Ahmad Abdi
Supervisor:
Ricardo Fukasawa and Bertrand Guenin
Project title:
Mixed-Integer Reformulations of Chance-Constrained Linear Programs, The Cycling Property for Binary Matroids
Comments:
The Undergraduate Research Program gave me an amazing opportunity to explore different areas of math and to basically do exciting stuff! The experience was awesome and it gave me a foresight of what graduate studies is like. The program was very socially interactive and I had a lot of discussions about math with professors and other researchers. I recommend this program to anyone interested in math.
Frank Ban
Supervisor:
Ian Goulden
Project title:
Manuel Candales
Supervisor:
Eric Katz
Project title:
Rank of effective divisors on polyhedral graphs
Lisa Elkin
Supervisor:
Stephen Vavasis
Project title:
Influence Maximization in Social Networks
Comments:
This summer I had the opportunity to work with Professor Stephen Vavasis on the influence maximization problem in social networks. The problem of identifying a group of individuals to target in a social network in order to maximize the spread of a given influence is NP-hard. My supervisor and I were able to create a model of a social network in which, if certain conditions apply, we may identify such a group. En route to obtaining this result, I gained a lot of experience in reading and discussing academic papers, working with mathematical software, and got a first-hand look at the world of research. This was a phenomenal experience that any student who is considering graduate studies would benefit from.
Guru Guruganesh
Supervisor:
Laura Sanita
Project title:
Improved Region-Growing and Combinatorial Algorithms for k-Route Cut Problems
Chuan Guo
Supervisor:
Bruce Richter
Project title:
Infinite families crossing-critical graphs
Comments:
The URA program let me experience research first-hand, which is ideal since I'm interested in pursuing graduate studies. Professor Richter met with me once a week to discuss progress and provide direction for future investigations. There were some expository papers on the area that I had to read to get a feel of what tools are available, but most of time I spent was on coming up with interesting examples and proving their properties. We produced some meaningful results, and some of that was presented in an end-of-term seminar.
Patricia Hongo
Home university:
University of Campinas
Supervisor:
Ricardo Fukasawa
Project title:
Generating cutting planes based on automatic decompositions of mixed-integer programs
Comments:
I have greatly enjoyed the experience at the Combinatorics and Optimization (C and O) department. Working in a research project under Professor Fukasawa's supervision has been very rewarding, and participating in the URA seminars has allowed me to learn more about a variety of research fields directly from renowned researchers and outstanding undergrads. I strongly recommend the URA program to all students who are interested in C and O and wish to acquire experience in research.
Egor Larionov
Supervisor:
Debbie Leung
Project title:
Analysis of quantum channels and the continuity of the two-way assisted quantum capacity
Comments:
I had a very rewarding semester working with Professor Debbie Leung on a variety of topics in quantum information theory. This term gave me the opportunity to discover the vast world of mathematical research in quantum information involving topics like topology, matrix analysis, functional analysis, measure theory, combinatorics, and information theory. Quantum research in particular, also involves connecting purely mathematical constructs to physical phenomena, which is interesting in its own right. At the end of the semester I gave a 40 minute talk to the fellow C and O URAs on introductory quantum computing, and in addition, a 20 minute talk at Institute for Quantum Computing (IQC) on my research in particular. I recommend this program to anybody who is looking to challenge themselves not only academically, but also psychologically. It is an excellent opportunity to explore ones interests, as well as identify ones strengths and weaknesses when it comes to research.
Michael Shantz
Supervisor:
Edlyn Teske-Wilson
Project title:
Solving the Elliptic Discrete Logarithm Problem Using Semaev Polynomials, Well Descent, and Groebner Basis Methods
Ruan Silva
Home university:
University of Campinas
Supervisor:
Ricardo Fukasawa
Project title:
Generating cutting planes based on automatic decompositions of mixed-integer programs
Comments:
I really enjoyed the experience of working in the summer as a URA. My research was centered in solving general mixed-integer programs using cutting planes, so I learned a lot about Integer Programming while working with Professor Fukasawa. I also had the opportunity to get to know some of the faculty members, students and staff of the C and O department, which received me very well during my stay in Waterloo. I would strongly recommend the program to students interested in learning what mathematical research is about.
Hao Sun
Supervisor:
Henry Wolkowicz
Project title:
Bandwidth Vertex Separators and Eigenvalue Optimization
Comments:
When I started this program I had little experience with optimization. This experience really allowed me to learn much about the subject. The weekly seminars really sparked my interest in combinatorics and optimization and made me seriously consider graduate studies in C and O. My project area was in solving symmetric linear systems with many zeros. We convert this to a graph theory problem via taking vertices 1 to n we connect vertices i,j if the ideal situation is to permute the rows and columns of the matrix so as to minimize the distance from the farthest non-zero entry from the main diagonal ie bandwidth However this is NP hard even when when the corresponding graph is a tree of maximum vertex degree 3. So we use a less ideal approach of a vertex separator that is everthing is close to the diagonal except a small band at the bottom and right most columns. This turns into a very nice classical linear algebra problem as we can convert this problem to an orthogonal optimization problem. It was very neat to learn about the application of linear algebra in optimization. This was a wonderful experience, and allowed me to broaden my horizons, I sincerely recommend this opportunity to any aspiring mathematician.
Hanson Wang
Supervisor:
Levent Tuncel and Bertrand Guenin
Project title:
Maximal lattice-free convex sets (polyhedra) in three-space
Comments:
This was actually my first experience with research of any kind, and I wasn't sure what to expect initially. However, Professors Tuncel and Guenin were extremely helpful and provided me with plenty of starting material and problems to attack. My work during the summer consisted of mainly proving some small results that may hopefully be used later to obtain a complete characterization of the three-dimensional maximal lattice-free convex sets. Along the way, I investigated integral lattice-free convex sets and existing results in the area, and classified some related classes of polyhedra. In addition, I was able to discover properties of one subproblem, maximal lattice-free simplices, using computer-aided enumeration. Overall, I found the URA program to be a great learning experience, and a perfect introduction into the realm of research. I definitely recommend it to anyone looking to further their studies in the C and O department.
Jonathan Zung
Home university:
University of Toronto
Supervisor:
Nick Wormald
Project title:
On the Longest Paths and the Diameter in Random Apollonian Networks