REU 2013

In the summer of 2013 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, 2013.

The program will run from June 23 to August 9, 2013. It will combine learning with research and include:

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 2013 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 Description

FUNCTIONAL ANALYSIS AND REPRESENTATION THEORY

INSTRUCTOR: Viorel Nitica, Professor of Mathematics

COURSE DESCRIPTION: Our main goal is to introduce as rigourously as possible the representation theory of SL(2, R). 
     We will assume as known introductory topics in analysis and topology: topological spaces, Euclidean topology, continuous functions, compact spaces, metric spaces, complete- ness, Heine-Borel theorem, Baire category. For standard references, see 1) and 2) below. If needed, some of these topics will be covered during the weekly seminar, as well as in the individual meetings with the groups. 
     We start with an introduction to Lebesgue integration theory: Lebesgue Monotone Convergence Theorem, Fatou’s Lemma, Lebesgue Dominated Convergence Theorem. As an application we investigate Lp spaces. We continue with standard topics in Banach spaces: definition and examples, linear operators, Banach-Steinhaus Theorem, Open Map- ping Theorem, Closed Graph Theorem, Hahn-Banach Theorem; standard topics in Hilbert spaces: definition and examples, orthogonality, spectral theorem, unbounded operators; standard topics in Fourier analysis: Fourier series, Fourier transform, distributions, PDE with constant coefficients. 
     For the rest of the course we will read through the book "Noncommutative Harmonic Analysis” by M. T. Taylor and try to understand classical representation theory of compact Lie groups and of SL(2, R).

BIBLIOGRAPHY: 
1) Topology without tears, web resource, 
     http://uob-community.ballarat.edu.au/~smorris/topbook.pdf 
2) W. Rudin, Principles of real analysis, Elsevier, 1998 
3) W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1966 
4) W. Rudin, Functional analysis, McGraw-Hill, 1991 
5) M.T. Taylor, Noncommutative harmonic analysis, Mathematical Surveys and Monographs, 
     Vol. 22, American Mathematical Society, Providence, 1986

Research Projects

Rigid Tilings by L-shaped n-ominoes and Notched Rectangles And The Impossibility Of Tiling Odd by Odd Rectangles by L-shaped OddTiles 

Aaron Calderon(The University of Nebraska-Lincoln) 
Herman Chau (Stanford University) 
Samantha Fairchild (Houghton College) 
Samuel Simon (Carnegie Mellon University) 
Report  Presentation

Semigroup problems for Aff+ and related groups 

Kevin Lui (UC Santa Barbara) 
Siddharth Venkatesh (UC Berkeley) 
Report submitted to Topology Proceedings Presentation

The Frog Problem, limits and bounds in a probabilistic system 

Gordon Rojas Kirby (Stanford University) 
Huy Mai (Brandeis University) 
Report Presentation

Hilbert Space Extensions of Anosov Diffeomorphisms

Thomas Silverman (Rice University) 
Report Presentation

Periodic Metrics

Alexander Payne (Princeton University) 
Zhaoning Yang (The Pennsylvania State University) 
Report

Billiards on Graphs

Michael Miller (SCU) 
Report Presentation

The Structure of Max-Plus Hemispaces

Daniel Ehrmann (University of Tampa) 
Zach Higgins (University of Florida) 
Woosub Shin (College of the Holy Cross) 
Report Presentation

Results to Improve the Efficiency of BCH and CRC Codes

Vishal Arul (Stanford University) 
Glen Frost (University of Florida) 
Derek Jung (UCLA) 
Report 1 Report 2 Presentation

Symplectic Topology and Area Preserving Maps of S^2

Andrew D. Hanlon (The Pennsylvania State University) 
Daniel N. Dore (Princeton University) 
Report submitted to Electronic Research Letters Presentation

Schedule

Wednesday, August 7 

10:00-10:05 Opening 

10:05-11:05 Rigid Tilings by L-shaped n-ominoes and Notched Rectangles And The Impossibility Of Tiling Odd by Odd Rectangles by L-shaped OddTiles 
    Aaron Calderon(The University of Nebraska-Lincoln) 
    Herman Chau (Stanford University) 
    Samantha Fairchild (Houghton College) 
    Samuel Simon (Carnegie Mellon University) 

11:05-11:15 Break 

11:15-11:45 Semigroup problems for Aff+ and related groups 
    Kevin Lui (UC Santa Barbara) 
    Siddharth Venkatesh (UC Berkeley) 

11:45-11:50 Break 

11:50-12:20 The Frog Problem, limits and bounds in a probabilistic system 
    Gordon Rojas Kirby (Stanford University) 
    Huy Mai (Brandeis University) 

12:20-2:00 Lunch Break 

2:00-2:50 Nigel Higson(The Pennsylvania State University) 

2:50-3:00 Break 

3:00-3:30 Hilbert Space Extensions of Anosov Diffeomorphisms 
    Thomas Silverman (Rice University) 

3:30-3:35 Break 

3:35-4:05 Periodic Metrics 
    Alexander Payne (Princeton University) 
    Zhaoning Yang (The Pennsylvania State University) 

4:05-4:10 Break 

4:10-4:30 Billiards on Graphs 
    Michael Miller (SCU) 

Thursday, August 8 

10:00-11:00 The Structure of Max-Plus Hemispaces 
    Daniel Ehrmann (University of Tampa) 
    Zach Higgins (University of Florida) 
    Woosub Shin (College of the Holy Cross) 

11:00-11:10 Break 

11:10-11:40 Results to Improve the Efficiency of BCH and CRC Codes 
    Vishal Arul (Stanford University) 
    Glen Frost (University of Florida) 
    Derek Jung (UCLA) 

11:40-11:45 Break 

11:45-12:15 Symplectic Topology and Area Preserving Maps of S^2 
    Andrew D. Hanlon (The Pennsylvania State University) 
    Daniel N. Dore (Princeton University)