Junior Geometric Group Theory Seminar
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Wed, 19/01/2011 16:00 |
Andrew Sale (Oxford University) |
Junior Geometric Group Theory Seminar  |
SR2 |
| A brief survey of the above. | |||
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Wed, 26/01/2011 16:00 |
Nicholas Touikan (Oxford University) |
Junior Geometric Group Theory Seminar |
SR2 |
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Wed, 02/02/2011 16:00 |
Nicholas Touikan (Oxford University) |
Junior Geometric Group Theory Seminar |
SR2 |
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Wed, 09/02/2011 16:00 |
Alessandro Sisto (Oxford University) |
Junior Geometric Group Theory Seminar |
SR2 |
| After a quick-and-dirty introduction to nonstandard analysis, we will define the asymptotic cones of a metric space and we will play around with nonstandard tools to show some results about them. For example, we will hopefully prove that any separable asymptotic cone is proper and we will classify real trees appearing as asymptotic cones of groups. | |||
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Wed, 16/02/2011 16:00 |
Lars Scheele (University Muenster) |
Junior Geometric Group Theory Seminar |
SR2 |
| The construction of the asymptotic cone of a metric space which allows one to capture the "large scale geometry" of that space has been introduced by Gromov and refined by van den Dries and Wilkie in the 1980's. Since then asymptotic cones have mainly been used as important invariants for finitely generated groups, regarded as metric spaces using the word metric. However since the construction of the cone requires non-principal ultrafilters, in many cases the cone itself is very hard to compute and seemingly basic questions about this construction have been open quite some time and only relatively recently been answered. In this talk I want to review the definition of the cone as well as considering iterated cones of metric spaces. I will show that every proper metric space can arise as asymptotic cone of some other proper space and I will answer a question of Drutu and Sapir regarding slow ultrafilters. | |||
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Wed, 23/02/2011 16:00 |
Hemanth Saratchandran (Oxford University) |
Junior Geometric Group Theory Seminar |
SR2 |
| I will give a brief introduction to the Steenrod squares and move on to show some applications of them in Topology and Geometry. | |||
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Wed, 02/03/2011 16:00 |
John Mackay (Oxford University) |
Junior Geometric Group Theory Seminar |
SR2 |
| We'll survey some of the ways that hyperbolic groups have been studied using analysis on their boundaries at infinity. | |||
