Gureyev is one of the originators of propagation-based X-ray phase-contrast imaging and the transport-of-intensity phase-retrieval methods that made it practical; his current work concerns the information-theoretic limits of imaging — how signal-to-noise, spatial resolution and radiation dose trade against one another — and the application of those limits to phase-contrast tomography, ptychography and electron microscopy, including biomedical imaging at clinically tolerable dose. Positioned against the established body of NV-ensemble quantum sensing work — DEER, nanoscale NMR and T1 relaxometry protocols operating at pT/sqrt(Hz) field sensitivity — the shared intellectual core is the noise-resolution-dose triangle: the same estimation-theory framework that sets the pT/sqrt(Hz) floor of an NV ensemble governs how many photons a phase-contrast image needs. Borderline inclusion (X-ray rather than quantum sensing), kept because the technique is explicitly about pushing resolution past conventional limits.

Varnavides leads the Curious Beams Lab, using scanning transmission electron microscopy, 4D-STEM/electron ptychography, and computational phase-retrieval to obtain atomic-resolution, three-dimensional maps of electrostatic and magnetic order (e.g., antiferromagnetic textures, charge/heat/spin transport) in quantum materials — a solid-state, electron-beam analogue to optical quantum-material imaging that similarly pushes spatial resolution past conventional limits. He joined TU Delft ImPhys as Assistant Professor in 2025 after a Miller Fellowship at UC Berkeley and is building out instrumentation for functional imaging of both materials and biological systems.