The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
1. Introduction
2. Preliminaries
3. Some properties of the algebraic convolution operation
4. Lie algebra word maps
5. Lie algebra word maps: Proof of the main theorems
6. The commutator map revisited
7. Local behavior of word maps and a lower bound on the log canonical
threshold of their fibers
8. Number theoretic interpretation of the flatness, $\varepsilon $-jet
flatness and (FRS) properties
9. Applications to the $p$-adic probabilistic Waring type problem
Itay Glazer, Northwestern University, Evanston, Illinois, and Yotam I. Hendel, Northwestern University, Evanston, Illinois.
