## 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)