Aspiring and Inspiring is a collection of essays from successful women and gender minority mathematicians on what it takes to build a career in mathematics. The individual essays are intended to advise, encourage, and inspire mathematicians throughout different stages of their careers. Themes emerge as these prominent individuals describe how they ......
This book discusses advances in maximal function methods related to Poincare and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary ......
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of ......
Understanding the behavior of basic sampling techniques and intrinsic geometric attributes of data is an invaluable skill that is in high demand for both graduate students and researchers in mathematics, machine learning, and theoretical computer science. The last ten years have seen significant progress in this area, with many open problems ......
Articles in this volume are based on talks given at the International Workshop on Hopf Algebras and Tensor Categories, held from September 9-13, 2019, at Nanjing University, Nanjing, China. The articles highlight the latest advances and further research directions in a variety of subjects related to tensor categories and Hopf algebras. Primary ......
Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published ......
This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo-Fraenkel set theory without ......
Erdos asked how many distinct distances must there be in a set of $n$ points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of a compact set in order to guarantee that the set of distinct distances has positive Lebesgue measure in $R$. The finite field distance problem poses ......
The goal of this book is to present a portrait of the $n$-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts. This space plays a fundamental role in the study of Cremona groups, as it ......
