Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., Princeton University 2009
  • M.Sc., Oxford University (United Kingdom) 2004
  • B.A., Princeton University 2002
• 

  Previous Appointments & Affiliations

  • Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2018 - 2020
  • Nicholas J. and Theresa M. Leonardy Associate Professor, Mathematics, Trinity College of Arts & Sciences 2018 - 2020
  • Assistant Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2014 - 2017
• 

  Leadership & Clinical Positions at Duke

  • Distinguished Lectures and Department Colloquium, August 2019
• Recognition
• 

  In the News

  • APR 1, 2022

    Quanta Magazine

    In Math and Music, Building Mental Landscapes With Lillian Pierce

  • JUL 8, 2019

    White House Honors Four Faculty for Early Career Research Accomplishments

  • MAR 6, 2019

    Duke Mathematician Lillian Pierce Awarded Birman Fellowship

  • FEB 16, 2018

    Duke Mathematician Lillian Pierce Wins 2018 Sloan Research Fellowship

  • JUN 5, 2017

    Pierce Honored for Work in Harmonic Analysis, Analytic Number Theory

  • SEP 26, 2014

    Lillian Pierce: A Head for Pure Mathematics
• 

  Awards & Honors

  • Fellow of the AMS. AMS. 2021
  • Joan and Joseph Birman Fellow. AMS. 2019
  • PECASE. Office of the President. 2019
  • AWM Sadosky Research Prize in Analysis. AWM. 2018
  • Sloan Research Fellowship. Sloan Foundation. 2018
  • von Neumann Fellow. Institute for Advanced Study. 2017
  • Member, School of Mathematics. Institute for Advanced Study. 2009
  • Rhodes Scholar. Rhodes Trust. 2002
• Expertise
• 

  Subject Headings

  • Harmonic analysis
  • Number theory
• Research
• 

  Selected Grants

  • Class Groups, Character Sums, and Oscillatory Integrals awarded by  National Science Foundation 2022 - 2025
  • CAREER: Research and Training at the Intersection of Number Theory and Analysis awarded by  National Science Foundation 2017 - 2023
  • Sloan Foundation Fellowship for Lillian Pierce in Mathematics awarded by Alfred P. Sloan Foundation 2018 - 2020
  • Re:boot Number Theory awarded by National Security Agency 2016 - 2018
  • The circle method, character sums, and sieves: Applications to number theory and harmonic analysis awarded by  National Science Foundation 2014 - 2017
• 

  Fellowships, Supported Research, & Other Grants

  • Seed Grant: Stammtisch awarded by Duke Office of Faculty Advancement 2020
  • von Neumann Fellow awarded by Institute for Advanced Study 2017 - 2018
• 

