Sparsifying Sums of Norms
The main theme I am interested in is sparsification and, more broadly, the discretization of continuous structures. One of the most beautiful and recent papers I have come across is the work of James R. Lee and his collaborators on the sparsification of sums of norms. To fully understand the technical aspects of this paper and the related unifying theories, I have designed a reading program consisting of papers and books that cover the history, background, and development of the subject.
In a sense, this paper can be viewed as a broad generalization of graph sparsification. The authors show that, for a very general class of norms, it is possible to construct sparse representations that approximate the original structure using only a limited number of entries while preserving the essential properties.