Fachbereich Mathematik 
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Programme of the Infinite Matroid Theory Summer School 2015

Each day there were talks in the morning by Nathan Bowler and Johannes Carmesin, with a chance to work on related exercises in the afternoon. There was also plenty of time to relax and get to know each other better. There are a great many open problems in infinite matroid theory which can be understood and attacked with few prerequisites, and so each day we outlined a couple of these problems related to the day's theme. These themes were also illustrated with appropriate examples. We paid particular attention to explaining the more generally applicable combinatorial techniques which are used. The themes, examples and techniques we explained are as follows:

Themes Examples Techniques
Axioms, finitary and cofinitary matroids, tameness Infinite matroids associated to graphs, the wild circle graph. Transfinite induction, Zorn's Lemma
Connectivity, Tutte decompositions Infinite uniform matroids, Psi-matroids, quircuit matroids Reframing finite concepts in a generalisable form, Separation systems
Representability and graph-like spaces Representations of earlier examples, the Sierpinski matroid, the Golden Gate matroid Compactness, topological methods
Trees of matroids, Topological perspectives on the axioms Psi-matroids revisited Infinite games and determinacy, viewing topological problems combinatorially
The Matroid Intersection Conjecture, the Aharoni-Berger Theorem. Infinite bureaucracies, unmatchable graphs Waves/Hindrances, `complementary slackness' formulations

  Seitenanfang  Impress 2015-08-10, Infinite Matroids