MATH 285C Algebra: Homology of algebras
Instructor: Christian Haesemeyer
Office: MS 6304
Time and Location:
MWF 11am, TBA
Classes on Wednesday, April 1st and Friday, April 3rd will be cancelled and made up later due to travel.
Syllabus and assignments:
This course is intended as an introduction to the homology and cohomology theory of algebras, concentrating on the construction and properties of Hochschild homology, cyclic homology and its variants.
These (co)homology theories have important applications in many areas, e.g. in commutative algebra, non-commutative algebra, algebraic K-theory and (in global versions) algebraic geometry and mathematical physics.
There are also generalizations using stable homotopy theory methods that allow us to study products structures up to infinite homotopy and the associated deformation theory.
The course will be accessible to anyone with a basic knowledge of algebra and homological algebra.
We will not use a single textbook, but the basics can be found in: C. Weibel Homological Algebra, Cambridge studies in advanced mathematics 38.