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Many statistical and computational tasks boil down to comparing probability measures expressed as density functions, clouds of data points, or generative models.  In this setting, we often are unable to match individual data points but rather need to deduce relationships between entire weighted and unweighted point sets. In this talk, I will summarize our team’s recent efforts to apply geometric techniques to problems in this space, using tools from optimal transport and spectral geometry. Motivated by applications in dataset comparison, time series analysis, and robust learning, our work reveals how to apply geometric reasoning to data expressed as probability measures without sacrificing computational efficiency.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by
(multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

The size Ramsey number of a graph $H$ is the minimum number of edges in a  graph $G$ with the property that no matter how we two-color the edges of  $G$, we can find a monochromatic copy of $H$. This notion was introduced  in 1978 by Erdős, Faudree, Rousseau, and Schelp, and despite more than  four decades of work, there is a lot that is still unknown; notably, of  the four questions that conclude the Erdős–Faudree–Rousseau–Schelp paper,  only one had been resolved as of last year. In this talk, I’ll discuss  recent work in which we resolve $\approx 2.5$ of the three remaining  questions, using a variety of new combinatorial and probabilistic constructions.

Based on joint work with David Conlon and Jacob Fox.