My current research interests lie in the intersection of harmonic analysis and matrix analysis, and their diverse uses in applied problems such as quantum tomography, speech recognition, radar reconstruction, and machine learning. My work thus far has centered on frame theory and Lipschitz analysis a la Kirszbraun, but has also brought to bear key ideas from differential geometry and the theory of analytic varieties (Whitney stratifications) in order to understand the phase retrieval problem in the case of impure states. I am also interested in the use of Lipschitz analysis and differential geometry to understand and improve generative models in machine learning as well as in the theory (and applications to signal processing) of higher order Fourier analysis.

**cdock@umd.edu**

Nobert Wiener Assistant Professor at Tufts University

- VQ-Flows: Vector Quantized Local Normalizing Flows Sahil Sidheekh, Chris B. Dock, Tushar Jain, Radu Balan, Maneesh K. Singh. Published as a conference paper in Uncertainty in Artificial Intelligence.
- Lipschitz Analysis of Generalized Phase Retrievable Matrix Frames Radu Balan, Chris B. Dock
- Measuring Quasiperiodicity Suddhasattwa Das, Chris B. Dock, Yoshitaka Saiki, Martin Salgado-Flores, Evelyn Sander, Jin Wu, James A. Yorke. Published in European Physical Letters.

- Lipschitz analysis of generalized phase retrievable frames at AMS Fall Western Virtual Sectional Meeting, Special Session on Harmonic Analysis: Geometry, Frames, and Sampling (2021)
- Lipschitz analysis of noisy quantum inference as phase retrieval at Approximation Theory 16 (2019)

- Towards an affine invariant generative model
- Gabor Frames, the Zak Transform and Balian-Low
- Fast iterative methods for reconstruction from non-uniform samples
- Wavelet packets and Walsh functions