Byung Chun
Home university:
University of Waterloo
Supervisor:
Joseph Cheriyan
Project title:
Researching Multicommodity cut-ratios
Research results:
I explored different possible ways to approach an approximation of the cut-ratio.
Comments:
The problem worked on was fascinating and I enjoyed working on it, but the open nature of the problem was both stimulating and frustrating. I am unsure of how to really attack problems without a reasonably good idea of where to approach it.
Kenny Fong
Home university:
University of Waterloo
Supervisor:
Alfred Menezes
Project title:
Performance Comparisons of Elliptic Curve Systems in Software
Research results:
The results will be presented at the ECC2001 Conference in October. A technical report on the results will be written.
Comments:
I studied various methods of efficiently implementing elliptic curve cryptosystems and finite field arithmetic, for example, point multiplication using efficient endomorphisms, optimal extension fields, and point halving. The algorithms were implemented on a PC using C, assembly and the OpenSSL library. The project allowed me to learn much about how mathematically-defined cryptosystems are actually implemented in practice, as well as clarified my goals and interests with respect to future graduate studies. I sincerely thank Professor Darrel Hankerson for his support and advice about the different aspects of the project.
Update 2008:
Senior Lecturer in the Department of Computer Science at Southern Illinois University Carbondale
Luis Serrano
Home University:
University of Waterloo
Supervisor:
Chris Godsil
Project Title:
Spin models, link invariants and association schemes
Comments:
The problem of determining if two knots (closed loops in space) are equivalent or not is still not completely solved. By constructing a link invariant one is able to tell in many cases. This construction leads to some amazing theory related to some special matrices called spin models (which also appear in physics), jones pairs and association schemes. Our main work was focused on finding new constructions for spin models (there are not too many known), mostly based on known results for Hadamard matrices and Nomura algebras, in order to construct better link invariants.
Update 2008:
PhD Student Department of Mathematics. University of Michigan
Craig Sloss
Home university:
University of Waterloo
Supervisor:
David Jackson
Project title:
Ribbon Tableaux and the Pattern Algebra
Research results:
The pattern algebra can be used to enumerate strings under quite general conditions. By inducing left-expansions of the sequence generator in various quotient rings it possible to solve a wide class of problems. We plan to look at ways of extending the theory further to include the concatenation of objects with internal structure. We also plan to look at a result relating the numbers of ribbon tableaux in two particular sets and to search for a combinatorial mapping between the sets, with the help of the pattern algebra. This is a long standing question of Greene.
Update 2008:
PhD Student, Department of Combinatorics & Optimization, University of Waterloo
Douglas Stebila
Home university:
University of Waterloo
Supervisor:
Stefan Wolf
Project title:
Oblivious Transfer Protocols on Binary Symmetric Channels
Research results:
Through the supervision of Professor Stefan Wolf, I was able to improve an existing communications protocol to work on a wider variety of communications channel. We will be submitting the result to the IEEE International Symposium on Information Theory, and, if accepted, give a presentation in July 2002.
Comments:
Undergraduate Research Assistantships are a great way for students considering graduate school to have a taste of the real thing. You have an opportunity to work closely with a professor, develop research skills, and see how graduate students spend their days. I really enjoyed the opportunity to give a talk during the term. An excellent introduction to the world of academic research.
Update 2008:
PhD student in mathematics at the University of Waterloo.
Joshua Tam
Home university:
University of Waterloo
Supervisor:
Michele Mosca
Project title:
On Quantum Lower Bounds for Generalized Boolean Functions
Research results:
A joint research paper is being prepared.
Comments:
This opportunity gave me a real taste of doing research in quantum computing which is a new promising field. I enjoyed working with Professor Mike Mosca who really gave me some insightful ideas. Also, I went to a conference in Toronto in May 2001 which was a new and exciting experience for me.
Adrian Tang
Home university:
University of Waterloo
Supervisor:
Jim Geelen
Project title:
Branch Decomposition and Branch Width of Graphs
Comments:
Branch decomposition and branch width of graphs contains applications in algorithmic graph theory and the study of NP-complete problems. I really enjoyed studying and researching this topic as it opened my eyes to a lot that is available in Combinatorics. My meetings with my supervisor were extremely helpful, enjoyable and inspiring. I highly recommend the Combinatorics and Optimization (C and O) Undergraduate Research Assistant (URA) program to anyone who is interested in a C and O topic.
Update 2008:
PhD Student, University of Calgary
Van Anh Truong
Home university:
University of Waterloo
Supervisor:
Levent Tuncel
Project title:
The Duality Mapping of Convex Cones
Comments:
I found this area of mathematics very beautiful and the research exciting. I really appreciated the fact that my supervisor always had several ideas at any moment for me to work on, so that whenever I found a problem too frustrating, I could work on something else and then return to the original problem later, often with new ideas and insights. The research also branched out in a few unexpected directions as a result.
Update 2008:
PhD student School of Operations Research and Industrial Engineering Cornell University
Matthew Tucker
Home university:
University of Waterloo
Supervisor:
Alfred Menezes
Project title:
Performance Comparisons of Elliptic Curve Systems in Software
Results:
We implemented new algorithms for elliptic point multiplication on curves over binary fields and prime fields, which were faster than previously existing algorithms. We also tried curves over Optimal Extension Fields, which turned out to be not as useful as originally thought. A technical report will be presented at ECC2001 in October.
Comments:
Definitely a worthwhile experience. I learned a lot about elliptic curve cryptography in general, and also about programming. The URA seminars were also a really interesting part of the summer research program.
Leo Tzou
Home university:
University of British Columbia
Supervisor:
Henry Wolkowicz
Project title:
Semi-Definite Programming and Dynamical Systems