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# 2011 participants and projects

### Home university:

University of Waterlo

B. Guenin

### Project title:

Packing odd circuit covers

I really enjoyed my summer doing research. It gave me a new perspective toward math. I strongly recommend this program for undergraduate students who are interested in doing math research.

## Frank Ban

### Home university:

University of Waterloo

D.G. Wagner

### Project title:

Structure of highly symmetric one-factorizations of complete graphs

## Yu Feng

### Home university:

University of Waterloo

S. Vavasis

### Project title:

Image Segmentation Problem Via Graph Cut and Convex Optimization

I worked with Professor Stephen Vavasis on image segmentation problems through graph cut and convex optimization. Before delving deeper into the formulation of the convex optimization problem, we first looked at a paper written by a group of professors in the Cornell University. This paper is based on a graph cut algorithm which involves two typical moves, called swap moves and expansion moves. This approach gave us a good segmentation when I applied this algorithm to a real image. Then we came up with an SDP problem for image segmentation. After comparing the pattern of the total energy using these two approaches, we found that our SDP objective function is actually a very reasonable one. This research experience required a lot of programming skills which widened my knowledge in MATLAB, specificaly in image processing. I loved this Undergraduate Research Assistant (URA) experience very much because it gave me a chance to think much more independently. At the end of this program, each of us did a 20-minute presentation about our work. This also gave us an idea of how life in graduate school would be.

## Shi Hu

### Home university:

University of Waterloo

### Supervisor:

D. Jao

I was the only student in the cryptography area this summer. I was lucky to be supervised by an amazing professor David Jao, from whom I have learned a lot about computer security and pure math. It was also a great pleasure to meet other talented students from the math faculty and listen to their presentations.

One of our research results was that we obtained the new speed records for bilinear pairing computations at the 128-bit security level on ARM processors. Personally, I am really happy about the opportunity, and would even recommend those who don't have enough background in Combinatorics and Optimization (C and O) to apply.

## Tyler Johnson

### Home university:

University of Waterloo

C. Swamy

### Project title:

The Matroid Steiner Tree Problem

## Brett Kolesnik

### Home university:

University of Manitoba

N. Wormald

### Project title:

Isoperimetic inequalities for random regular graphs

I have thoroughly enjoyed my time at C and O this summer. I am very thankful for this opportunity to work closely with an experienced researcher. I benefited greatly from the weekly seminar series that was organized for URAs. Also, I would often get together with my supervisor and his graduate students to talk about interesting papers. During my stay here I have been exposed to new developments in mathematics and learned more about what research is all about. Overall, I would recommend the URA Program at C and O to anyone who loves mathematics and is considering graduate studies in the future - C and O is a great place to be!

## Alexander Remorov

### Home university:

University of Toronto

J. Koenemann

### Project title:

Combinatorial Algorithms for Market Equilibria

## Max Tabord-Meehan

### Home university:

University of Waterloo

B. Richter

### Project title:

Generalizing the Jordan Curve Theorem

## Jonathan Zung

### Home university:

University of Toronto

M. Mosca

Quantum Money