Mathematics & Statistics Graduate Student Seminar: topological dynamics and Ramsey theory

The Mathematics & Statistics Graduate Student Seminar will convene again this week at 1:00pm on Friday, March 22, in the Main Lounge (Burnside 1025). As usual, there will be pizza.

This week, Adrien Abgrall will talk to us about topological dynamics and Ramsey theory:

A topological group is said to be "extremely amenable" when any (continuous) action of it on a compact Hausdorff space has a global fixed point. Apart from the trivial group, very few extremely amenable groups were known until in 1998, V.G. Pestov published a proof of extreme amenability with a surprising ingredient : a well known theorem of Ramsey about colorings of finite sets. From there, the method was generalised by Kechris, Pestov and Todorcevic in 2005, building the foundations of a deep correspondence between the actions of topological groups on compact sets, and a realization of those groups as automorphism groups of structures which satisfy "Ramsey properties", that is to say where in any coloring (in a sense to be defined) one can find arbitrary monochromatic substructures. We will try to present all the key ideas underlying this unexpected correspondence, which has been interestingly refined since, and see how it provides numerous examples of extremely amenable groups.

See you all there!

All graduate students are invited. As with all talks in the graduate student seminar, this talk will be accessible to all graduate students in math and stats. This seminar was made possible by funding from the McGill Mathematics and Statistics Department and PGSS.