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2009 participants and projects

Faisal Al-Faisal

Home university:

University of Waterloo

Supervisor: 

K. Purbhoo

Project title: 

Schubert Calculus

Comments:

I worked with Professor Kevin Purbhoo on a project that dealt with Schubert calculus and the Wronski map. More specifically, we looked at what the fibres of the Wronski map say (and don't say) about the intersection of certain Schubert varieties.

Working as a Undergraduate Research Assistant (URA) was definitely an enjoyable and interesting experience. I have no reservations about recommending it to anyone interested in pursuing mathematics at a higher level. This was my third time as a URA (although my first in the Combinatorics and Optimization (C and O) department), and each time I learned a great deal both about doing mathematical research and about myself. This knowledge will no doubt be very helpful when it comes to, say, getting the most out of graduate school.

Shalev Ben-David

Home university: 

University of Waterloo

Supervisor: 

J. Geelen

Project title: 

Representability of Matroids

Comments: 

I thought the research term went very well and was a very good experience. I ended up co-authoring two papers with my supervisor.

Carmen Bruni

Home university: 

University of Waterloo

Supervisor: 

D.M. Jackson

Project title: 

Knots, Links and Invariants

Ming Ben Feng

Home university: 

University of Waterloo

Supervisor: 

C. Swamy

Project title: 

Stackelberg Minimum Spanning Tree Game

Comments:

This summer research program provides good research facilities and experience to every participant, and is an extremely good platform to meet talented people with similar interests.
I did research on a specific subclass of profit-maximization pricing problems, which can be modeled as a combinatorial game. My problem is to set prices on some edges in a graph, so that my revenue is maximized when a minimum spanning tree of the graph is purchased.
There is existing approximation algorithm for this class of problems based on trivial pricing strategy. My supervisor and I tried to tackle the problem based on a somewhat more sophisticated algorithmic approach. And the remaining task is to analyze the performance of our algorithm.

Elyot Grant

Home university: 

University of Waterloo

Supervisor:

J. Koenemann

Project title: 

Solving and Approximating Priority Cover

Comments:

This summer, I worked on providing algorithms to find exact and approximate solutions to a family of covering problems known as Priority Covering Problems. Our initial research led us to many new and exciting techniques for solving them, with relevant applications to capacitated covering problems on lines and trees. Many of my results were incorporated into a research paper in the topic. Additionally, my research led to many unforseen connections between combinatorial optimization results and known problems in computational geometry and computational learning theory. Despite the fact that both me and my supervisor were not familiar with these topics, we dove right in, read some papers, and were able to make insightful connections that were immediately relevant to our research. The summer is almost over and I still feel like I have dozens of uncharted directions in which to continue exploring. The URA experience has, for me, been extremely satisfying.

Stacey Jeffery

Home university: 

University of Waterloo

Supervisor: 

M. Mosca

Project title: 

Exact, Efficient and Information-Theoretically Secure Voting with an Arbitrary Number of Cheaters

Comments:

As a URA this summer, and in the previous year, I've had the opportunity to work on several interesting projects with some great people.
With Anne Broadbent and Alain Tapp, I worked on a voting protocol which is secure against an arbitrary number of corrupt participants. This was a really interesting and important result, which I feel very lucky to have been a part of. We are currently finishing up the paper. Anne and Alain have been really great to work with, and have let me play a big role in the actual writing of the paper and proving of results, which has been very useful experience for my future as a researcher.
Another project I've been working on, under the supervision of Anne Broadbent, is a survey of nonlocality. From this experience, I have gotten a good grounding in the subject, and now hope to attack some open problems. Nonlocality is a very broad and interesting topic, and in writing this survey I've had a chance to learn all the relevent background and important results, and organize them into a paper, which will also be useful to people wanting an overview of the subject in the future.

Steven Karp

Home university: 

University of Waterloo

Supervisor: 

I.P. Goulden

Project title: 

The Harer-Zagier Formula

Will Ma

Home university: 

University of Waterloo

Supervisor: 

P. Haxell

Project title: 

Triangle Packings and Triangle Edge Covers

Comments:

I liked how in combinatorics there is usually less background material to read, so you can dive into your problem right away. I really enjoyed the term; I felt like I was really immersed in the subject.
My supervisor and I ended up co-authoring a paper with Professor Qing Cui from China.

Malcolm Sharpe

Home university: 

University of Waterloo

Supervisor: 

L. Tunçel

Project title: 

Some Theory of Optimally Pricing Products

Vladimir Soukharev

Home university: 

University of Waterloo

Supervisor: 

D. Jao

Project title: 

Evaluating Large Prime Degree Isogenies Efficiently

Comments:

This term we have worked in the area of elliptic curve isogenies. Previous best known results for evaluating isogenies of large prime degree had an exponential running time. We were able to develop an algorithm that solves this problem in subexponential running time for horizontal isogenies. I enjoyed working in the C and O department as a URA and will continue my studies here at the graduate level.

Leanne Stuive

Home university: 

University of Waterloo

Supervisor: 

B. Guenin

Project title: 

Relationships between Grafts with the Same Even Cuts

Yi Su

Home university: 

University of Waterloo

Supervisor: 

D. Wagner

Project title: 

The lattice of integer flow of a graph (regular matroid)

Comment:

The URA program is a great experience in my life. Here I learned so much knowledge from my supervisor and my fellow students. It also taught me how difficult the research is, which in some sense makes me realize how inadequate I am. I still have a lot to learn before I can conduct any sorts of research. But this motivates me to learn more mathematics. I think that's what I get from this program.

Rachael Taylor

Home university: 

University of Waterloo

Supervisor: 

A. Childs

Project title: 

Quantum Query Complexity of Linear Functions

Comments:

We considered an unknown linear function mapping points on the n-dimensional hypercube to the real numbers. We were interested in how many queries of this function are required to determine the function.
Thoughts on program: I was exposed to many of the areas of combinatorics and optimization with an in-depth look at quantum algorithms. This was a very well organized program which provided a first hand experience in mathematical research that you would not find anywhere else.

Nathan Yeung

Home university: 

University of Waterloo

Supervisor: 

H. Wolkowicz

Project title: 

Perturbations and Sensitivity Analysis in Linear Programming