Student Commutative Algebra Seminar: Degenerations of Ideals and Rings

We may think of degeneration as a way to approximate a given ideal or ring by a possibly simpler ideal or ring. We will begin by understanding degenerations of an ideal in a polynomial ring to a monomial ideal (called Grobner degeneration). Analogously, we will also consider toric degenerations of rings. Finally, we will see some concrete applications of these techniques. Time permitting, we will also discuss different techniques for producing such degenerations.