What We Are Reading Today: Brave New Artic: The Untold Story of the Melting North

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Updated 24 March 2020

What We Are Reading Today: Brave New Artic: The Untold Story of the Melting North

Author: Mark C. Serreze

In the 1990s, researchers in the Arctic noticed that floating summer sea ice had begun receding.
This was accompanied by shifts in ocean circulation and unexpected changes in weather patterns throughout the world. The Arctic’s perennially frozen ground, known as permafrost, was warming, and treeless tundra was being overtaken by shrubs. What was going on? Brave New Arctic is Mark Serreze’s riveting firsthand account of how scientists from around the globe came together to find answers. In a sweeping tale of discovery spanning three decades, Serreze describes how puzzlement turned to alarm as researchers concluded that the Arctic is rapidly thawing due to climate change—and humans are to blame.


What We Are Reading Today: Introductory Lectures on Equivariant Cohomology

Updated 31 March 2020

What We Are Reading Today: Introductory Lectures on Equivariant Cohomology

Author: Loring W. Tu

This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology.
Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics.
Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology.