In this talk, Rachel Diethorn, assistant professor of mathematics at Oberlin College, will tell you a little bit about her research in commutative algebra with a focus on her favorite object: a free resolution. Free resolutions are central objects in commutative algebra that store important data describing commutative rings. In some sense, free resolutions approximate commutative rings by simpler algebraic objects and can reduce complicated algebraic problems to ones that can be handled using basic tools from linear algebra.
In this talk, we will define commutative rings, the main objects of study in commutative algebra, and give some concrete examples. Next, we will learn some methods for constructing free resolutions using tools from linear algebra and computational methods. Finally, we will discuss some related results in Diethorn's research and in projects that she worked on with her undergraduate students at Yale. This talk is meant to be accessible to students who have seen some basic linear algebra.
Join us on Monday, Mar. 25, at 3:10 p.m. in Hayes 109 to hear this exciting virtual presentation from Rachel Diethorn. We hope to see you there!