  External Relationships

  • Banff International Research Station
  • Finnish centre of excellence in Randomness and STructures (FiRST)
  • Hausdorff Center for Mathematics
  • Institute for Advanced Study, governing board for Women and Math
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Gressman, P. T., S. Guo, L. B. Pierce, J. Roos, and P. L. Yung. “Reversing a Philosophy: From Counting to Square Functions and Decoupling.” Journal of Geometric Analysis 31, no. 7 (July 1, 2021): 7075–95. https://doi.org/10.1007/s12220-020-00593-x.
       Full Text
    • Pierce, L. B. “On Superorthogonality.” Journal of Geometric Analysis 31, no. 7 (July 1, 2021): 7096–7183. https://doi.org/10.1007/s12220-021-00606-3.
       Full Text
    • Pierce, Lillian B., William Beckner, Galia Dafni, Charles Fefferman, Alexandru Ionescu, Vickie Kearn, Carlos E. Kenig, et al. “Elias M. Stein (1931–2018).” Notices of the American Mathematical Society 68, no. 04 (April 1, 2021): 1–1. https://doi.org/10.1090/noti2264.
       Full Text
    • An, Chen, Rena Chu, and Lillian B. Pierce. “Counterexamples for high-degree generalizations of the Schrödinger maximal operator,” 2021.
       Link to Item
    • Pierce, Lillian B., Caroline L. Turnage-Butterbaugh, and Melanie Matchett Wood. “On a conjecture for $\ell$-torsion in class groups of number fields: from the perspective of moments.” Mathematical Research Letters 28, no. 2 (2021): 575–621.
       Link to Item
    • Pierce, Lillian, Alina Bucur, Alina Cojocaru, and Matilde Lalin. “Geometric generalizations of the square sieve, with an application to cyclic covers,” 2021.
       Link to Item
    • Pierce, Lillian, Philip Gressman, Shaoming Guo, Joris Roos, and Po-Lam Yung. “On the strict majorant property in arbitrary dimensions,” 2021.
       Link to Item
    • Pierce, Lillian. “Counting problems: class groups, primes, and number fields, ICM 2022 Proceedings (accepted, in press),” 2021.
    • Pierce, L. B. “ON BOURGAIN’S COUNTEREXAMPLE for the SCHRÖDINGER MAXIMAL FUNCTION.” Quarterly Journal of Mathematics 71, no. 4 (December 1, 2020): 1309–44. https://doi.org/10.1093/qmath/haaa032.
       Full Text
    • Fefferman, Charles, Alex Ionescu, Terence Tao, and Stephen Wainger. “Analysis and applications: The mathematical work of Elias Stein.” Bulletin of the American Mathematical Society 57, no. 4 (March 3, 2020): 523–94. https://doi.org/10.1090/bull/1691.
       Full Text
    • Alaifari, R., X. Cheng, L. B. Pierce, and S. Steinerberger. “On matrix rearrangement inequalities.” Proceedings of the American Mathematical Society 148, no. 5 (January 1, 2020): 1835–48. https://doi.org/10.1090/proc/14831.
       Full Text
    • Pierce, L. B., C. L. Turnage-Butterbaugh, and M. M. Wood. “An effective Chebotarev density theorem for families of number fields, with an application to $\ell$-torsion in class groups.” Inventiones Mathematicae 219 (2020): 707–78.
       Open Access Copy  Link to Item
    • Pierce, L. B., and J. Xu. “Burgess bounds for short character sums evaluated at forms.” Algebra and Number Theory 14, no. 7 (January 1, 2020): 1911–51. https://doi.org/10.2140/ant.2020.14.1911.
       Full Text
    • Pierce, Lillian B. “Burgess bounds for short character sums evaluated at forms II: the mixed case,” 2020.
       Link to Item
    • Chruściel, P. T., A. De Mesmay, M. Păun, E. Peyre, F. Barthe, H. A. Helfgott, M. Kontsevich, et al. “Séminaire Bourbaki Volume 2016/2017 Exposés 1120-1135.” Asterisque 407 (January 1, 2019): 1–602. https://doi.org/10.24033/ast.1057.
       Full Text
    • Pierce, L. B., and P. L. Yung. “A polynomial Carleson operator along the paraboloid.” Revista Matemática Iberoamericana, 2018.
       Link to Item
    • Carneiro, E., J. Madrid, and L. B. Pierce. “Endpoint Sobolev and BV continuity for maximal operators.” Journal of Functional Analysis 273, no. 10 (November 2017): 3262–94. https://doi.org/10.1016/j.jfa.2017.08.012.
       Full Text
    • Pierce, L. B. “The Vinogradov Mean Value Theorem [after Wooley, and Bourgain, Demeter and Guth].” Astérisque, July 4, 2017.
       Link to Item
    • Heath-Brown, D. R., and L. B. Pierce. “Simultaneous integer values of pairs of quadratic forms.” Journal Fur Die Reine Und Angewandte Mathematik 2017, no. 727 (June 1, 2017): 85–143. https://doi.org/10.1515/crelle-2014-0112.
       Full Text  Open Access Copy
    • Ellenberg, J., L. B. Pierce, and M. M. Wood. “On ℓ-torsion in class groups of number fields.” Algebra and Number Theory 11, no. 8 (2017): 1739–78. https://doi.org/10.2140/ant.2017.11.1739.
