What We Are Reading Today: Dante by John Took

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Updated 11 January 2020

What We Are Reading Today: Dante by John Took

For all that has been written about the author of the Divine Comedy, Dante Alighieri (1265–1321) remains the best guide to his own life and work. 

Dante’s writings are therefore never far away in this authoritative and comprehensive intellectual biography, which offers a fresh account of the medieval Florentine poet’s life and thought before and after his exile in 1302.

Beginning with the often violent circumstances of Dante’s life, the book examines his successive works as testimony to the course of his passionate humanity — his lyric poetry through to the Vita Nova as the great work of his first period; the Convivio, De vulgari eloquentia and the poems of his early years in exile; and the Monarchia and the Commedia as the product of his maturity. 

Describing as it does a journey of the mind, the book confirms the nature of Dante’s undertaking as an exploration of what he himself speaks of as “maturity in the flame of love,” says a review on the Princeton University Press website. 

The result is an original synthesis of Dante’s life and work.


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.