Research Experiences for Undergraduates

Program Information

for Summer 2006

The REU program at Cal Poly, San Luis Obispo will provide an opportunity for up to eight undergraduates to conduct research. The program will take place during the summer of 2006. The term will run from June 19 through August 11.

We are currently taking applications for participation in the REU program. The deadline for applications is March 3, 2006. Applications can be submitted with the web-based application form.

There will be two permanent REU faculty, Jonathan Shapiro and Joseph Borzellino, in charge of coordinating all aspects of the program. In addition, we expect that up to five additional summer REU faculty, primarily in the fields of operator theory and topology, will work as advisors with students on research problems.

The areas of operator theory and topology at Cal
Poly lend themselves particularly well to undergraduate research. The
many
operator theorists all have somewhat different areas of emphasis in
their
research, including random matrix theory, symbolic computation, control
theory,
and analytic function theory. Each area has many suitable problems that
can
be studied with a limited linear algebra background. A background
in complex variables is useful to most of the operator theory projects.

The faculty that comprise the topology group at Cal
Poly also have many different but complementary research interests.
These include differential topology, differential geometry, dynamical
systems, low dimensional topology, geometric group theory, and
algebraic geometry. Many problems in these areas are exciting for
undergraduate research. This is not only because of the inherent
geometric beauty that underlies many of these problems, but also
because these problems often require a synthesis of the topics students
will typically see in the undergraduate mathematics curriculum.

Please look at the descriptions of sample research
topics suggested by each participating faculty member.

Our program targets students who have completed their junior year with at least one rigorous course in linear algebra (for the operator theory project). All participants must be undergraduates who have not yet received their degree. Because of our funding from the NSF, participants must be U. S. citizens or permanent residents.

The Cal Poly REU program will be structured so that students have the opportunity to work in a variety of environments: closely with a faculty member, with other students, and independently.

Students will be working on open research problems, but in many instances will concentrate on building intuition through examples and through computer experimentation.

On the first day of the program, students will be introduced to each other and to participating faculty members. Their orientation will consist of a tour of the campus, including the computer labs, library, offices, and a social gathering.

In the first week, the students will be introduced to possible research projects. During these introductory lectures, students will receive extra material to read and will begin exploring some topics outside the lectures in depth. Reading material will include professional articles of an expository nature. The students will be encouraged to work collaboratively on the outside topics.

By the end of the first week, the REU faculty will discuss their research problems with the students, and the students will begin working on their problems with their faculty advisors. Students will be encouraged to work in pairs if they desire. Each student will meet individually with his/her faculty advisor for at least three hours per week, and faculty will be available every day for an informal question and answer period. Towards the end of the program, students will give short presentations describing their progress.

During the period of the program, addresses may be given by speakers chosen both internally and externally to Cal Poly. Speakers will be chosen for their ability to describe research or advanced mathematical topics in a manner accessible to undergraduates.

Please see our page on the REU Environment for more information about things students will be able to do.

During the eighth week, students will write a final report on their research results and give a final presentation. All participants will receive copies of all the reports. Students who have written reports of publishable quality will then work with their advisors to prepare papers for publication. This collaboration will continue as long as necessary.

Return to the Cal Poly Mathematics REU homepage.