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Modules and Group Algebras
The notes in this volume were written as a part of a Nachdiplom course that I gave at the ETH in the summer semester of 1995. The aim of my lectures was the development of some of the basics of the interaction of homological algebra, or more specifically the cohomology of groups, and modular representation theory. Every time that I had given such a course in the past fifteen years, the choice of the material and the order of presentation of the results have followed more or less the same basic pattern. Such a course began with the fundamentals of group cohomology, and then investigated the structure of cohomology rings, and their maximal ideal spectra. Then the variety of a module was defined and related to actual module structure through the rank variety. Applications followed. The standard approach was used in my University of Essen Lecture Notes [e1] in 1984. Evens [E] and Benson [B2] have written it up in much clearer detail and included it as part of their books on the subject.
Carlson's Guide to Landscape Painting
The whys and hows of the various aspects of landscape painting: angles and consequent values, perspective, painting of trees, more. 34 black-and-white reproductions of paintings by Carlson. 58 explanatory diagrams.
Geometric and Topological Aspects of the Representation Theory of Finite Groups
These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Cohomology Rings of Finite Groups
Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the fi...
American Commando
Before the Green Berets...Before the Navy SEALs...Before the Army Rangers...There was the Long Patrol. November 1942: in the hellish combat zone of Guadalcanal, one man would make history. Lt. Col. Evans Carlson was considered a maverick by many of his comrades-and an outright traitor by others. He spent years observing guerrilla tactics all over the world, and knew that those tactics could be used effectively by the Marines. Carlson and an elite fighting force-the 2nd Raider Battalion-embarked upon a thirty-day mission behind enemy lines where they disrupted Japanese supplies, inflicted a string of defeats on the enemy in open combat, and gathered invaluable intelligence on Japanese operations on Guadalcanal. And in the process they laid the foundation for every branch of Special Forces in the modern military. Here, for the first time, is a riveting account of one man, one battalion, and one mission that would forever change the ways of warfare.
John F. Carlson and Artists of the Broadmoor Academy
A comprehensive overview of the Broadmoor Academy in Colorado Springs, Colorado (forerunner to the Colorado Springs Fine Arts Center). Includes an essay by Stanley Cuba, 44 color plates and biographies of artists including, John F. Carlson, Sven Birger Sandzen, Ernest Lawson, Boardman Robinson, Robert Reid, Willard Nash, Charles Ragland Bunnell, and more.
An Invitation to Computational Homotopy
An Invitation to Computational Homotopy is an introduction to elementary algebraic topology for those with an interest in computers and computer programming. It expertly illustrates how the basics of the subject can be implemented on a computer through its focus on fully-worked examples designed to develop problem solving techniques. The transition from basic theory to practical computation raises a range of non-trivial algorithmic issues which will appeal to readers already familiar with basic theory and who are interested in developing computational aspects. The book covers a subset of standard introductory material on fundamental groups, covering spaces, homology, cohomology and classifyi...
