Shaun Fallat
Research Interests
Matrix theory, discrete mathematics, graph theory, combinatorial matrix analysis
Current Courses
MATH 327 Introductory Combinatorics
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) Shaun M. Fallat, Valerii Maliuk, Seyed Ahmad Mojallal, and Sandra Zilles. Learning hypertrees from shortest path queries. In Algorithmic learning theory 2024, volume 237 of Mach. Learn. Res. (PMLR), pages 16 pp. [574–589]. Proceedings of Machine Learning Research PMLR, [2024] '2024.
2) Shaun M. Fallat and Prateek Kumar Vishwakarma. Inequalities for totally nonnegative matrices: Gantmacher-Krein, Karlin, and Laplace. Linear Algebra Appl., 694:360–413, 2024.
3) Honghai Li, Li Su, and Shaun Fallat. On a relationship between the characteristic and matching polynomials of a uniform hypertree. Discrete Math., 347(5):Paper No. 113915, 22, 2024.
4) Sarah Allred, Emelie Curl, Shaun Fallat, Shahla Nasserasr, Houston Schuerger, Ralihe R. Villagr´an, and Prateek K. Vishwakarma. The strong spectral property of graphs: graph operations and barbell partitions. Graphs Combin., 40(2):Paper No. 20, 25, 2024.
5) Shaun Fallat, Neha Joshi, Roghayeh Maleki, Karen Meagher, Seyed Ahmad Mojallal, Shahla Nasserasr, Mahsa N. Shirazi, Andriaherimanana Sarobidy Razafimahatratra, and Brett Stevens. The q-analogue of zero forcing for certain families of graphs. Discrete Appl. Math., 348:91–104, 2024.
6) Louis Deaett, Shaun Fallat, Veronika Furst, John Hutchens, Lon Mitchell, and Yaqi Zhang. Sparks of symmetric matrices and their graphs. J. Linear Algebra, 39:591–606, 2023.
Books
1) S.M. Fallat, C.R. Johnson, Totally nonnegative matrices. Princeton University Press, Princeton. 2011.