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SUMMARY:Forbidden bipartite configurations in subsets of finite groups - G
 abriel Conant (University of Cambridge)
DTSTART:20191023T124500Z
DTEND:20191023T134500Z
UID:TALK132325@talks.cam.ac.uk
CONTACT:Thomas Bloom
DESCRIPTION:A common theme in additive combinatorics is that if a subset o
 f a group is “approximately structured”\, then it can be approximated 
 by a set that is “perfectly structured”. In this talk\, I will conside
 r subsets A of groups G that are approximately structured in the sense tha
 t the bipartite graph defined by the relation “xy is in A” omits some 
 bipartite graph\, of a fixed finite size\, as an induced subgraph. This ca
 n also be quantified using the VC-dimension of the set system of (left) tr
 anslates of A. I will present several results showing that if a subset of 
 an arbitrary finite group is approximately structured in this way\, then i
 t can be approximated by “perfectly structured” sets such as subgroups
  and Bohr sets. These results qualitatively generalize work of Terry and W
 olf\, and of Alon\, Fox\, and Zhao\, on tame forms of arithmetic regularit
 y in finite abelian groups. The proofs rely on model theory\, as well as c
 lassical results from the structure theory for compact groups. Joint with 
 A. Pillay and C. Terry. 
LOCATION:MR5\, CMS
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