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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Forbidden bipartite configurations in subsets of f
inite groups - Gabriel Conant (University of Cambr
idge)
DTSTART;TZID=Europe/London:20191023T134500
DTEND;TZID=Europe/London:20191023T144500
UID:TALK132325AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/132325
DESCRIPTION:A common theme in additive combinatorics is that i
f a subset of a group is “approximately structured
”\, then it can be approximated by a set that is “
perfectly structured”. In this talk\, I will consi
der subsets A of groups G that are approximately s
tructured in the sense that the bipartite graph de
fined by the relation “xy is in A” omits some bipa
rtite graph\, of a fixed finite size\, as an induc
ed subgraph. This can also be quantified using the
VC-dimension of the set system of (left) translat
es of A. I will present several results showing th
at if a subset of an arbitrary finite group is app
roximately structured in this way\, then it can be
approximated by “perfectly structured” sets such
as subgroups and Bohr sets. These results qualitat
ively generalize work of Terry and Wolf\, and of A
lon\, Fox\, and Zhao\, on tame forms of arithmetic
regularity in finite abelian groups. The proofs r
ely on model theory\, as well as classical results
from the structure theory for compact groups. Joi
nt with A. Pillay and C. Terry.
LOCATION:MR5\, CMS
CONTACT:Thomas Bloom
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