Colloquium October 17
Date: Friday October 17
Time: 16:00 to 17:00
Place: 210 McBryde
Speaker: Sarah Witherspoon of Amherst College
Title: Cohomology in algebra
Abstract
A fundamental question about two objects, such as a tetrahedron
and a sphere, is: In what ways are they alike or not alike?
Poincare defined cohomology in geometry over 100 years ago to
encode such information as numbers. Analogous questions may
be asked about algebraic objects such as groups, rings, and
modules. Cohomology in algebra appeared during the middle of
last century as one way to deal with these questions. Since
then it has become a central tool in various algebraic subjects.
This talk will begin with an introduction to cohomology in
algebra, specifically to two flavors: Hochschild and group
cohomology. We will discuss applications such as an answer to
the above question and connections to geometry. Then we will
present various results on the cohomology of certain types of
rings, such as group rings and crossed products (which arise
naturally whenever a group acts on a ring or on a space).
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