This REU site award supports six undergraduate researchers working under the supervision of two faculty advisors. The program will run for eight weeks. Students will divide their time between experimental calculations and mathematical analysis. Depending on their interests, students will be assigned to one of two groups. One group will work on a project in algebraic geometry and computer algebra. A useful tool in this effort is the Macaulay software which is available and not difficult to learn. The other project will be in analysis and representation theory. Students will be required to produce written reports at the end of the program and summarize their work in oral presentations to the other students and Mathematics Department.