Quy Pham

My research lies at the interface of harmonic analysis, geometric measure theory, and combinatorics, centered on understanding how the geometric and combinatorial structure of a set constrains the configurations of distances, areas, and other geometric quantities it can generate. Many such questions, from continuous settings in Euclidean spaces to their discrete and finite field analogues, can be reformulated as problems about controlling these configurations, which frequently leads to the study of decay and boundedness properties of associated operators using tools from Fourier and harmonic analysis.

My primary tools are Fourier integral operators and microlocal analysis, which I use to obtain sharp dimensional thresholds for configuration set problems, generalizing the Falconer distance conjecture to a broad class of k-point configurations.

As a Patricia Caldwell Postdoctoral Fellow at Virginia Tech, mentored by Eyvindur Ari Palsson, I continue to pursue these questions alongside related problems in point configurations and multilinear analysis.