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Undergraduate Network Meeting:
Research in Combinatorics
November 27
10:00 a.m. - 4:00 p.m.
at the University of Waterloo
Mathematics and Computer Science Building (MC)
Room MC1085
Speakers:
Balazs Szegedy (Toronto)
Levent Tuncel (Waterloo)
Dave Wagner (Waterloo)
Abstracts
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Organizers: Richard Cerezo (rcerezo(at)fields.utoronto.ca),
Sarah Sun, and Yifan Li (pmclub(at)gmail.com)
Faculty Advisor: Matthias Neufang |
Undergraduate Network includes a series of mathematical talks aimed
at undergraduates, and organized into a network involving the local
universities. We will be stating with trial run of four events for
next year with faculty members as consultants.
Talks:
Levent Tuncel, University of Waterloo
A Guided tour of Mathematical Optimization
We will start the talk with linear optimization problems (optimizing
a linear function subject to linear inequalities). This will take
us to convex geometry, we will see an open problem related to the
combinatorics of polytopes (and computational complexity) as well
as some theorems of Caratheodory and Helly. Then, we will move on
to hyperplane separation theorem and duality theory of convex optimization.
We will introduce the semidefinite optimization problem (a class
of convex optimization problems with matrices as the variables).
Our path will lead us to optimization problems cast over multivariate
polynomial inequalities and we will conclude by making a connection
to real algebraic geometry and mentioning a new area of research
``convex algebraic geometry.'' Many open problems will be sprinkled
throughout the presentation.
Dave Wagner, University of Waterloo
Integer flows in graphs and regular matroids
Imagine a graph G as a collection of pipes (the edges) and junctions
(the vertices). Water currents can flow through these pipes at many
different rates as long as mass is conserved at each junction. The
set of all flows is in fact a real inner product space. The set
of vectors with integer coordinates is the lattice ?(G) of integer
flows of G.
If one forgets the coordinates of the integer flows and remembers
only the geometric "shape" of the whole lattice ?(G),
can one recover the original graph? There are a few obvious ambiguities,
and in 1997 it was conjectured that these are the only ones. In
2008, together with my undergraduate research assistant Yi Su, we
proved this conjecture.
I will sketch the main ideas of our proof, which is most naturally
cast in terms of regular matroids. Of course, I will assume no knowledge
of matroid theory, and will begin by explaining what regular matroids
are and why they are as good as graphs in many ways
Balazs Szegedy, University of Toronto
Topics in Additive Combinatorics
Final List of Participants:
| Full Name |
University/Affiliation |
| Aftab, Umar |
University of Waterloo |
| Ben-David, Shalev |
University of Waterloo |
| Bering, Edgar |
University of Waterloo |
| Boyko, Mariya |
University of Toronto (Mississauga) |
| Bradley, Nick |
Queen's University |
| Burton, Peter |
University of Toronto |
| Cerezo, Richard |
University of Toronto |
| Chammah, Tarek |
University of Waterloo |
| Chow, Kevin |
University of Waterloo |
| Dosseva, Annamaria |
University of Waterloo |
| Drabek, Rafal |
|
| Dranovski, Anne |
University of Toronto |
| Du, Chen Fei |
University of Waterloo |
| Duong, Adrian |
University of Waterloo |
| Kabir, Ifaz |
University of Waterloo |
| Lacharité, Marie-Sarah |
University of Waterloo |
| Li, Bing |
University of Toronto |
| Li, Yifan |
University of Waterloo |
| Liang, Jiayu |
University of Toronto |
| Ma, David |
University of Waterloo |
| Mauger, Philippe |
University of Waterloo |
| McLaughlin, David |
University of Waterloo |
| Mohammadi, Mohammadreza |
University of Toronto |
| Ng, Keith |
University of Toronto |
| Pashley, Bryanne |
University of Waterloo |
| Pistone, Jamie |
University of Toronto |
| Poon, Alexander |
McMaster University |
| Rhee, Donguk |
University of Waterloo |
| Sagatov, Sergei |
University of Toronto |
| Schaeffer, Luke |
University of Waterloo |
| Tham, Emin |
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| Wesolowski, Michael |
University of Waterloo |
| Yeung, Tiffany |
University of Toronto |
| Zhu, Ren |
University of Waterloo |
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