April 25, 2014

Undergraduate Network Meeting
September 25, 2010
at the Fields Institute

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.


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


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  
Zhu, Ren University of Waterloo

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