2018 Winner: Lillian Pierce
The 2018 AWM Sadosky Research Prize in Analysis is awarded to Lillian Pierce in recognition of her outstanding contributions to harmonic analysis and analytic number theory. Pierce is one of the most talented, original and visionary analysts of her generation. Her research spans and connects a broad spectrum of problems ranging from character sums in number theory to singular integral operators in Euclidean spaces. She has made far-reaching contributions to the study of discrete analogs of harmonic-analytic integral operators, taking inspiration in classical Fourier analysis, but drawing also on methods from analytic number theory such as the circle method and diophantine approximation. In her recent work with Po Lam Yung, hailed as a remarkable breakthrough and a tour de force, she proved a polynomial Carleson theorem for manifolds, connecting two major directions of research in harmonic analysis and opening up entirely new research programs. Pierce’s work on estimating short character sums, on her own and then in collaboration with Roger Heath-Brown, has produced the first significant advance in several decades on this central and difficult problem in analytic number theory. Pierce is highly regarded for her broad vision, deep knowledge of several areas of mathematics, and outstanding technical skill. Her leadership and influence in the field are widely acknowledged.
Lillian Pierce received her Ph.D. degree in 2009 from Princeton University, and has held appointments at the Institute for Advanced Study, Oxford University, and the Hausdorff Center for Mathematics before assuming her current position at Duke University. She is the recipient of a Marie Curie Fellowship, NSF Mathematical Sciences Postdoctoral Research Fellowship, and an NSF CAREER award. She has a visible and active presence in the mathematical community. Her award of the AWM Sadosky Prize is a worthy testament to her excellence.
I am greatly honored to receive the AWM Sadosky Research Prize in Analysis. The frontier between harmonic analysis and number theory seems to become more vivid and intriguing with each year, and I am delighted that results in both fields, and their intersection, are cited for this award, including collaborations with Roger Heath-Brown and Po-Lam Yung. Although I did not get to meet Cora Sadosky, I indulge in feeling a kinship with her, as two descendants in the Calderón-Zygmund family. In reading reminiscences of Cora’s work and life, it seems that one of her lessons for us is how effectively a mentor’s personal impact can set a young career in motion. That was true for me, starting with the courses in analysis Elias Stein gave at Princeton when I was an undergraduate. The crystalline clarity of his lectures, writings, and discussions led me to a career in mathematics, and harmonic analysis in particular; then the mentorship of Roger Heath-Brown and Peter Sarnak allowed me to make a leap into analytic number theory. I feel tremendous gratitude for these generous mentors who continue to inspire me with new problems, and also for the creativity and technical expertise of my collaborators, from whom I have learned so much.