|
|
|
|
Lillian
Pierce
Current appointments
Marie Curie International Fellow
Research Fellow
National Science Foundation Postdoctoral Fellow
Research Interests
Number Theory
In analytic number theory, my interests include the circle method, sieves, exponential sums, quadratic forms, Burgess' method, and counting points on varieties. Recently, I have worked on the application of such methods to problems in abstract harmonic analysis. I am now working on more classically number theoretic problems, under a Marie Curie grant.
I have also made progress on a long-standing problem relating to class numbers of quadratic fields, proving several nontrivial bounds for the 3-part of such class numbers via variants of Burgess' method, the square sieve, and the q-analogue of van der Corput's method.
Harmonic Analysis
I am interested in problems in harmonic analysis related to Fourier multipliers, singular integral operators, and Radon transforms. Recently I have worked on discrete analogues of classical operators in harmonic analysis, proving results for broad classes of families ranging from twisted discrete singular Radon transforms to discrete fractional integral operators along quadratic surfaces and a discrete analogue of fractional integration on the Heisenberg group. The techniques I developed require intricate number theoretic methods as well as substantial analytic machinery. Currently I am also working on problems relating to Carleson operators of Radon type.
|