Leclerc and Zelevinsky, motivated by the study of quasi-commuting quantum flag minors, introduced the notions of strongly separated and weakly separated collections. These notions are closely related to the theory of cluster algebras, to the combinatorics of the double Bruhat cells, and to the totally positive Grassmannian. A key feature, called ......
Generalized permutahedra are polytopes that arise in combinatorics, algebraic geometry, representation theory, topology, and optimization. They possess a rich combinatorial structure. Out of this structure we build a Hopf monoid in the category of species. Species provide a unifying framework for organizing families of combinatorial objects. Many ......
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13-17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and ......
This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early ......
This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to ......
This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to ......
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 volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13-17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various ......
Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course. Sophie Germain (1776-1831) was largely self-taught in mathematics and, two centuries ago, in solitude, devised and implemented a plan to prove Fermat's Last Theorem. We have only recently completely understood ......
