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Rachel, 3rd Year

Dr Johannes Carmesin

Photo of Dr Johannes Carmesin

MA PhD (Hamburg)

Research Fellow

Biography

So far I spent my whole academic career at Hamburg in Germany (except for some research visits and conferences).

My main interest is finite and infinite graph theory.

Most of my free time is dedicated to my wife and my children.



Research

My main interest is finite and infinite graph theory. For example, I studied how one can decompose a graph in a tree-like way such that this decomposition separates the globally highly connected substructures such as complete subgraphs or grid minors.

I also proved Halin's end-faithful spanning tree conjecture (in amended form); it says in rough terms that every infinite graph can be approximated by a tree that displays the end boundary of the graph.

Beyond that I am mainly involved in the development of Infinite Matroid Theory, a new rapidly emerging field, which began to be systematically studied after a breakthrough of Diestel et al in 2011.
The main conjecture in that field can be traced back to Nash-Williams, who suggested a way how to extend Edmonds' Intersection theorem to infinite matroids. This conjecture implies the Infinite Menger theorem, a deep result of Aharoni and Berger, which had been open for almost 50 years.

I also have a couple of papers on harmonic functions on infinite electrical networks; together with Georgakopoulos, I showed that every planar graph with the Liouville property is amenable.



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