Yu-Ru Liu

Yu-Ru Liu
Professor
Location: MC 5018
Status: Active

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.