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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.
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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 Monge-Ampere 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 Monge-Ampere 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 well-known 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/1404/1404-001.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 cross-fertilization
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, Seung-Jae |
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 |
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| Zhu, Ren |
University of Waterloo |
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