University at Albany, College of Arts and Sciences

Department of Mathematics and Statistics

AMAT 721: Homological Algebra, Spring 2016


Prof. Marco Varisco,,
Office: ES-120C, Office Hours: MWF 10:25–11:20, or by appointment.


MWF 11:30–12:25 in ES-153.


Permission of instructor.


Quoting from Wikipedia: “Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert.

The development of homological algebra was closely intertwined with the emergence of category theory. By and large, homological algebra is the study of homological functors and the intricate algebraic structures that they entail. One quite useful and ubiquitous concept in mathematics is that of chain complexes, which can be studied both through their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings, modules, topological spaces, and other ‘tangible’ mathematical objects. A powerful tool for doing this is provided by spectral sequences.

From its very origins, homological algebra has played an enormous role in algebraic topology. Its sphere of influence has gradually expanded and presently includes commutative algebra, algebraic geometry, algebraic number theory, representation theory, mathematical physics, operator algebras, complex analysis, and the theory of partial differential equations. K-theory is an independent discipline which draws upon methods of homological algebra.”


None, but the following book is an excellent reference:


Weekly homework assignments.

Of course, students are expected to follow the University’s Standards of Academic Integrity.

This syllabus is subject to change. All official announcements and assignments are given in class, and this web page may not be up to date.
Marco Varisco.