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Joonkyung Lee (이준경), Sidorenko’s conjecture for blow-ups

Thursday, January 3, 2019 @ 4:00 PM - 5:00 PM KST

Room B232, IBS (기초과학연구원)

Speaker

Joonkyung Lee (이준경)
Department of Mathematics, University of Hamburg, Germany
https://sites.google.com/site/joonkyungleemaths/
A celebrated conjecture of Sidorenko and Erdős–Simonovits states that, for all bipartite graphs H, quasirandom graphs contain asymptotically the minimum number of copies of H taken over all graphs with the same order and edge density. This conjecture has attracted considerable interest over the last decade and is now known to hold for a broad range of bipartite graphs, with the overall trend saying that a graph satisfies the conjecture if it can be built from simple building blocks such as trees in a certain recursive fashion.

Our contribution here, which goes beyond this paradigm, is to show that the conjecture holds for any bipartite graph H with bipartition A∪B where the number of vertices in B of degree k satisfies a certain divisibility condition for each k. As a corollary, we have that for every bipartite graph H with bipartition A∪B, there is a positive integer p such that the blow-up HAp formed by taking p vertex-disjoint copies of H and gluing all copies of A along corresponding vertices satisfies the conjecture. Joint work with David Conlon.

Details

Date:
Thursday, January 3, 2019
Time:
4:00 PM - 5:00 PM KST
Event Category:
Event Tags:
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Venue

Room B232
IBS (기초과학연구원)

Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/