The symposium emphasizes a common unifying geometrical structure in medical imaging applications. A second twist on “flattening the world” related to the above topics is the flattening of high-dimensional problems by selecting appropriate features, in this case through the use of sparsity. Medical imaging, particularly MRI and its applications to neuroscience, is a part of science that uses mathematics at many different levels. Image acquisition depends on the design of acquistion protocols to optimally reconstruct an image subject to physical and physiological constraints. Detection of consistent differences in functional or anatomical structure across different populations requires the mathematical tools of statistical inference. Prediction of behavior based on functional data requires the mathematical tools of machine learning. Another commonality in these three aspects of medical imaging is geometry. State-of-the-art acquisition methods rely on compressive sensing for which methodology is deeply rooted in the geometry of convex optimization. A common approach to signal detection involves the geometry of the level sets of random functions and the structure of their critical points. Common machine learning techniques also rely on the geometry of convex optimization.