Here are a few project ideas:
Elliptic curves (characterize them, algebraic structure, analytic properties,etc.)
Blowing-up (plane curve) singularities
Newton polygons and Puiseux expansions
Genus of a curve, or other topological properties
Kinematics problem for robotics
Automatic geometric theorem proving
Improvements to Buchberger's algorithm, other algorithmic methods
Investigate a distinguished curve
These are just a few ideas, with some introductory sources. Your talk should be somehow related to algebraic geometry (and hopefully plane curves), but beyond this, you can research almost anything. You can also see what past seminars have done, along with abstracts, from 2006 and 2005. These should give you some idea of what kind of projects people have done in the past. You might want to study one of these topics, also. Please talk with me about the plan for your project to get some ideas or sources, or if you want some other project ideas.
Back to Math 499.