*** Applications for the Summer 2009 program are welcome until February 22, 2009. ***
10 positions will be available in Summer 2009.
Program announcement
Application Form

Congratulations to Naomi Brownstein and Kevin Wilson, former REU participants,
for receiving graduate research fellowships from the National Science Foundation in 2008.

Tomar, Portugal

September 2006
F. Blanchet-Sadri, "Partial Words,"

F. Blanchet-Sadri, "Algorithmic Combinatorics on Words,"

Nathan D. Wetzler, "Counting Unbordered Partial Words,"

Joel Dodge, "Partial Words and the Critical Factorization Theorem,"

Thirteenth International Conference on Interdisciplinary Mathematical & Statistical Techniques, New University of Lisbon-Tomar Polytechnic Institute.

Tarragona, Spain

May 12-13, 2006
F. Blanchet-Sadri, "Partial Words," 5th International Ph.D. School in Formal Languages and Applications.

Mar 29-Apr 4, 2007
F. Blanchet-Sadri, "Fine and Wilf's periodicity result on partial words and consequences," 1st International Conference on Language and Automata Theory and Applications.

Apr 2-8, 2009
Cameron Byrum, "How many holes can an unbordered partial word contain?," 3rd International Conference on Language and Automata Theory and Applications.

Apr 2-8, 2009
Robert Mercas, "An answer to a conjecture on overlaps in partial words using periodicity algorithms," 3rd International Conference on Language and Automata Theory and Applications.

Paris, France

November 18, 2005
F. Blanchet-Sadri, "Mots partiels: Equations et Applications," LIAFA Laboratoire d'Informatique Algorithmique: Fondements et Applications.

Aachen, Germany

February 22, 2007
Kevin Wilson, "Correlations of Partial Words," STACS 2007, 24th International Symposium on Theoretical Aspects of Computer Science, joint work with F. Blanchet-Sadri a nd Joshua D. Gafni.

Stuttgart, Germany

June 30, 2009
Josh Gunter, "Complexity of Deciding Avoidability of Partial Words," DLT 2009, 13th International Conference on Developments in Language Theory, joint work with Brandon Blakeley, F. Blanchet-Sadri and Narad Rampersad.

Stara Lesna, Slovakia

Aug 28-Sep 1, 2006
Dakota Blair, "Equations on Partial Words," MFCS 2006, 31st International Symposium on Mathematical Foundations of Computer Science, joint work with F. Blanchet-Sadri and Rebeca V. Lewis.

Debrecen,Hungary

October 27, 2005
F. Blanchet-Sadri, "Partial words and three periodicity results," University of Debrecen.

October 28, 2005
F. Blanchet-Sadri, "On partial words," University of Debrecen.

October 21-24, 2008
Emily Allen, "Counting Distinct Partial Words," International Conference on Automata, Languages and Related Topics, (joint work with F. Blanchet-Sadri, Cameron Byrum, Mihai Cucuringu and Robert Mercas).

October 21-24, 2008
Michelle Cordier, "Combinatorics on Border Correlations of Partial Words," International Conference on Automata, Languages and Related Topics, (joint work with F. Blanchet-Sadri, Mihai Cucuringu and Rachel Kirsch).

Balatonfured, Hungary

May 27-30, 2008
F. Blanchet-Sadri, "Computing Weak Periods of Partial Words," FL 2008, 12th International Conference on Automata and Formal Languages, (joint work with Taktin Oey and Timothy Rankin).

May 27-30, 2008
Geoffrey Scott, "Counting Distinct Squares in Partial Words," AFL 2008, 12th International Conference on Automata and Formal Languages, (joint work with F. Blanchet-Sadri and Robert Mercas).

Nyigeryhaza, Hungary

May 23, 2008
F. Blanchet-Sadri, "Counting Unbordered Partial Words," College of Nyíregyháza, Institute of Mathematics and Computer Science, (joint work with Mihai Cucuringu, Joel Dodge and Robert Mercas).

