BiblioVault - Books about Zimmer, Robert J.

Essential Results of Functional Analysis

Robert J. Zimmer

University of Chicago Press, 1990

Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach.

Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter.

For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.

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Group Actions in Ergodic Theory, Geometry, and Topology

Selected Papers

Robert J. Zimmer

University of Chicago Press, 2019

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology.

In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

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The University of Chicago

A History

John W. Boyer

University of Chicago Press, 2024

An expanded narrative of the rich, unique history of the University of Chicago.

One of the most influential institutions of higher learning in the world, the University of Chicago has a powerful and distinct identity, and its name is synonymous with intellectual rigor. With nearly 170,000 alumni living and working in more than one hundred and fifty countries, its impact is far-reaching and long-lasting.

With The University of Chicago: A History, John W. Boyer, Dean of the College from 1992 to 2023, thoroughly engages with the history and the lived politics of the university. Boyer presents a history of a complex academic community, focusing on the nature of its academic culture and curricula, the experience of its students, its engagement with Chicago’s civic community, and the resources and conditions that have enabled the university to sustain itself through decades of change. He has mined the archives, exploring the school’s complex and sometimes controversial past to set myth and hearsay apart from fact.

Boyer’s extensive research shows that the University of Chicago’s identity is profoundly interwoven with its history, and that history is unique in the annals of American higher education. After a little-known false start in the mid-nineteenth century, it achieved remarkable early successes, yet in the 1950s it faced a collapse of undergraduate enrollment, which proved fiscally debilitating for decades. Throughout, the university retained its fierce commitment to a distinctive, intense academic culture marked by intellectual merit and free debate, allowing it to rise to international acclaim. Today it maintains a strong obligation to serve the larger community through its connections to alumni, to the city of Chicago, and increasingly to its global community. Boyer’s tale is filled with larger-than-life characters—John D. Rockefeller, Robert Maynard Hutchins, and many other famous figures among them—and episodes that reveal the establishment and rise of today’s institution.

Newly updated, this edition extends through the presidency of Robert Zimmer, whose long tenure was marked by significant developments and controversies over subjects as varied as free speech, medical inequity, and community relations.

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