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 longterm 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:
 One minicourse: Functional Analysis and Representation Theory
Instructor: Viorel Nitica, 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 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: 8148658462
FAX: 8148653735
Email: 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, HeineBorel 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, BanachSteinhaus Theorem, Open Map ping Theorem, Closed Graph Theorem, HahnBanach 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://uobcommunity.ballarat.edu.au/~smorris/topbook.pdf
2) W. Rudin, Principles of real analysis, Elsevier, 1998
3) W. Rudin, Real and complex analysis, McGrawHill, New York, 1966
4) W. Rudin, Functional analysis, McGrawHill, 1991
5) M.T. Taylor, Noncommutative harmonic analysis, Mathematical Surveys and Monographs,
Vol. 22, American Mathematical Society, Providence, 1986
Research Projects
Rigid Tilings by Lshaped nominoes and Notched Rectangles And The Impossibility Of Tiling Odd by Odd Rectangles by Lshaped OddTiles
Aaron Calderon(The University of NebraskaLincoln)
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 MaxPlus 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
10:0010:05 Opening
10:0511:05 Rigid Tilings by Lshaped nominoes and Notched Rectangles And The Impossibility Of Tiling Odd by Odd Rectangles by Lshaped OddTiles
Aaron Calderon(The University of NebraskaLincoln)
Herman Chau (Stanford University)
Samantha Fairchild (Houghton College)
Samuel Simon (Carnegie Mellon University)
11:0511:15 Break
11:1511:45 Semigroup problems for Aff+ and related groups
Kevin Lui (UC Santa Barbara)
Siddharth Venkatesh (UC Berkeley)
11:4511:50 Break
11:5012:20 The Frog Problem, limits and bounds in a probabilistic system
Gordon Rojas Kirby (Stanford University)
Huy Mai (Brandeis University)
12:202:00 Lunch Break
2:002:50 Nigel Higson(The Pennsylvania State University)
2:503:00 Break
3:003:30 Hilbert Space Extensions of Anosov Diffeomorphisms
Thomas Silverman (Rice University)
3:303:35 Break
3:354:05 Periodic Metrics
Alexander Payne (Princeton University)
Zhaoning Yang (The Pennsylvania State University)
4:054:10 Break
4:104:30 Billiards on Graphs
Michael Miller (SCU)
Thursday, August 8
10:0011:00 The Structure of MaxPlus Hemispaces
Daniel Ehrmann (University of Tampa)
Zach Higgins (University of Florida)
Woosub Shin (College of the Holy Cross)
11:0011:10 Break
11:1011:40 Results to Improve the Efficiency of BCH and CRC Codes
Vishal Arul (Stanford University)
Glen Frost (University of Florida)
Derek Jung (UCLA)
11:4011:45 Break
11:4512:15 Symplectic Topology and Area Preserving Maps of S^2
Andrew D. Hanlon (The Pennsylvania State University)
Daniel N. Dore (Princeton University)