Course Descriptions

16:640:560 - Homological Algebra

Spring 2021 - Ian Coley

Course Description:

Homological algebra is an essential tool in algebraic geometry and algebraic topology and find use in representation theory, Lie theory, and much more. Roughly, it is a first step in applying some category theory to questions of concrete interest. Main topics: chain complexes, abelian and triangulated categories, derived functors, (co)homology. Actual computations will be emphasized!

Prerequisites:

451-2 (or permission)

Text:

 An introduction to Homological Algebra, Weibel [other resources TBD]

 

Schedule of Sections:

Previous Semesters:

Fall 2018

Daniel Krashen

Text:

An introduction to homological algebra, by C. Weibel, Cambridge U. Press

Prerequisites:

First-year knowledge of groups and modules.

Course Description:

From some perspectives, homological algebra is the study of the failure of modules over rings (and related objects) to behave like vector spaces. Somewhat more precisely, homological algebra collects a number of ideas and tools with origins in topology, such as chain complexes and derived functors, to study categories of modules and other Abelian categories. Homological algebra is fairly ubiquitous, and finds applications in 

module theory over rings

representations of groups and Lie algebras

sheaves on algebraic varieties

algebraic topology

various other subjects