       Full Text
    • Guo, S., L. B. Pierce, J. Roos, and P. Yung. “Polynomial Carleson operators along monomial curves in the plane.” Journal of Geometric Analysis, 2017.
       Link to Item
    • Pierce, L. B. “Burgess bounds for multi-dimensional short mixed character sums.” Journal of Number Theory 163 (June 1, 2016): 172–210. https://doi.org/10.1016/j.jnt.2015.08.022.
       Full Text
    • Pierce, L. B., D. Schindler, and M. M. Wood. “Representations of integers by systems of three quadratic forms.” Proceedings of the London Mathematical Society 3, no. 113 (2016): 289–344.
       Link to Item
    • Bober, J., E. Carneiro, K. Hughes, D. Kosz, and L. B. Pierce. “Corrigendum to “on a discrete version of Tanaka’s theorem for maximal functions”.” Proceedings of the American Mathematical Society 143, no. 12 (2015): 5471–73. https://doi.org/10.1090/proc/12778.
       Full Text
    • Heath-Brown, D. R., and L. B. Pierce. “Burgess bounds for short mixed character sums.” Journal of the London Mathematical Society 91, no. 3 (2015): 693–708. https://doi.org/10.1112/jlms/jdv009.
       Full Text
    • Alaifari, R., L. B. Pierce, and S. Steinerberger. “Lower bounds for the truncated Hilbert transform.” Arxiv:1311.6845 [Math], November 26, 2013.
       Link to Item
    • Pierce, L. B. “Correction to "discrete fractional radon transforms and quadratic forms," duke math. J. 161 2012, 69-106.” Duke Mathematical Journal 162, no. 6 (2013): 1203–4. https://doi.org/10.1215/00127094-2210146.
       Full Text
    • Bober, J., E. Carneiro, K. Hughes, and L. B. Pierce. “On a discrete version of Tanaka's theorem for maximal functions.” Proceedings of the American Mathematical Society 140, no. 5 (May 1, 2012): 1669–80. https://doi.org/10.1090/S0002-9939-2011-11008-6.
       Full Text  Link to Item
    • Heath-Brown, D. R., and L. B. Pierce. “Counting rational points on smooth cyclic covers.” Journal of Number Theory 132, no. 8 (2012): 1741–57. https://doi.org/10.1016/j.jnt.2012.02.010.
       Full Text
    • Pierce, L. B. “A note on discrete fractional integral operators on the heisenberg group.” International Mathematics Research Notices 2012, no. 1 (2012): 17–33. https://doi.org/10.1093/imrn/rnr008.
       Full Text
    • Pierce, L. B. “Discrete fractional radon transforms and quadratic forms.” Duke Mathematical Journal 161, no. 1 (2012): 69–106. https://doi.org/10.1215/00127094-1507288.
       Full Text
    • Pierce, L. B. “On discrete fractional integral operators and mean values of Weyl sums.” Bulletin of the London Mathematical Society 43, no. 3 (2011): 597–612. https://doi.org/10.1112/blms/bdq127.
       Full Text
    • Pierce, L. B. “A note on twisted discrete singular Radon transforms.” Mathematical Research Letters 17, no. 4 (2010): 701–20.
    • Pierce, L. B. “A bound for the 3-part of class numbers of quadratic fields by means of the square sieve.” Forum Mathematicum 18, no. 4 (2006): 677–98. https://doi.org/10.1515/FORUM.2006.034.
       Full Text
    • Pierce, L. B. “The 3-part of class numbers of quadratic fields.” Journal of the London Mathematical Society 71, no. 3 (2005): 579–98. https://doi.org/10.1112/S002461070500637X.
       Full Text
    • Pierce, L. B., and D. R. Heath-Brown. “Averages and moments associated to class numbers of imaginary quadratic fields,” n.d.
       Link to Item

  • Preprints

    • Bonolis, Dante, and Lillian B. Pierce. “Application of a polynomial sieve: beyond separation of variables,” September 6, 2022.
       Link to Item
    • Pierce, Lillian B. “Counting problems: class groups, primes, and number fields,” June 16, 2022.
       Link to Item
    • Bucur, Alina, Alina Carmen Cojocaru, Matilde N. Lalín, and Lillian B. Pierce. “Geometric generalizations of the square sieve, with an application to cyclic covers,” September 23, 2021.
       Link to Item
    • Gressman, Philip T., Shaoming Guo, Lillian B. Pierce, Joris Roos, and Po-Lam Yung. “On the strict majorant property in arbitrary dimensions,” June 23, 2021.
       Link to Item
• Scholarly, Clinical, & Service Activities
• 

  Service to Duke

  • Anti-Racism Committee. 2020  2020
  • Centennial Task Force. 2020  2020
  • Co-Director of Distinguished Lectures and Dept. Colloquium. Duke Mathematics Department. August 2019  2019

Some information on this profile has been compiled automatically from Duke databases and external sources. (Our About page explains how this works.) If you see a problem with the information, please write to Scholars@Duke and let us know. We will reply promptly.