UIUC Dept. of Mathematics Seminar Calendar

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Wednesday, October 20, 2010

Special Analysis Seminar
3:00 pm in 347 Altgeld Hall, Wednesday, October 20, 2010

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Enrico Le Donne (ETH)
Embeddings and non-embeddings of the subRiemannian Heisenberg group: old and new results
Abstract: This talk addresses the embedding problem for a particular example: the Heisenberg group equipped with the Carnot-Caratheodory distance. Such a metric space will be introduced and some of its properties will be mentioned. There will be a summary of previous results: existence or non-existence of embeddings for some classes of maps and some targets. Then some new results will be presented, e.g., the subRiemannian Heisenberg group can be embedded into R^4 preserving the length of all the curves.

Math 499: Introduction to Graduate Mathematics
4:10 pm in 245 Altgeld Hall, Wednesday, October 20, 2010

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Lee DeVille (Department of Mathematics, University of Illinois)
Randomness and Nature
Abstract: The world is a noisy place, and every complex mechanism must take this into account. Sometimes it is that a process needs to be stable to random perturbations; other times, it is that a process exploits these random perturbations to work properly. In either case, to understand any of this, we need to understand the effect of randomness and its interaction with complex systems. In this talk, we'll show a few examples of random dynamical systems in the real world, and then give a glimpse into the mathematical structures which can explain them.