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Min-Max theorems in infinite combinatorics

Presented by: 
J Carmesin University of Cambridge
Friday 9th October 2015 - 13:30 to 14:25
INI Seminar Room 2
The start of my talk is the extension of the marriage theorem to infinite bipartite graphs due to Aharoni, Nash-Williams and Shelah. This is implied by the Infinite Menger Conjecture, which was proved recently by Aharoni and Berger. Next I will talk about related packing and covering conjectures in infinite graphs.

Then I will give a short introduction to infinite matroids. The matroidal point of view allows us to understand the above statements as different perspectives or special cases of the same central problem of Infinite Matroid Theory, which can be traced back to Nash-Williams.

At the end, I will mention a link between Determinacy of infinite games and that conjecture of Nash-Williams. More precisely, there is a special case of the conjecture which is equivalent to the statement that a certain family of infinite games is determined if and only if a second family of infinite games is.

This talk is self contained and I will not assume any special knowledge of the audience.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons