Shaun Fallat

Contact Info

Research Interests

Matrix theory, discrete mathematics, graph theory, combinatorial matrix analysis

Current Courses

MATH 328 Introduction to Graph Theory, MATH 422/822 Abstract Linear Algebra

Biography

I am Professor in the Mathematics and Statistics Department at the University of Regina. I received my Ph.D. in Applied Mathematics from the College of William and Mary in 1999.

My research interests include: combinatorial matrix theory, algebraic graph theory, matrix positivity and total positivity.

I value teaching both in the classroom and as a mentor to aspiring students and postdoctoral fellows. I have taught mathematics and statistics classes at all levels both undergraduate and graduate.

As a Professor I am dedicated to serving both the university community and the surrounding community at large. I have had the privilege to present numerous scientific papers at research conferences all over the world. In addition, I have delivered public lectures and visited school classrooms to engage with students across all grades.

Recent Publications

1) Barioli, Francesco, Shaun M. Fallat, Himanshu Gupta, and Zhongshan Li. 2026. “The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture.” Discrete Math. 349 (3): Paper No. 114861, 14. https://doi.org/10.1016/j.disc.2025.114861.

2) Fallat, Shaun, Himanshu Gupta, and Charles R. Johnson. 2025. “Sufficient Conditions for Total Positivity, Compounds, and Dodgson Condensation.” Linear Algebra Appl. 709: 189–202. https://doi.org/10.1016/j.laa.2025.01.016.

3) Fallat, Shaun, Himanshu Gupta, and Jephian C.-H. Lin. 2025. “Inverse Eigenvalue Problem for Laplacian Matrices of a Graph.” SIAM J. Matrix Anal. Appl. 46 (3): 1866–86. https://doi.org/10.1137/24M1714472.

4) Thaghizadeh, Davod, Moshen Zahraei, Narges Haj Aboutalebi, Aljoša Peperko, and Shaun Fallat. 2025. “Correction to: On the Numerical Ranges of Matrices in Max Algebra.” Banach J. Math. Anal. 19 (1): Paper No. 3, 26. https://doi.org/10.1007/s43037-024-00391-5.

 

 

Books

1)  S.M. Fallat, C.R. Johnson, Totally nonnegative matrices. Princeton University Press, Princeton. 2011.