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 
Monday

Axioms, finitary and cofinitary matroids, tameness 
Infinite matroids associated to graphs, the wild circle
graph. 
Transfinite induction, Zorn's Lemma 
Tuesday

Connectivity, Tutte decompositions 
Infinite uniform matroids, Psimatroids, quircuit matroids

Reframing finite concepts in a generalisable form,
Separation systems 
Wednesday

Representability and graphlike spaces 
Representations of earlier examples, the Sierpinski
matroid, the Golden Gate matroid 
Compactness, topological methods 
Thursday

Trees of matroids, Topological perspectives on the axioms 
Psimatroids revisited 
Infinite games and determinacy, viewing topological
problems combinatorially 
Friday

The Matroid Intersection Conjecture, the AharoniBerger
Theorem. 
Infinite bureaucracies, unmatchable graphs 
Waves/Hindrances, `complementary slackness' formulations 
