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%Write your title here: 
\noindent{\bf\Large Sparsity and dimension}

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\noindent  \underline{Gwenaël Joret} -- {\small Université Libre de Bruxelles, Bruxelles, Belgium}


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\noindent{\bf Abstract:} %Here write your abstract
In this talk we will look at posets and their dimension through the
lens of the Nesetril-Ossona de Mendez theory of sparsity for graphs.
The type of questions studied here are of the following form: Given
some fixed sparse class of graphs, is it true that posets whose cover
graphs are in the class have dimension bounded in terms of their
height? This is the case for instance for planar graphs, as shown by
Streib and Trotter. There has been a flurry of positive results in
that direction recently, including classes with bounded treewidth,
bounded genus, and more generally excluding a fixed minor. I will
first give an introduction to this area, assuming no background
knowledge on posets. Then I will sketch a proof that the above
property holds more generally for every class with bounded expansion,
a result obtained jointly with Piotr Micek and Veit Wiechert. This is
in a sense best possible, as it cannot be extended to nowhere dense
classes; in fact, it already fails for classes with locally bounded
treewidth.
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