School of Mathematics
Institute for Advanced Study
Einstein Drive
Princeton, NJ 08540
lbpierce at math dot ias dot edu
Research Interests
Harmonic Analysis
Recently I have worked on discrete analogues in harmonic analysis. In my 2009 Princeton PhD thesis, I proved 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.
Number Theory
In analytic number theory, I have 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.
Current Interests
Currently I am a Member at the Institute for Advanced Study, where I am participating in the 2009-2010 special year in analytic number theory. My interests include the circle method, sieves, exponential sums, quadratic forms, Burgess' method, and counting points on varieties.
