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DESCRIPTION: There has recently been a lot of interplay between extremal gr
aph theory and the theory of graph limits. After a brief survey of the theo
ry of dense graph limits\, we focus on exploring a link between Sidorenko's
Conjecture\, one of the most prominent open problems in extremal graph the
ory\, and weakly norming graphs\, one of the concepts studied in the theory
of graph limits. Sidorenko's Conjecture asserts that every bipartite graph
H has the Sidorenko property\, i.e.\, a quasirandom graph minimizes the de
nsity of H among all graphs with the same edge density. We are interested i
n a stronger property\, which we call the step Sidorenko property. We relat
e this property to weakly norming graphs and use our results to construct a
bipartite edge-transitive graph that is not weakly norming - this answers
a question of Hatami [Israel J. Math. 175 (2010)\, 125-150]. The talk is b
ased on joint work with Taisa Martins\, Peter Pal Pach and Marcin Wrochna.
DTSTAMP:20181002T181600
DTSTART:20181008T140000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin Institut für Mathematik Straße des 1
7. Juni 136 10623 Berlin room MA 041 (ground floor)
SEQUENCE:0
SUMMARY:Pre Semester Lecture - Dan Kral (Brno): Step Sidorenko property and
weakly norming graphs
UID:93206714@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20181008-L-Pre-Monday.html
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