

Undergraduate Network Meeting
September 25, 2010
at the Fields Institute
Organizers:
Richard Cerezo, (mu(at)math.toronto.edu) and Sergio Da Silva,
(sergio.dasilva(at)utoronto.ca)
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.
Schedule:
10:00 a.m. Introduction: Matthias Neufang, Fields Institute
Lecture: Eli Glasner, Tel Aviv Universit
How to define chaos?
10:45 a.m.Break
11:15 a.m. Eric Sawyer, McMaster University
The corona problem, the MongeAmpere equation and two weight inequalities
for the Hilbert transform.
12:00 p.m. Break
1:00 p.m. Vladimir Pestov, University of Ottawa
Ultralimits, Ultraproducts, and Some Open Problems About Groups
1:45 p.m.Break
2:15 p.m. Ed Barbeau, University of Toronto
Analysis as a Process
3:00 p.m. Panel Discussion
Abstracts
Eli Glasner, Tel Aviv University
How to define chaos?
The great popularity of the notion of Chaos attracted many mathematicians
to this subject. As a consequence we have today many different interpretations
of what a chaotic behaviour should mean. I will discuss briefly
several definitions of Chaos in the theory of Dynamical Systems
and try to demonstrate, with a few simple examples, how they relate
to each other.
Eric Sawyer, McMaster University
The corona problem, the MongeAmpere equation and two weight
inequalities for the Hilbert transform.
We discuss three open problems each with a long history  what has
been done with them, what might be done in the near future, and
some connections between them.
Reference: http://www.math.mcmaster.ca/~sawyer/Publications/description.pdf
Vladimir Pestov, University of Ottawa
Ultralimits, Ultraproducts, and Some Open Problems About Groups
The mapping assigning to each convergent bounded sequence its limit
has certain natural properties wellknown since high school: it
is linear, multiplicative (the limit of the product is the product
of limits), sends a constant sequence to the corresponding constant
value, the limit of a positive sequence is positive, etc. What if
one tries to define an assignment of a number, having similar properties,
to every bounded sequence (not necessarily a convergent one)? This
way, one naturally arrives at the concept of an ultrafilter and
ultralimit, and with a little bit more effort, of an ultraproduct
of metric structures. We will discuss this construction, as well
the role played by it, particularly in group theory, and offer some
presently open questions about groups that can be stated in this
language.
References: http://arxiv.org/abs/0911.4266,
http://www.math.ucla.edu/~asl/bsl/1404/1404001.ps
Ed Barbeau, University of Toronto
Final Thoughts: Analysis as a Process
Basically, analysis is the process of taking apart some representation
of a situation, and taking it apart to understand how it works.
This necessitates a degree of abstraction and the creation of a
language to express and manipulate abstract concepts. As mathematics
develops and patterns emerge, it becomes desirable to formulate
abstract structures and these in turn allow for the crossfertilization
of different areas of mathematics. I will look at a couple of examples.
List of Participants
Full Name 
University/Affiliation 
Ban, Frank 
University of Waterloo 
Barbeau, Edward 
University of Toronto 
Barfuss, Peter 
University of Waterloo 
Bathurst, Scott 
Prism Valuation 
Bin, Wu 
University of Waterloo 
Cerezo, Richard 
University of Toronto 
Chan, Yuk Fung 
University of Toronto 
Charlesworth, Ian 
University of Waterloo 
Chen, Si Yu 
University of Toronto 
Chow, Kevin 
University of Waterloo 
Chung, Ha Yoon 
University of Toronto 
Cousins, Greg 
McMaster University 
Cui, Qitan 
University of Toronto 
da Silva, Segio 
University of Toronto 
Dawson, Sean 
University of Toronto 
Deng, Wei 
McMaster University 
Dranovski, Anne 
University of Toronto 
Ginsberg, Dan 
University of Toronto 
Glasner, Eli 
Tel Aviv University 
Gold, Nathan 
York University 
Grajo, Ramon 
University of Toronto 
Guilbault, Chris 
University of Toronto 
Han, Changho 
University of Toronto 
Hurst, Michelle 
McMaster University 
Ji, Jia 
University of Toronto 
Jung, Andrew 
University of Waterloo 
Kabir, Ifaz 
University of Waterloo 
Kim, Dy 

Kim, Joo Ho 
University of Toronto 
Kohar, Richard 
McMaster University 
Lee, SeungJae 
University of Toronto 
Lee, Yohan 
McMaster University 
Levin, Kirill 
University of Toronto 
Li, Fangda 
University of Toronto 
McDonald, Daniel 
University of Toronto 
Milcak, Juraj 
University of Toronto 
Mohsin, Faizan Khalid 
University of Toronto 
Moon, SeokHwan 
University of Toronto 
Mountford, Carrie 
University of Guelph 
Neufang, Matthias 
Carleton University, Fields Institute 
Neymanov, Tural 
University of Toronto 
Park, Daniel 
University of Toronto 
Park, Sang Hee 
University of Toronto 
Pestov, Vladimir 
University of Ottawa 
Rush, Stephen 
University of Guelph 
Sawyer, Eric 
McMaster University 
Seaton, Joshua 
University of Toronto 
Song, Gary 
University of Waterloo 
Sourisseau, Matt 
University of Toronto 
Sun, Sarah 
University of Waterloo 
Tan, Jan Kevin 
University of Toronto 
Teng, Chieh 
University of Toronto 
Tour, Dennis 
McMaster University 
Walton, Laura 
McMaster University 
Wang, Shirley 
University of Toronto 
Wang, Tuo 
Polytechnic Institute of NYU 
Wesolowski, Michael 
University of Waterloo 
Yakubovich, Alexander 
McMaster University 
Yang, John 

Zhu, Ren 
University of Waterloo 
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