**UM Math Graduate Student Seminar**

Chris Langdon

* University of Miami *

**will present**

**Groebner Bases**

Friday, October 30, 2015, 5:00pm

Ungar Building Room 402

**Abstract: **

Given an ideal I in k[x1,...xn] and a fixed monomial ordering, there exists a special generating set called a Groebner basis. We will look at the construction of these bases and see what information they encode about the affine algebraic variety defined by I. We will see that one of these bases gives the dimension of the variety while another gives information about the projections of the variety onto subspaces of k^n.

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