Yu-Ru Liu
Research Interests
Analytic number theory, number theory in function fields, the circle method, sieve methods
Education
2003, Ph.D. Mathematics, Harvard University, Thesis Advisor: Barry C. Mazur
1998, M.S. Mathematics, Queen’s University, Thesis Advisor: M. Ram Murty
1998, B.A. Mathematics, McGill University
Awards
2026 Krieger-Nelson Prize, Canadian Mathematical Society
2025 Equity and Inclusive Award for Women in Mathematics Committee, Faculty Association of the University of Waterloo
2024 Equity and Inclusive Community Award for Women in Mathematics Committee, Faculty of Mathematics, University of Waterloo
2013 Distinction in Teaching Award, Faculty of Mathematics, University of Waterloo
2012 Outstanding Performance Award, University of Waterloo
2011 Instructor of the Year, Mathematical Society at the University of Waterloo
2005 G. de B. Robinson Award, Canadian Mathematical Society
2003–2008 University Faculty Award, Natural Sciences and Engineering Research Council
Service
Chair, Women in Mathematics Committee, Canadian Mathematical Society, 2025-present
Director, Women in Mathematics Committee, University of Waterloo, 2023-present
Teaching*
- MATH 135 - Algebra for Honours Mathematics
- Taught in 2021, 2022
- PMATH 347 - Groups and Rings
- Taught in 2022, 2023, 2024, 2025
- PMATH 348 - Fields and Galois Theory
- Taught in 2021, 2022, 2024, 2025, 2026
- PMATH 940 - Topics in Number Theory
- Taught in 2023
* Only courses taught in the past 5 years are displayed.
Selected/Recent Publications
For a comprehensive list of publications, please refer to CV
J. Champagne, Z. Ge, T. H. Lê, Y.-R. Liu and T. D. Wooley, Equidistribution of Polynomial Sequences in Function Fields: Resolution of a Conjecture, submitted, 14 pages.
S. Das, W. Kuo and Y.-R. Liu, Generalization of Erdos-Kac theorem with applications, accepted by Canad. J. Math., 38 pages.
W. Kuo, Y.-R. Liu and T. Totani, Sums of Two Squares over F_q[T], accepted by Finite Fields Appl., 12 pages.
J. Champagne, T. H. Lê, Y.-R. Liu and T. D. Wooley, Well-distribution modulo one and the primes, accepted by Prod. Amer. Math. Soc., 5 pages.
T. H. Lê, Y.-R. Liu and T. D. Wooley, Equidistribution of polynomial sequences in function fields with applications, Adv. Math., 479 (2025) 110424, 44 pages.
J. C. Sounders and Y.-R. Liu, Sieve Methods in Random Graph Theory, Graphs and Combinatorics 39 (2023), Article number: 39, 22 pages.
S. Das, E. Elma, W. Kuo and Y.-R. Liu, On the number of irreducible factors with a given multiplicity in function fields, Finite Fields Appl. 92 (2023), Page No. 102281, 22 pages.
W. Kuo, Y.-R. Liu, S. Ribas and K. Zhou, The shifted Turán sieve method on tournaments II, Discrete Mathematics, 344 (2021), Page No. 112602, 11 pages.
W. Kuo, Y.-R. Liu and X. Zhao, The asymptotic estimates and Hasse principle for multidimensional Waring’s problem, Adv. Math. 353 (2019), 1-66.
W. Kuo, Y.-R. Liu, S. Ribas and K. Zhou, The shifted Turán sieve method on tournaments, Canad. Math. Bull. 62 (2019), 841-855.
A. Bhowmick, T. H. Lê and Y.-R. Liu, A note on character sums in finite fields, Finite Fields Appl. 46 (2017), 247-254.
W. Kuo, Y.-R. Liu and X. Zhao, Multidimensional Vinogradov-type estimates in function fields, Canad. J. Math 66 (2014), 844-873.
Y.-R. Liu and X. Zhao, A generalization of Roth's theorem in function fields, Michigan Math. J. 61 (2012), 839-866.
Y.-R. Liu, C. V. Spencer and X. Zhao, A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression (II), European J. of Combin. 32 (2011), 258-264.
Y.-R. Liu and T. D. Wooley, Waring's problem in function fields, J. Reine Angew. Math., 638 (2010), 1-67.
Y.-R Liu and C. V. Spencer, A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression, Des. Codes Cryptogr. 52 (2009), 83-91.
W. Kuo and Y.-R. Liu, Cyclicity of finite Drinfeld modules, J. London Math. Soc. 80 (2009), 567-584.
W. Kuo and Y.-R. Liu, A Carlitz module analogue of a conjecture of Erdos and Pomerance, Trans. Amer. Math. Soc. 361 (2009), 4519-4539.
Y.-R. Liu, A prime analogue of Erdos-Pomerance's conjecture for elliptic curves, Comment. Math. Helv. 80 (2005), 755-769.
Y.-R. Liu and M. R. Murty, Sieve methods in combinatorics, J. Combin. Theory Ser. A 111 (2005), 1-23.
Y.-R. Liu, A generalization of the Erdos-Kac theorem and its applications, Canad. Math. Bull. 47 (2004), 589-606.
Y.-R. Liu, A generalization of the Turán theorem and its applications, Canad. Math. Bull. 47 (2004), 573-588.