Schur polynomials are the characters of finite-dimensional irreducible representations of the general linear group. We will discuss both continuous and discrete concavity property of Schur polynomials. There will be one theorem and eight conjectures. No background beyond basic representation theory will be necessary to enjoy the talk. Based on joint work with Jacob Matherne, Karola Mészáros, and Avery St. Dizier.
In a recent result, Buckmaster and Vicol proved non-uniqueness of weak solutions to the Navier-Stokes equations which have bounded kinetic energy and integrable vorticity.
We discuss the existence of such solutions, which in addition are regular outside a set of times of dimension less than 1.
In various applications, one is given the advice or predictions of several classifiers of unknown reliability, over multiple questions or queries. This scenario is different from standard supervised learning where classifier accuracy can be assessed from available labeled training or validation data, and raises several questions: given only the predictions of several classifiers of unknown accuracies, over a large set of unlabeled test data, is it possible to
a) reliably rank them, and
The first lecture in this series is an introduction to the theory of asymptotic spectra. This theory describes asymptotic behavior of basic objects in mathematics like graphs and tensors. Example applications that we will see are the matrix multiplication problem, the cap set problem, the sunflower problem, the quantum entanglement problem, and the problem of efficient communication over a noisy channel. We will start from scratch.
Most people interact with machine learning systems on a daily basis. Such interactions often happen in strategic environments where people have incentives to manipulate the learning algorithms. As machine learning plays a more prominent role in our society, it is important to understand whether existing algorithms are vulnerable to adversarial attacks and, if so, design new algorithms that are robust in these strategic environments.
This talk is about qualitative properties of the underlying scheme of Rapoport-Zink formal moduli spaces of p-divisible groups, resp. Shtukas. We single out those cases when the dimension of this underlying scheme is zero, resp. those where the dimension is maximal possible. The model case for the first alternative is the Lubin-Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.