Titlebook: Analysis at Large; Dedicated to the Lif Artur Avila,Michael Th. Rassias,Yakov Sinai Book 2022 The Editor(s) (if applicable) and The Author(

Nebulizer

GEAR

Equidistribution of Affine Random Walks on Some Nilmanifolds,ld. Combined with equidistribution results on the torus, this leads to an equidistribution statement on some nilmanifolds such as Heisenberg nilmanifolds. In an appendix we strengthen results of de Saxce and the first named author regarding random walks on the torus by eliminating an assumption on Zariski connectedness of the acting group.

神经

The Slicing Problem by Bourgain,s innocent and seemingly obvious question (which remains unanswered!) has established a new direction in high-dimensional geometry. It has emerged as an “engine” that inspired the discovery of many deep results and unexpected connections. Here we provide a survey of these developments, including many of Bourgain’s results.

vitreous-humor

Flatus

不容置疑

Book 2022interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-prod

引起

吞下

离开可分裂

The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows, for the weights for the error functional. In the limit, as the number of parameters tends to infinity, this gives rise to a family of parabolic equations. This survey aims to discuss this relation, focusing on the associated theoretical aspects appealing to the mathematical community and providing

亵渎

,A Weighted Prékopa–Leindler Inequality and Sumsets with Quasicubes,r inequality. This is then applied to show that if . are finite sets and . is a subset of a “quasicube”, then .. This result is a key ingredient in forthcoming work of the fifth author and Pälvölgyi on the sum-product phenomenon.