Jingbo Liu

Jingbo Liu

Assistant Professor of Mathematics
College Of Arts And Sciences
Department of Mathematical, Physical, and Engineering Sciences
Academic and Administration Building 314T

210-784-2812   |jliu@tamusa.edu

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My academic forefathers dating back ten generations include: Carl Friedrich GaussJohann Franz EnckeKarl Christian BruhnsHugo von Seeliger → Gustav Herglotz and Ludwig Otto Hölder Emil Artin Nesmith Ankeny (Princeton University)John Sollion Hsia (Massachusetts Institute of Technology) Wai Kiu Chan (Ohio State University) Jingbo Liu (Wesleyan University)

Dr. Liu received her Ph.D. in Mathematics from Wesleyan University, Middletown, CT in 2016 and held a two-year post-doctoral scholar position at University of Hong Kong before joining A&M-SA in 2018 for family reunion. She has visited MSRI at University of California, Berkeley, Banff International Research Station at Canada, La Trobe University, Australia, Seoul National University, South Korea, and Imperial College London, UK etc.

Dr. Liu has conducted research mainly in quadratic and Hermitian forms/lattices and applications to lattice-based cryptography; her recent research appeared in Bulletin des Sciences Mathématiques, International Mathematics Research Notices IMRN, Journal of Algebra, Journal of Number Theory, and Transactions of the American Mathematical Society, all of which are top-tier journals in the field.

Dr. Liu has presented at the Association for Women in Mathematics research symposia at University of California, Los Angeles and Texas A&M University, and at conferences hosted/organized by the American Mathematical Society, Imperial College London, UK, Louisiana State University, Seoul National University, South Korea, Tufts University, University of Hong Kong, University of Illinois at Chicago, University of Sydney, Australia, and Wake Forest University etc.

Dr. Liu has taught various undergraduate courses in the U.S. both at Wesleyan and A&M-SA including college algebra, pre-calculus, differential calculus, integral calculus, discrete mathematics, linear algebra, mathematical structures and proofs, probability, and modern algebra, and truly enjoys mathematics teaching. She has also taught a business related statistics course many years ago at Shandong University, China.

As dedicated to excellence in educating particularly the first-generation students, she is very interested in directing rigorous undergraduate research projects that lead to good publications*. One of her undergraduate mentees presented the work 3 below both at MAA MathFest 2021 and JMM AMS-PME 2022.

Dr. Liu has served as the single PI and sole director for an MAA-NREUP funded by NSF between June and August 2023 on a probabilistic/statistical study of the parameter α in the LLL-algorithm regarding some intrinsic quantities of a lattice. Her mentees have presented their joint research findings at MAA MathFest 2023 and will present a refined work at the forthcoming JMM AMS-PME 2024; all associated travels are financially supported by NSF via AMS/MAA.

Selected Publications: (All my publications follow the tradition in mathematics research listing authors on joint papers in alphabetical order)

  1. Jingbo Liu. An algorithm for g-invariant on unary Hermitian lattices over imaginary quadratic fields. (Under review) https://doi.org/10.48550/arXiv.2309.16138
  2. Jingbo Liu. g-invariant on unary Hermitian lattices over imaginary quadratic fields with class number 2 or 3. Journal of Algebra, 622 (2023), 636-675. (SCI) https://www.sciencedirect.com/science/article/pii/S0021869322005695
  3. Jingbo Liu and Bruce McOsker* (Undergraduate student). A new proof of Legendre's theorem on the Diophantine equation ax2+by2+cz2=0. (Under review) https://doi.org/10.48550/arXiv.2309.06616
  4. Jingbo Liu. On a Waring's problem for Hermitian lattices. Bulletin des Sciences Mathématiques, 174 (2022), Article 102970 (25 Pages)(SCI) https://www.sciencedirect.com/science/article/pii/S0007449721000269
  5. Qi Han and Jingbo Liu. Algebraic differential independence regarding the Riemann ζ-function and the Euler Γ-function. Journal of Number Theory, 221 (2021), 109-121. (SCI) https://www.sciencedirect.com/science/article/pii/S0022314X20300147
  6. Ben Kane and Jingbo Liu. Universal sums of m-gonal numbers. International Mathematics Research Notices IMRN, (2020), 6999-7036(SCI) https://academic.oup.com/imrn/article-abstract/2020/20/6999/5345052?redirectedFrom=fulltext https://ieeexplore.ieee.org/document/9519216
  7. Qi Han and Jingbo Liu. On differential independence of ζ and Γ. Annales Polonici Mathematici, 124 (2020), 151-159. (SCIE) https://www.impan.pl/en/publishing-house/journals-and-series/annales-polonici-mathematici/all/124/2/113414
  8. Constantin Nicolae Beli, Wai Kiu Chan, María Inés Icaza, and Jingbo Liu. On a Waring’s problem for quadratic and Hermitian forms. Transactions of the American Mathematical Society, 371 (2019), 5505-5527(SCI) https://www.ams.org/journals/tran/2019-371-08/S0002-9947-2018-07571-7
  9. Wei Chen, Qi Han and Jingbo Liu. On Fermat Diophantine functional equations, little Picard theorem, and beyond. Aequationes Mathematicae, 93 (2019), 425-432. (SCIE) https://link.springer.com/article/10.1007/s00010-018-0614-z
  10. Jingbo Liu and Alicia Marino. Strictly regular ternary Hermitian forms. Journal of Number Theory, 168 (2016), 374-385(SCI) https://www.sciencedirect.com/science/article/pii/S0022314X16300907
  11. Amy Feaver, Anna Haensch, Jingbo Liu, and Gabriele Nebe. Kneser-Hecke-operators for codes over finite chain rings. Directions in number theory, 245-270. Proceedings of the 2014 WIN3 Workshop Women in Numbers.” Association for Women in Mathematics Series. Springer, Switzerland, 2016. https://link.springer.com/chapter/10.1007/978-3-319-30976-7_8

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Courses Teaching

Subject Number Section Description Term Syllabus
MATH 1314 001 College Algebra Fall 2023 Syllabi
MATH 3325 001 Intro to Mathematical Proofs Fall 2023 Syllabi
MATH 2312 002 Pre-Calculus Fall 2023 Syllabi
MATH 1014 001 College Algebra Recitation Fall 2023 Syllabi