Lillian Beatrix Pierce
Nicholas J. and Theresa M. Leonardy Professor
Current Research Interests
Pierce works on questions in mathematics spanning from analytic number theory to harmonic analysis.
Current Appointments & Affiliations
- Nicholas J. and Theresa M. Leonardy Professor, Mathematics, Trinity College of Arts & Sciences 2020 - 2023
- Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020
Contact Information
- Duke Box 90320 120 Science Drive,, Durham, NC 27708
- Duke Box 90320, Room 117 Physics Building, Durham, NC 27708
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pierce@math.duke.edu
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Personal website
- Background
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Education, Training, & Certifications
- Ph.D., Princeton University 2009
- M.Sc., Oxford University (United Kingdom) 2004
- B.A., Princeton University 2002
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Duke Appointment History
- Associate Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2018 - 2020
- Assistant Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2014 - 2017
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Leadership & Clinical Positions at Duke
- Distinguished Lectures and Department Colloquium, August 2019
- Recognition
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In the News
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JUL 8, 2019 -
MAR 6, 2019 -
FEB 16, 2018 -
JUN 5, 2017 -
SEP 26, 2014
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Awards & Honors
- Fellow of the AMS. AMS. 2020
- 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
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Subject Headings
- Research
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Selected Grants
- CAREER: Research and Training at the Intersection of Number Theory and Analysis awarded by National Science Foundation 2017 - 2022
- 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
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Fellowships, Supported Research, & Other Grants
- von Neumann Fellow awarded by Institute for Advanced Study 2017 - 2018
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External Relationships
- Institute for Advanced Study, governing board for Women and Math
- Publications & Artistic Works
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Selected Publications
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Academic Articles
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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, January 1, 2021. https://doi.org/10.1007/s12220-020-00593-x.Full Text
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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
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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.Full Text
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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
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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.Full Text
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Pierce, L. B., and P. L. Yung. “A polynomial Carleson operator along the paraboloid (null).” Revista Matemática Iberoamericana, 2018.Link to Item
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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.Full Text
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Heath-Brown, D. R., and L. B. Pierce. “Averages and moments associated to class numbers of imaginary quadratic fields.” Compositio Mathematica 153, no. 11 (November 1, 2017): 2287–2309. https://doi.org/10.1112/S0010437X1700728X.Full Text
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Pierce, L. B. “The Vinogradov Mean Value Theorem [after Wooley, and Bourgain, Demeter and Guth] (null).” Astérisque, July 4, 2017.Link to Item
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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.Full Text Open Access Copy
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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.Full Text
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Guo, S., L. B. Pierce, J. Roos, and P. Yung. “Polynomial Carleson operators along monomial curves in the plane (null).” Journal of Geometric Analysis, 2017.Link to Item
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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 (null).” (Submitted), 2017.Open Access Copy Link to Item
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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.Full Text
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Pierce, L. B., D. Schindler, and M. M. Wood. “Representations of integers by systems of three quadratic forms (null).” Proceedings of the London Mathematical Society 3, no. 113 (2016): 289–344.Link to Item
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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” (null).” Proceedings of the American Mathematical Society 143, no. 12 (2015): 5471–73. https://doi.org/10.1090/proc/12778.Full Text
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Heath-Brown, D. R., and L. B. Pierce. “Burgess bounds for short mixed character sums (null).” Journal of the London Mathematical Society 91, no. 3 (2015): 693–708. https://doi.org/10.1112/jlms/jdv009.Full Text
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Alaifari, R., L. B. Pierce, and S. Steinerberger. “Lower bounds for the truncated Hilbert transform (null).” Arxiv:1311.6845 [Math], November 26, 2013.Link to Item
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Pierce, L. B. “Correction to "discrete fractional radon transforms and quadratic forms," duke math. J. 161 2012, 69-106 (null).” Duke Mathematical Journal 162, no. 6 (2013): 1203–4. https://doi.org/10.1215/00127094-2210146.Full Text
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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 (null).” 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
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Heath-Brown, D. R., and L. B. Pierce. “Counting rational points on smooth cyclic covers (null).” Journal of Number Theory 132, no. 8 (2012): 1741–57. https://doi.org/10.1016/j.jnt.2012.02.010.Full Text
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Pierce, L. B. “A note on discrete fractional integral operators on the heisenberg group (null).” International Mathematics Research Notices 2012, no. 1 (2012): 17–33. https://doi.org/10.1093/imrn/rnr008.Full Text
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Pierce, L. B. “Discrete fractional radon transforms and quadratic forms (null).” Duke Mathematical Journal 161, no. 1 (2012): 69–106. https://doi.org/10.1215/00127094-1507288.Full Text
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Pierce, L. B. “On discrete fractional integral operators and mean values of Weyl sums (null).” Bulletin of the London Mathematical Society 43, no. 3 (2011): 597–612. https://doi.org/10.1112/blms/bdq127.Full Text
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Pierce, L. B. “A note on twisted discrete singular Radon transforms (null).” Mathematical Research Letters 17, no. 4 (2010): 701–20.
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Pierce, L. B. “A bound for the 3-part of class numbers of quadratic fields by means of the square sieve (null).” Forum Mathematicum 18, no. 4 (2006): 677–98. https://doi.org/10.1515/FORUM.2006.034.Full Text
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Pierce, L. B. “The 3-part of class numbers of quadratic fields (null).” Journal of the London Mathematical Society 71, no. 3 (2005): 579–98. https://doi.org/10.1112/S002461070500637X.Full Text
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Pierce, Lillian B. “Burgess bounds for short character sums evaluated at forms II: the mixed case (null),” n.d.Link to Item
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Pierce, Lillian B. “On superorthogonality,” n.d.Link to Item
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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 (null),” n.d.Link to Item
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- Scholarly, Clinical, & Service Activities
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Service to Duke
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