Final Project

Prompt. Write a 5-ish page essay about a topic in, or related to, algebraic geometry. Submit via Gradescope.

Remarks. If you’d like to, you may work in groups. \(\TeX\) is encouraged but not required.

Possible Topics. There are many! Feel free to be creative; the only requirement is that it not be something we have (or will have) talked about together in class. Here are some possibilities, some of which can be found in [CLO15] or [Ful08].

• Improved Gröbner basis algorithms
• Elimination theorem
• Robot arms
• Noether normalization theorem
• Quadric hypersurfaces
• Max Noether’s fundamental theorem
• Blowing up
• Riemann-Roch theorem
• Grassmannians and the Plücker embedding
• Elliptic curves and/or elliptic curve cryptography
• Algebraic geometry and error-correcting codes
• Affine toric varieties
• Algebraic geometry and phylogenetics
• Algebraic statistics

You may find it helpful to browse the references if you’re looking for more inspiration.