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The study of exponential sums with multiplicative coefficients is classical in analytic number theory, yet our understanding of them is far from complete. This is unsurprising, seeing as multiplicative functions alone are often difficult objects to grasp. However, in recent years, our…
The Ramsey number r(s,t) denotes the minimum N such that in any red-blue coloring of the edges of the complete graph on N vertices, there exists a red complete graph on s vertices or a blue complete graph on t vertices. While the study of these quantities goes back almost one hundred…
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In recent years, machine learning has motivated the study of what one might call "nonlinear random matrices." This broad term includes various random matrices whose construction involves the entrywise application of some deterministic nonlinear function, such as ReLU. We study one such…
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In recent years, researchers have developed a number of fast, randomized algorithms for linear algebra problems. But for widespread deployment of these methods, speed is not enough. To safely incorporate randomized algorithms into general-purpose linear algebra software, we need algorithms which…
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