My areas of research are Algebraic and Geometric Number Thoery, more specifically in
Classical and adelic geometry of numbers
Lattices
Theory of height functions and Mahler's measure
Quadratic and linear forms; polynomials
Diophantine approximations, equations, and problems
Below are my publications in chronological order (see my papers with reviews on MathSciNet. arXiv link is provided on the title.):
(with Lenny Fukshansky) Diophantine avoidance and small-height primitive elements in ideals of number fields, Combinatorics and Number Theory, vol. 13 no. 4 (2024), p. 333-350.
(with Lenny Fukshansky) Integral zeros of quadratic polynomials avoiding sublattices, The Ramanujan Journal, vol. 66 no. 2 (2025) Paper no. 26, 10 pp.
Below are my invited talks (Slides are provided on the title.):
Primitive elements in number fields and Diophantine avoidance
Southern California Number Theory Day 2025 at UC Irvine, Irvine, CA, October 18, 2025
Integral quadratic forms and lattice angles
Southern California Discrete Mathematics Symposium 2025 at UC Irvine, Irvine, CA, April 6, 2025
Primitive elements in number fields and Diophantine avoidance
Number Theory Seminar at UC Irvine, Irvine, CA, October 10, 2024
Primitive elements in number fields and Diophantine avoidance
2024 Langenhop Lecture & Southern Illinois University Conference, Carbondale, IL, May 16-17, 2024
Below are additional manuscripts that I have written:
(with Lenny Fukshansky) On small-height elements in number fields, unpublished manuscript; improved to my publication #1.
Below is my Ph.D. Thesis:
Diophantine Avoidance, Number Fields, and Quadratic Forms
Take a look at my mathematical genealogy page, my Google Scholar profile, and my ResearchGate profile. My Erdős number is 3. (Thanks to my advisor, Professor Lenny Fukshansky, for having Erdős number 2.)