Final Project Topics

Possible topics:

Schemes (Jacob B.)
Elliptic curve cryptography (Elaine, Jacob S.)
Klein's quartic curve and the simple group of order 168 (Julia)
Determinantal varieties
Syzygies
Grassmannians (Dhruv)
Rational normal scrolls (Palmer)
Toric varieties (Olivia, Jack)
Gröbner bases
Fast Gröbner Basis Computation for Boolean Polynomials is a recent preprint which describes an implementation of Buchberger's algorithm for a certain class of polynomials, and gives applications to biology and Sudoku.
Riemann curves
Algebraic groups
Kummer surfaces (Max)
Solving polynomial equations
Check out Independent Project 4 in Cox, Little, and O'Shea
Curve singularities
Moduli spaces of curves (Don)