Zoom, Germany. (2022 - 2022).
  • Trang, N. (Author & Presenter), UC Irvine logic seminar, Ideals and determinacy, UC Irvine, via Zoom, United States of America. (2021 - 2021).
  • Trang, N. (Author & Presenter), Carnegie Mellon University logic seminar, Ideals and determinacy, CMU, Virtual, via Zoom, United States of America. (2020 - 2020).
  • Trang, N. (Author & Presenter), Berkeley Logic Colloquium, Sealing the Universally Baire sets, UC Berkeley, UC Berkeley, Berkeley, CA, United States of America. (2020 - 2020).
  • 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. (2019 - 2019).
  • Trang, N. (Author & Presenter), The XV Luminy workshop in Set Theory, The consistency strength of sealing of Hom_\infty, Luminy, France, France. (2019 - 2019).
  • Trang, N. (Author & Presenter), Rutgers MAMLS 2018, Forcing over models of determinacy, Rutgers University, Rutgers University, New Brunswick, United States of America. (2018 - 2018).
  • Trang, N.D. (Author & Presenter), Berkeley Logic Colloquium, Forcing and determinacy, UC Berkeley, Berkeley, CA, United States of America. (2018 - 2018).
  • Trang, N.D. (Author & Presenter), Joint Math Meeting, Forcing, elementary embeddings, and determinacy, American Mathematical Society, San Diego, CA, United States of America. (2018 - 2018).
  • Trang, N. (Author & Presenter), UCLA Logic Colloquium, Compactness of \omega_1, UCLA, UCLA, United States of America. (2017 - 2017).
  • Trang, N. (Author & Presenter), UIC Set Theory workshop, Compactness of \omega_1, University of Illinois, Chicago, Chicago, United States of America. (2016 - 2016).
  • , N. (Author & Presenter), Logic Colloquium, Large cardinals, determinacy, and forcing axioms, Association of Symbolic Logic, Leeds, UK, United Kingdom. (2016 - 2016).
  • 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. (2016 - 2016).

Media Contributions

    Magazine

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

Contracts, Grants, 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. (2023 - 2025).
  • Trang, N.D., "CAREER: CURRENT AND FUTURE DEVELOPMENTS OF THE CORE MODEL INDUCTION," sponsored by National Science Foundation, Federal, $403716 Funded. (2020 - 2025).
  • Trang, N.D. (Principal), "Descriptive Inner Model Theory and its Applications," sponsored by National Science Foundation, Federal, $120591 Funded. (2019 - 2022).
  • Trang, N., "UNT Junior Research Grant," sponsored by UNT, University of North Texas, $5000 Funded. (2020 - 2020).
  • Trang, N., "UNT Junior Faculty Research Grant," sponsored by University of North Texas, University of North Texas, $5000 Funded. (2019 - 2019).
  • Trang, N. (Principal), "NSF grant," sponsored by The National Science Foundation, Federal, $95359 Funded. (2016 - 2019).
  • Trang, N.D. (Principal), "CAREER: Current and Future Developments of the Core Model Induction," sponsored by National Science Foundation, FED, Funded. (2020 - 2025).
  • Trang, N.D. (Principal), "Descriptive Inner Model Theory, Large Cardinals, and Combinatorics," sponsored by National Science Foundation, FED, Funded. (2018 - 2020).
  • Trang, N.D. (Principal), "Descriptive Inner Model Theory and Its Applications," sponsored by National Science Foundation, FED, Funded. (2019 - 2020).
  • Trang, N. (Principal), "NSF grant," sponsored by The National Science Foundation, Federal, Funded. (2016 - 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, 2021 - May 1, 2022).
  • Chairperson, Outreach committee. (June 1, 2020 - May 30, 2021).
  • Chairperson, Topology Qualifying Exam Committee. (June 1, 2020 - May 30, 2021).
  • Committee Member, Newsletter Committee. (December 2019 - May 2020).
  • Committee Member, Topology Qual Committee. (December 2019 - January 2020).
  • Committee Member, Topology Qual Committee. (May 2019 - August 2019).
  • Committee Member, Hiring Committee for Math/Data Science Assistant Professor position. (December 2018 - March 2019).
  • Committee Member, Topology Qualifying Exam Committee. (August 2018 - August 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, 2019 - December 31, 2024).
  • Reviewer, Grant Proposal, Funding Agency. (November 18, 2020 - November 20, 2020).
  • Reviewer, Journal Article, Proceedings of the American Mathematical Society. (July 1, 2019 - November 1, 2020).
  • Reviewer, Journal Article, Journal of Symbolic Logic. (October 1, 2019 - July 1, 2020).
  • Reviewer, Journal Article, Advances in Mathematics. (September 1, 2019 - June 1, 2020).
  • Reviewer, Journal Article, Israel Journal of Mathematics. (September 1, 2019 - May 1, 2020).
  • Reviewer, Grant Proposal, Funding Agency. (November 2017 - November 2017).