Hyman Bass

Alexander Lubotzky

This monograph extends this approach to the more general investigation of X-lattices, and these "tree lattices" are the main object of study. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems. Tree Lattices should be a helpful resource to researchers in the field, and may also be used for a graduate course on geometric methods in group theory.

Tree Lattices

Tsit-Yuen Lam

Andy Roy Magid

This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass, and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.

On the Occasion of Hyman Bass's 65th Birthday

Algebra, $K$-Theory, Groups, and Education

John Willard Milnor

Jeane Pierre Serre

Solution of the Subgroup Problem for SLn̳ (n[greater Than Or Equal to Sign] 3) and Spn̳ (n[greater Than Or Equal to Sign] 2)

Maria V. Otero-Espinar

Daniel Rockmore

Charles Tresser

The theme of the monograph is an interplay between dynamical systems and group theory. The authors formalize and study "cyclic renormalization", a phenomenon which appears naturally for some interval dynamical systems. A possibly infinite hierarchy of such renormalizations is naturally represented by a rooted tree, together with a "spherically transitive" automorphism; the infinite case corresponds to maps with an invariant Cantor set, a class of particular interest for its relevance to the description of the transition to chaos and of the Mandelbrot set. The normal subgroup structure of the automorphism group of such "spherically homogeneous" rooted trees is investigated in some detail. This work will be of interest to researchers in both dynamical systems and group theory.

Cyclic Renormalization and Automorphism Groups of Rooted Trees

Thomas J. Watson IBM Research Center

Amit Roy

Lectures on Topics in Algebraic K-theory

Hyman Bass

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