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In this talk, I am going to talk about the nonlinear inviscid damping for a class of monotone shear flows in the finite channel for initial perturbation in Gevrey class with compact support. The main idea of the proof is to use the wave operator of a slightly modified Rayleigh operator in a well chosen coordinate system. (...)

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Since the outbreak of the coronavirus pandemic, the entire world has been forced to slow down. The scientific community has been no exception with cancellations of conferences, seminars and research visits. We are all forced to build up new communication channels, the One World Probability Seminar is an attempt to keep our community together. (...)

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Directed type theory is an analogue of homotopy type theory where types represent ∞-categories, generalizing groupoids. A bisimplicial approach to directed type theory, developed by Riehl and Shulman, is based on equipping each type with both a notion of path and a separate notion of directed morphism. (...)

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Matroids were introduced by Whitney in 1935 to provide an abstract generalization of the notion of linear independence. Whitney noted that matroids arise naturally from graphs and from matrices. More recently, people have discovered ties to matroid theory and algebraic geometry. In this talk, I will first introduce matroid theory, along with some key examples, and central questions. (...)

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Starting from any operad P, one can consider on one hand the free operad on P, and on the other hand the Baez–Dolan construction on P. These two new operads have the same space of operations, but with very different notions of arity and substitution. The main result is that the incidence bialgebras of the two-sided bar constructions of the two operads constitute together a comodule bialgebra. (...)

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It is known, by work of Bochi, Ma~n'e, Viana and others that Lyapunov exponents are highly sensitive to perturbations of a dynamical system. On the other hand, work of Ledrappier, Young and my work with Froyland and Gonz'alez-Tokman has shown that in some situations, under “noise-like” perturbations, Lyapunov exponents vary continuously. (...)

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Given a CAT(-1) space, we can associate to it a boundary at infinity and a cross ratio on said boundary. There is a series of results that tell us that, for sufficiently nice CAT(-1) spaces, the boundary together with the cross ratio uniquely determines the interior space. (...)

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If $f :\mathbb D \to C$ is locally univalent, the Schwarzian derivative is defined as $$ \mathcal S(f) = \left( \frac{f’'}{f’} \right)’ - \frac 1 2 \left( \frac{f’'}{f’} \right)^2 $$ If $f$ is univalent, this operator is conformally invariant and has a growth given by (...)

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We describe connections between invariant theory and maximum likelihood estimation (ML estimation), in the context of matrix normal models. Namely, we link ML estimation in that case to the left right action of SLxSL on tuples of matrices. This enables us to characterize ML estimation by stability under that group action. (...)

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In this talk, based on joint work with Corentin Caillaud and Thomas Pock, I will discuss the merits of some finite differences or finite elements discretizations of the total variation functional. I will mention error bounds for the recovery of sharp discontinuities, inpainting straight lines in 2D, and trying to improve on some recent approaches proposed in the literature. (...)

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Symmetric monoidal categories with duals, a.k.a. compact monoidal categories, have a pleasing string diagram calculus. In particular, any compact monoidal category is closed with [A,B] = (A* ⊗ B), and the transpose of A ⊗ B → C to A → [B,C] is represented by simply bending a string. (...)

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I will review basics of epidemic modeling including eponential growth, compartmental models and self-exciting point process models. I will illustrate how such models have been used in the past for previous pandemics and what the challenges are for forecasting the current COVID-19 pandemic. I will show some examples of fitting of data to US states and what one can do with those results. (...)

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It has long been known that holomorphic field theories on twistor space lead to “physical” field theories on Minkowski space. In this talk I will discuss a type I (unoriented) version of the topological B model on twistor space. The corresponding theory on Minkowski space is a sigma-model with target the group SO(8). (...)

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Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (...)