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 14, 2023

    Trinity College of Arts and Sciences

    Four Trinity Faculty, Three Alums Win Guggenheim Fellowships

  • 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: Duke's Society for Women in Science awarded by Duke Office of Faculty Advancement 2020
  • von Neumann Fellow awarded by Institute for Advanced Study 2017 - 2018
• 

  External Relationships

  • 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

    • An, Chen, Rena Chu, and Lillian B. Pierce. “Counterexamples for High-Degree Generalizations of the Schrödinger Maximal Operator.” International Mathematics Research Notices 2023, no. 10 (May 11, 2023): 8371–8418. https://doi.org/10.1093/imrn/rnac088.
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    • Bonolis, Dante, and Lillian B. Pierce. “Application of a polynomial sieve: beyond separation of variables,” September 6, 2022.
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    • Bucur, Alina, Alina Carmen Cojocaru, Matilde N. Lalín, and Lillian B. Pierce. “Geometric generalizations of the square sieve, with an application to cyclic covers.” Mathematika: A Journal of Pure and Applied Mathematics, 2022.
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    • Gressman, Philip T., Shaoming Guo, Lillian B. Pierce, Joris Roos, and Po-Lam Yung. “On the strict majorant property in arbitrary dimensions.” Quarterly Journal of Mathematics, 2022.
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    • Pierce, Lillian, Theresa Anderson, and Dominique Maldague. “On polynomial Carleson operators along quadratic hypersurfaces,” 2022.
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    • 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.
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    • 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.
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    • 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.
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    • Pierce, L. B. “Burgess bounds for short character sums evaluated at forms II: the mixed case.” Rivista Di Matematica Della Universita Di Parma 12, no. 1 (January 1, 2021): 151–79.
    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • Pierce, Lillian B. “Burgess bounds for short character sums evaluated at forms II: the mixed case,” 2020.
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    • 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.
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    • Pierce, L. B., and P. L. Yung. “A polynomial Carleson operator along the paraboloid.” Revista Matemática Iberoamericana, 2018.
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    • 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.
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    • Pierce, L. B. “The Vinogradov Mean Value Theorem [after Wooley, and Bourgain, Demeter and Guth].” Astérisque, July 4, 2017.
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    • 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.
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    • 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.
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    • Guo, S., L. B. Pierce, J. Roos, and P. Yung. “Polynomial Carleson operators along monomial curves in the plane.” Journal of Geometric Analysis, 2017.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • Alaifari, R., L. B. Pierce, and S. Steinerberger. “Lower bounds for the truncated Hilbert transform.” Arxiv:1311.6845 [Math], November 26, 2013.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • Pierce, L. B., and D. R. Heath-Brown. “Averages and moments associated to class numbers of imaginary quadratic fields,” n.d.
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  • Preprints

    • Browning, Tim, Lillian B. Pierce, and Damaris Schindler. “Generalised quadratic forms over totally real number fields,” December 21, 2022.
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    • Gressman, Philip T., Lillian B. Pierce, Joris Roos, and Po-Lam Yung. “A new type of superorthogonality,” December 17, 2022.
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    • Anderson, Theresa C., Dominique Maldague, and Lillian Pierce. “On Polynomial Carleson operators along quadratic hypersurfaces,” November 28, 2022.
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• 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

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