The deadline for the REU application has passed. Students accepted into the REU can find information on Info Page for REU Students.

The Mathematics Department at the University of Houston will be running a Research Experience for Undergraduates (REU) in Summer 2014. The REU will be conducted over 8 weeks, and there will be four different research projects supervised by five faculty members. Students will work on one project under the supervision of a faculty member, and have opportunities to interact with the other research groups as well as participate in professional development activities. This is a wonderful opportunity and excellent preparation for math students who expect to go to graduate school in mathematics or have a career that involves mathematical research, applications, or modeling.

We expect to obtain a large room in the Honors College for the duration of the REU, and there may also be some space available in the Math Department on the 6th floor of PGH, where the work and meetings may occur. Every other week there will be a common meeting where each group will present an informal summary of their research progress for the other faculty and students, listing their next research steps as well as their final research goals. The presentation will be delivered by students only and should be organized such that each student in the team is given the opportunity to talk.

In the last 2 weeks of the REU, each research group will work on preparing a written research summary of the results obtained during the summer and also give a final oral presentation of their results. Faculty will be actively engaged in editing the write-up, helping students prepare for the presentation, and providing feedback.

In addition to the research performed, REU students will be expected to participate in the following professional development activities.

**Professional Development Activities**

- Bi-weekly colloquium presentations about applications of scientific research.
- Social picnic.
- Participate in the SURF Brown Bag Lecture Series (once per week).
- Regular participation in SURF activities such as the writing workshop.
- Visits with summer seminar speakers.

We will try to understand how the structure of the
network impacts its ability to robustly store spatial
position, which ultimately helps an animal explore its
environment effectively. Mathematical techniques we will
develop will include perturbation theory, asymptotics, and
stochastic analysis. This will include both analytic and
numerical techniques. The results should be applicable to a
broad range of problems in spatiotemporal pattern formation.

This approach leads to the study of open dynamical systems. Here we study escape rates, hitting times, and other probabilistic concepts.

Our project is an example of what we call a micro to macro scientific
problem. How does behavior on the microscopic scale translate to
dynamics on the macroscopic scale?

In this project we will develop an understanding of the
mathematics behind the PageRank algorithm and compare it
to other ranking algorithms for webpages (e.g., the
HITS algorithm, the IBM CLEVER project, the
TrustRank algorithm, the hummingbird algorithm).
We will then seek to modify the PageRank algorithm or describe
a new algorithm that can be used to give alternate
(and hopefully better) ranking of webpages.