Tung T. Nguyen

I am a joint postdoc at Western University and Onepick Inc. At Western, my mentors are Professor Ján Mináč and Professor Lyle Muller. I am an interdisciplinary mathematician. My primary research interests are in computational/algebraic number theory and computational neuroscience. I have also worked on several side projects on spectral graph theory, representation theory, and Galois modules. I am strongly interested in applying my math skills to solve real-world problems. In particular, I am working with Dr. Thanh Nguyen (Onepick Inc) on the Vehicle Routing Problem and its generalizations. I enjoy finding hidden patterns from experimental data. A large part of my research is inspired and guided by big data and simulations (for example, see here for some data that I generated for our work on Fekete polynomials). I obtained my Ph.D. at the University of Chicago in December 2020. My advisor is Professor Kazuya Kato. Before coming to Chicago, I was an undergraduate student at Vietnam National University. I wrote my senior thesis under the supervision of Professor Ralph Greenberg. Here is my Google Scholar profile. Email: nguyenthotung@gmail.com I will be a on the job market in Fall 2022. Here is my CV.

I am a joint postdoc at Western University and Onepick Inc. At Western, my mentors are Professor Ján Mináč and Professor Lyle Muller.

I am an interdisciplinary mathematician. My primary research interests are in computational/algebraic number theory and computational neuroscience. I have also worked on several side projects on spectral graph theory, representation theory, and Galois modules. I am strongly interested in applying my math skills to solve real-world problems. In particular, I am working with Dr. Thanh Nguyen (Onepick Inc) on the Vehicle Routing Problem and its generalizations.

I enjoy finding hidden patterns from experimental data. A large part of my research is inspired and guided by big data and simulations (for example, see here for some data that I generated for our work on Fekete polynomials).

I obtained my Ph.D. at the University of Chicago in December 2020. My advisor is Professor Kazuya Kato.

Before coming to Chicago, I was an undergraduate student at Vietnam National University. I wrote my senior thesis under the supervision of Professor Ralph Greenberg.

Here is my Google Scholar profile.

Email: nguyenthotung@gmail.com

I will be a on the job market in Fall 2022. Here is my CV.

What's new

I am organizing a virtual conference to celebrate the 85th birthday of Professor Moshe Rosenfeld who is my teacher, collaborator, and lifelong friend.
The website for this conference is here.

Publications

1. Tung T. Nguyen, Heights and Tamagawa numbers of motives (Published in the Journal of Pure and Applied Algebra, 2021.) (Arxiv version) (Journal version)

2. Lyle Muller, Ján Mináč, Tung T. Nguyen, An algebraic approach to the Kuramoto model (Published in Physical Review E, 2021). (Arxiv version) (Journal version)

3. Roberto Budzinski, Tung T. Nguyen, Jacqueline Đoàn, Ján Mináč, Terrence J. Sejnowski, Lyle Muller, Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks (Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022). (Arxiv version) (Journal version)

4. Tung T. Nguyen, Jacqueline Đoàn, Federico Pasini, Ján Mináč, Lyle Muller, Join of circulant matrices (Published in Linear Algebra and its Applications, 2022). (Arxiv version) (Journal version)

5. Ján Mináč, Duy Tan Nguyen, Tung T. Nguyen, Fekete polynomials, quadratic residues, and arithmetic (Accepted to Journal of Number Theory, 2022). (Arxiv version) (Journal version)

6. Ján Mináč, Duy Tan Nguyen, Tung T. Nguyen, Further insights into the mysteries of the values of zeta functions at integers (Accepted to Mathematica Slovaca, 2022). (Arxiv version)

7. Tung T. Nguyen, Roberto Budzinski, Jacqueline Đoàn, Federico Pasini, Ján Mináč, Lyle Muller, Equilibria in Kuramoto oscillator networks: An algebraic approach (Accepted to SIAM Journal on Applied Dynamical Systems, 2022). (Arxiv version)

8. Lauren Heller, Ján Mináč, Tung T. Nguyen, Andrew Schultz, and Nguyễn Duy Tân, Galois module structure of some elementary p-abelian (Accepted to Israel Journal of Mathematics, 2022). (Arxiv version).

9. Roberto C. Budzinski, Tung T. Nguyen, Gabriel B. Benigno, Jacqueline Doan, Ján Mináč, Terrence J. Sejnowski, and Lyle E. Muller, Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays (Accepted to Physical Review Research, 2023). (Final version)

10. Tung T. Nguyen, Roberto C. Budzinski, Federico W. Pasini, Robin Delabays, Ján Mináč, and Lyle E. Muller, Broadcasting solutions on networked systems of phase oscillators (Accepted to Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, 2023) (Arxiv version)

11. Sunil Chebolu, Jon Merzel, Ján Mináč, Lyle Muller, Federico Pasini, Tung T. Nguyen, Duy Tan Nguyen, On the joins of group rings (To appear in the Journal of Pure and Applied Algebra, 2023) (Arxiv version) .

Preprints

1. Frank Chemotti, Ján Mináč, Tung T. Nguyen, Andrew Schultz, John Swallow, Nguyen Duy Tân, Quaternion algebras and square power classes over biquadratic extensions (submitted). (Arxiv version).

