With Nam H. Le, Dr. Dave Karpuk, and Dr. Ha Tran.

Summary: In this project, we tried to apply certain properties available on real quadratic fields to cubic fields. From that, we explored some new results about lattices yielded by twisting original full-rank lattices in $R^3$.

Result: We submitted our new paper.

Well-Rounded Twists of the Ring of Integers in Cyclic Cubic Fields, with Nam H. Le, David Karpuk, and Ha T. N. Tran (preprint, 2025).

With Dr. Ha Tran N. T. and Nam Le H.

Summary: In this project, we first study Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart and David Tall to acquire a solid foundation in the theory of lattice and geometric representation of algebraic number. After that, we read some paper about well-rounded lattices and investigate well-roundedness of certain ideals from certain fields, such as quadratic, cyclic cubic, and cyclic quartic fields.

Result: We had the following publications:

• Well-rounded ideal lattices of cyclic cubic and quartic fields, with Nam H. Le and Ha Tran, Journal of Algebra and Its Applications, Vol. 21, No. 07, 2250133 (2022).

• Well-Rounded ideal lattices of cyclic cubic and quartic fields, with Nam H. Le and Ha Tran, Communications in Mathematics, October 18, 2023, Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications).

Well-Rounded Twists of the Ring of Integers in Cyclic Cubic Fields, with Nam H. Le, David Karpuk, and Ha T. N. Tran (preprint, 2025).