REU 2011

In the summer of 2011 the Mathematics Department of the Pennsylvania State University will host a Research Experiences for Undergraduates site. Participants will be selected from qualified applicants. We encourage students to apply for both, Summer REU and our MASS program which runs in the Fall semester of each year. Participation in REU followed by MASS provides an opportunity for completing a more substantial long-term research project.

Application deadline is February 28, 2011.

The program will run from June 29 to August 12, 2011. It will combine learning with research and include:

• Two mini-courses
  • Curved manifolds: from soap bubbles to crumpled paper
    Instructor: Andrew Belmonte, Associate of Mathematics 
  • From linear algebra to functional analysis: an introduction
    Instructor: Nate Brown, Associate Professor of Mathematics
• Weekly seminar run by the program coordinator Misha Guysinsky
• Research projects
• MASS Fest, a two day conference Conference schedule

Only US citizens and permanent residents are eligible for funding. Applications from international students are accepted, but if admitted, they will have to cover their own expenses.

Each eligible REU 2011 participant will receive a stipend of $2,500, reimbursement for room and board, and travel reimbursement up to $500.

International applicants:

(1) If English is not your native language please ask your recommenders to comment on your English proficiency in their letters;

(2) If admitted to the program, you will need to provide a proof of health insurance that meets the Exchange Visitor regulations or proof of personal funds sufficient to purchase such an insurance, and a proof of additional personal funds of $550 for miscellaneous expenses;

(3) Please make sure that your transcripts are translated into English.

Application Materials

Applications will be considered as long as positions are still available.

• Application Form
• Transcript
• Record of Mathematics courses
• Essay describing student's interest in mathematics
• Two Faculty Recommendations

Send your applications to:

REU Summer Program
111 McAllister Building
Department of Mathematics
The Pennsylvania State University
University Park, PA 16802

Make other inquiries at:

Phone: 814-865-8462
FAX: 814-865-3735
E-mail: reu@math.psu.edu

Course Descriptions

CURVED MANIFOLDS: FROM SOAP BUBBLES TO CRUMPLED PAPER

June 29 - July 8

TIME: 10:00 am - 12:20 pm

INSTRUCTOR: Andrew Belmonte

COURSE DESCRIPTION: The concept of a manifold will be introduced for the specific case of curves and surfaces embedded in Euclidean 3D space. We will start with the parameterization and geometry of a curve, and eventually surfaces. There will be some focus on curves and surfaces that satisfy variational equations, as these often correspond to things in the physical world.

FROM LINEAR ALGEBRA TO FUNCTIONAL ANALYSIS: AN INTRODUCTION

July 25 - August 5

TIME: MTWR 10:00 am - 12:15 pm

INSTRUCTOR: Nate Brown

COURSE DESCRIPTION: I will spend the first couple days on basic linear algebra (vector spaces, linear operators, etc.), but this is only to motivate and illustrate the functional analysis that will follow. We will travel as far into functional analysis as the students' background and interest allow, hopefully covering some fundamental results such as the Hahn-Banach theorem.

Research Projects

• Entropy of Z² actions , by  Allison Beemer, Travis Morrison, Savannah Smith, JJ Zanazzi 
• Z² -actions by symplectic automorphisms of a torus, by Catherine Cannizzo, Alexander Leaf, Nina Sakharova
• The Steinhaus conditon for sets in Rⁿ and Urysohn universal space, by Samuel Bloom,  James Moody,Elisabeth Berg, Joshua Keneda
• Areas of Countries and Benford’s Law, by Alex Janke and Xiangyu Wang
• A General Consideration of DNA Geometric Inequality, by Wenfang Xu  and Jiequn Han 
• Fundamental domains and the attractor of the Bowen-Series map, by Lisa Amen, Eduard Duriev and Don Laackman
• Around Livshitz Theorem, by Alena Erchenko and Yipu Wang 
• Hyperbolic Outer Billiards, by Bif (Andrew) Reiser and Henry Gorman

Schedule

Thursday, August 11

                 11:30-12:05 Bif Reiser, Henry Gorman
                           Outer Billiards in the Hyperbolic Plane
                 12:40-1:10 Efim Abrikosov
                           Poncelet type theorems

                 Lunch Break

                2:30-3:00 Ao Wang and Clara Hess
                        On periodic billiard trajectories in non-convex domains: a geometric approach.
                3:10-4:10 Josh Keneda, Elisabeth Berg, James Moody, Chenchao Chen, Xiangyu Wang, and Sam Bloom
                        Steinhaus Sets in Euclidean Space and the Urysohn Universal Space.
                4:15-4:45 Dmitri Gekhtman
                         Flying beetles

Friday, August 12

               10:00-10:30  Andrey Voinov
                         How large a variation of geodesic's normal is possible?
               10:35-11:05 Xiangyu Wang and Alex Janke
                         Areas of Countries and Benford's Law
               11:10-11:40 Cathy Cannizzo, Alexander Leaf, Nina Sakharova
                        Z2-actions by Symplectic Automorphisms of a Torus
               11:45-12:15 Allison Beemer, Travis Morrison,Savannah Smith and John Zanazzi
                        Minimal Entropy of Z2 actions

               Lunch break

               2:00-2:30 Don Laackman, Lisa Amen, and Edward Duriev
                       A Dynamical System of the Fuchsian Group Associated to Surfaces of Genus at least 2.
               2:35- 2:55 Chenchao Chen
                      Further Results on Partions with Early Conditions
               3:00-3:20 Ao Wang
                      On the polyhedral origam.
               3:20-3:40 Clara Hess
                     Crocheting curvature
               3:45-4:15 Wenfang Xu and Jiequn Han
                      A General Consideration of DNA Geometric Inequality.
               4:20-4:50 Alena Erchenko and Yipu Wang
                      Around Livshitz Theorem.