2. Jon Merzel, Ján Mináč, Lyle Muller, Federico Pasini, Tung T. Nguyen, Spectral perturbation by rank-m matrices ( preliminary version.)

3. Tung T. Nguyen, Jacqueline Đoàn, Federico Pasini, Ján Mináč, Lyle Muller, Join of normal matrices with constant row sums (submitted), (Arxiv version).

4. Sunil Chebolu, Jon Merzel, Ján Mináč, Lyle Muller, Federico Pasini, Tung T. Nguyen, Duy Tan Nguyen, On the arithmetic of the joins of group rings over finite fields (in preparation).

5. Ján Mináč, Duy Tan Nguyen, Tung T. Nguyen, On the arithmetic of generalized Fekete polynomials (submitted) (Arxiv version)

6. Jan Mináč, Lyle Muller, Duy Tan Nguyen, Tung T. Nguyen, On the Paley graph of a quadratic character (submitted) (Arxiv version)

7. Korey Brownstein, Tung T. Nguyen, Utilization of a natural language processing-based approach to determine the composition of artifact residues (submitted). Github repository for the code.

8. Shiva Chidambaram, Ján Mináč, Duy Tan Nguyen, Tung T. Nguyen, Fekete polynomials of principal Dirichlet characters ( preliminary version. )

Other writing

When I was an undergraduate student at Vietnam National University, I co-authored a book on research experiences for undergraduates in mathematics. It is available here. See here for a media coverage about this book.

I also wrote some of the things that I learned during my internship at Kibo Commerce. They are available here.

In my free time, I worked on some side projects in Machine Learning and Data Science. These projects are documented here.

I occasionally propose math olympiad-style problems for the PI journal (a Vietnamese general journal for all people who share the love for mathematics.) I highly recommend you to contribute to this meaningful journal.

Teaching and Services

I have been an instructor for the Calculus sequence at UChicago (Calculus 1 through Calculus 3) for more than four years.

In the summer of 2019, I designed a curriculum for and taught a summer course "Introduction to Mathematicstics via proofs-based methods'' for incoming UChicago students thorough the Chicago Academic Achievement Program. It is a memorable experience. Click here for a picture of me with some students in this course.

I mentored three students in the Directed reading program and two students in the REU program at UChicago.

Co-supervised (joint with Ján Mináč and Lyle Muller) four students in the 2021 Fields Undergraduate Summer Research Program. We are completing a paper on spectral graph theory and matrix algebra.

Co-supervised the PhD student Priya B. Chain (joint with Ján Mináč and Lyle Muller). Topic: Broadcasting solutions on multiplex systems of oscillator networks.

Upcoming talks

ISU Algebra Seminar, Illinois State University, September 2022.

34th Midwestern Conference on Combinatorics and Combinatorial Computing, Illinois State University, October 2022.

Fields Number Theory Seminar, Fields Institute, October 2022.

2nd International workshop on matrix analysis and applications, November 2022.

Korea-Taiwan-Vietnam joint seminar in Combinatorics and Analysis, November 2022.

Contributed Talk, Special Session Rethinking Number Theory, AMS Joint Meeting, Boston 2023.

Selected talks and presentations

Connecticut Number Theory 2022 Conference, Unniversity of Connecticut, June 2022 (note for my talk).

Zassenhaus Groups and Friends Conference, Binghamton University, May 2022, (slide of my talk with minor modifications).

New Developments in Number Theory, February 2022, (slide of my talk).

Undergraduate colloquium, Illinois State University, October 2021, (slide of my talk).

First SIBAU-NU Workshop on Matrix Analysis and Linear Algebra, October 2021, (slide of my talk).

Mathematics and Statistics Colloqium, Loyola University, October 2021.

AMS Fall Western Sectional Meeting, October 2021.

Algebra & Number Theory Seminar, Texas Tech University, November 2021.

Algebra Seminar, Binghamton University, November 2021.

Northwestern Number Theory Seminar, December 2021.

Hanoi, Chicago, Boston and Western: A panoramic view of absolute Galois groups (joint talk with Ján Mináč), joint seminar between
- Mini-workshop on Algebra and homogeneous spaces

- Online seminar on quadratic forms, linear algebraic groups and beyond

- Recorded talk and slide

Fekete polynomials, quadratic residues, and arithmetic, GTA: Philadelphia 2021, May 2021 (slide).

Some arithmetic properties of Fekete polynomials, Lightning talk, Front Range Number Theory Day, April 2021.

Power sums and special values of L-functions, Algebra Seminar, Western University, March 2021, (slide).

Heights and Tamagawa numbers of motives, Algebra Seminar, Western University, February 2021, (slide).

Hurwitz zeta functions, What is ... a seminar? February 2021, (my note for the talk).

Heights and Tamagawa numbers of motives, HUJI-BGU Number Theory Seminar, December 2020, (slide).

Special values of the Riemann zeta function at negative integers, The Trojan Math Seminar, Troy University, December 2020. (slide).

Heights and Tamagawa numbers of mixed motives, Interactions between Representation Theory and Algebraic Geometry, Chicago 2017 (poster session).

Other activities

In the summer of 2020, I had a fantastic internship as a data scientist at Kibo Commerce through the PI4-IMA program, where I implemented several A/B testing algorithms. My mentor is Austin Rochford.