Name: Mike O’Sullivan

Faculty/Rank: Assistant Professor

Department: Mathematics and Statistics

College: Sciences

Office phone: 594-6697

Other phone

E mail address: mosulliv@math.sdsu.edu

Proposal title:
Research Collaboration in Applied Algebra
with the National University of Ireland

Country/ies visited: Republic of Ireland

Institution visited:
University College Cork
University College Dublin

Dates of travel: May 20- June 4, 2005

Number of student participants: 2

Previous IP proposals submitted and grants awarded
(list titles, countries and dates):
none

Have all required reports been submitted? n/a

Other funding for this activity available/applied for: none

Proposal Abstract (75 word maximum):

We propose a collaborative research program between San Diego State University and the National University of Ireland. The mathematics department at San Diego State has a research group in the mathematics of communications and offers a master’s degree concentration in that area. The National University of Ireland has several faculty members, with whom our group has collaborated, that also work in this area. We would like to establish a yearly joint research seminar on applications of algebra in communications and related areas for graduate students and faculty. We will also initiate a faculty exchange program.

Travel report:

I. Opening/overview of intentions/activity

II. In preparation for the trip abroad
- I communicated with Patrick Fitzpatrick and Emanuel Popovici (a former doctoral student that I co-supervised with Fitzpatrick) both of University College Cork, and with Marcus Greferath and Eimear Byrne of University College Dublin. Fitzpatrick has been organizing a yearly workshop on coding and cryptography in which I have participated twice.
- We discussed international exchange of faculty and students. We decided to focus on exchange of faculty and research opportunities for graduate students. Eimear Byrne felt that Irish undergraduate students rarely travel abroad.
- I planned with M. Greferath to work on a research paper begun while he was at SDSU.
- I planned with E. Popovici and R. Moberly to discuss Moberly’s dissertation plans and opportunities for collaboration.

III. Upon arrival/specific activity
- I discussed with Fitzpatrick, who is acting Dean of Science at UCC, and with Stephen Gardiner, Head of the Maths Dept at UCD, the possibility of a faculty exchange program with the same format as we currently have with Ulm. Both were supportive. The proposal will be carried forward to the international programs office at UCD by M. Greferath. Fitzpatrick will work on it at UCC.
- I discussed with Fitzpatrick the possibility of a student “semester abroad” relationship. UCC currently has one with UC Berkeley and Fitzpatrick has met recently with representatives of other US colleges and universities. He was encouraging in this regard.
- I spoke at the 5th annual UCC Workshop on Coding and Cryptography in Cork. SDSU student Bernadette Miller (M.S program in Computer Science) spoke on elliptic curve cryptography. Raymond Moberly attended.
- Raymond Moberly (SDSU doctoral program in computational sciences) and I worked with Popovici, who is a specialist in hardware implementation of coding and cryptography. We plan to collaborate on implementation of LDPC codes (Moberly’s research).
- Marcus Greferath and I finished our work on the linear programming bound for ring linear codes, and we are now writing an article for publication. We also worked with Gary McGuire of University College, Monouth on a related topic, Hadamard matrices, that has application in design of statistical experiments. We hope to finish a paper on that material this summer.

IV. Conclusion, recommendation, and next step?
- Ireland has a very strong research community in applications of algebra, particularly to communications, with representatives at several universities. The Boole Centre and the annual workshop at UCC have established collaborative links between the different universities.
- There is an active group of electrical and micro-electronic engineers at UCC who work closely with mathematicians to implement cryptographic and error correction algorithms.
- Therefore, establishing a relationship with the Irish universities could be quite valuable to the Communications Group at SDSU, and to students in the graduate program.
- Establishment of a faculty exchange program seems to be supported, so that should be pursued. I will continue to work with Fitzpatrick at UCC and with Greferath and Byrne at UCD on this goal.
- Funding should be sought for SDSU graduate students to participate in the Workshop on Coding and Cryptography. This would primarily serve graduate students in the mathematics of communications, but would also appeal to graduate students in computer science, computational science and electrical engineering.
- I would like to see the workshop either evolve into a full week program or be supplemented by a less formal period for discussion and working groups devoted to a particular topic. Students would present their own work in a poster session or as a lecture. The long-term relationship with Irish institutions will allow students to work on ongoing research projects.
- I will investigate funding sources. SAIC, which has hired several of our graduates, Qualcomm, and other companies involved in communications work will be asked to fund student travel awards.
- Student exchange in the form of a “semester abroad” is worth pursuing (Fitzpatrick was more encouraging than those at UCD), but is second priority.