Topology Seminar- Ideals in the ring of polynomials, Laurent polynomials and infinite series.
Tuesday, September 22, 2026
5:00 pm - 6:00 pm
Place and time: Phillips 730, 5:00-6:00pm
Speaker: Rashik Khan (GWU)
Title: Ideals in the ring of polynomials, Laurent polynomials and infinite series.
Abstract. The ring of Laurent polynomials over the integers 
is not a principal ideal domain, leading the classification of its ideals to become nontrivial. In this seminar, we use classical results in abstract algebra such as Gauss’ Lemma and Hilbert’s Basis Theorem to categorize the prime ideals of 
. We then explore computational methods such as Buchberger’s algorithm and Groebner bases that provide canonical forms for arbitrary ideals before finishing with a discussion on the application of Laurent polynomials to knot theory through the Alexander module.
Admission