**Dr. Amanda Knecht**

Friday, September 23, 2016

Location : Mendal, Room 154 , 2:30-3:25

**Title: Looking for Surfaces with Lots of Lines**

**Abstract: **Degree two del Pezzo surfaces are the solution spaces to polynomials of the form w^2= f(x,y,z), where f is a homogeneous degree four polynomial in the variables x, y, and z. These surfaces are two-dimensional objects that contain up to 56 lines. In this talk, we will consider surfaces who contain all 56 possible lines and all the solutions to the equation w^2= f(x,y,z) are contained in the set of lines. All work is done over small finite fields, which we will "define”. This talk is aimed to be accessible to everyone who has had a course in Modern Algebra.