Turku, Finland

July 3-6, 2007
Justin Palumbo, "Two Element Unavoidable Sets of Partial Words.," DLT 2007 11th International Conference on Developments in Language Theory. joint work with F. Blanchet-Sadri and N.C. Brownstein

European countries where papers from this REU program have been presented at international conferences so far are colored.
To see details of the presentations, move the cursor on the cities marked in the colored countries.

Greensboro, North Carolina

October 12-14, 2007
Naomi Brownstein, "Two Element Unavoidable Sets of Partial Words." International Conference on Advances in Interdisciplinary Statistics and Combinatorics, (joint work with F. Blanchet-Sadri and Justin Palumbo).

Memphis, Tennessee

May 15-18, 2008
Naomi Brownstein, "Two Element Unavoidable Sets of Partial Words", International Conference on Interdisciplinary Mathematical and Statistical Techniques IMST 2008/FIM XVI, (joint work with F. Blanchet-Sadri and Justin Palumbo).

Washington, District of Columbia

January 6, 2009
Rachel Kirsch, "Combinatorics on Border Correlations of Partial Words", Joint Mathematics Meetings, AMS Session on Combinatorics, II (joint work with F. Blanchet-Sadri, Michelle Cordier and Mihai Cucuringu).

Burlington, Vermont

June 19, 2008
Brian Shirey, "Periods, Partial Words, and a Result of Guibas and Odlyzko," SIAM Conference on Discrete Mathematics, (joint work with F. Blanchet-Sadri).

American states where papers from this REU program have been presented at international conferences so far are colored.
To see details of the presentations, move the cursor on the cities marked in the colored states.

This "Research Experiences for Undergraduates (REU)" project entitled Algorithmic Combinatorics on Words involves students in research at the crossroads between Mathematics and Computer Science.

Words, or strings over a finite alphabet, are natural objects in several research areas including group theory, number theory, automata and formal language theory, coding theory, and theory of algorithms.

The University of North Carolina at Greensboro will provide unique opportunities for summer research for ten students per year for an eight-week period each year. The Principal Investigator, Dr. Francine Blanchet-Sadri, can be contacted by phone at (336)256-1125 or via email at blanchet@uncg.edu.

A first objective of this interdisciplinary project is to investigate challenging problems of current interest related in particular to unavoidable sets of partial words, freeness of partial words, counting distinct partial words, and computing periods in partial words (partial words are sequences that may contain some "do not know" symbols). Research in combinatorics on partial words has the potential for impacts in numerous areas, notably in molecular biology, nano-technology, and DNA computing.

Two types of research opportunities will be provided:

1. computer related research, with students writing programs to perform experiments on partial words and to implement algorithms
   
   
2. combinatorics related research, with students investigating properties on partial words to generate conjectures and to prove theorems

These opportunities will result in the discovery of combinatorial algorithms on words that can prove useful in string searching algorithm design for instance. Students will be exposed to the techniques of language theory since this is a natural framework for formalizing and investigating strings and operations on them. While achieving this objective, a second objective of the project is for students to develop superior skills in mathematical writing and oral communication.

A third objective of this project is to submit the resulting original and high quality research on algorithmic combinatorics on words done with undergraduate students to leading journals and to encourage them to present it at national/international meetings or conferences.

A fourth objective is for students to gain experience in the use of computers and their interaction in mathematical research. As a result, World Wide Web server interfaces for automated use of the programs related to the combinatorial algorithms will be established (source code will be made available to interested parties).

Although student participants will be selected based on merit after a nationwide recruitment from a broad range of colleges and universities, a fifth objective of the project is to broaden the participation of underrepresented groups including minorities, women, and students with disabilities.

Through participating in this project, students will get motivated to pursue graduate studies in mathematical sciences as they feel the excitement and reward of making original contributions.

Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-0452020 and DMS-0754154.

Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.