BEGIN:VCALENDAR
VERSION:2.0
PRODID:www.imperial.ac.uk
BEGIN:VEVENT
UID:641c03f479501
DTSTART:20210519T151500Z
SEQUENCE:0
TRANSP:OPAQUE
DTEND:20210519T161500Z
URL:https://www.imperial.ac.uk/events/134355/artem-chernikov/
LOCATION:United Kingdom
SUMMARY:Idempotent Keisler measures – Artem Chernikov
CLASS:PUBLIC
DESCRIPTION:Idempotent Keisler measures – Artem Chernikov\n \nIn model t
heory\, a type is an ultrafilter on the Boolean algebra of definable sets\
, and is the same thing as a finitely additive {0\,1}-valued measure. This
is a special kind of a Keisler measure\, which is just a finitely additiv
e real-valued probability measure on the Boolean algebra of definable sets
. If the structure we are considering expands a group (i.e. the group oper
ations are definable)\, it often lifts to a natural semigroup operation on
the space of its types/measures\, and it makes sense to talk about the id
empotent ones among them. For instance\, idempotent ultrafilters on the in
tegers provide an elegant proof of Hindman’s theorem\, and fit into this
setting taking the structure to be (Z\,+) with all of its subsets named b
y predicates. On the other hand\, in the context of locally compact abelia
n groups\, classical work by Wendel\, Rudin\, Cohen (before inventing forc
ing) and others classifies idempotent Borel measures\, showing that they a
re precisely the Haar measures of compact subgroups. I will discuss recent
joint work with Kyle Gannon aiming to unify these two settings\, leading
in particular to a classification of idempotent Keisler measures in stable
groups and further results on NIP.
X-ALT-DESC;FMTTYPE=text/html:#### Idempotent Keisler measures – Artem Cher
nikov

\n

\nIn model theory\, a *type* is an ultrafilte
r on the Boolean algebra of definable sets\, and is the same thing as a fi
nitely additive {0\,1}-valued measure. This is a special kind of a Keisler
measure\, which is just a finitely additive real-valued probability measu
re on the Boolean algebra of definable sets. If the structure we are consi
dering expands a group (i.e. the group operations are definable)\, it ofte
n lifts to a natural semigroup operation on the space of its types/measure
s\, and it makes sense to talk about the idempotent ones among them. For i
nstance\, idempotent ultrafilters on the integers provide an elegant proof
of Hindman’s theorem\, and fit into this setting taking the structure t
o be (Z\,+) with all of its subsets named by predicates. On the other hand
\, in the context of locally compact abelian groups\, classical work by We
ndel\, Rudin\, Cohen (before inventing forcing) and others classifies idem
potent Borel measures\, showing that they are precisely the Haar measures
of compact subgroups. I will discuss recent joint work with Kyle Gannon ai
ming to unify these two settings\, leading in particular to a classificati
on of idempotent Keisler measures in stable groups and further results on
NIP.

DTSTAMP:20230323T074700Z
END:VEVENT
END:VCALENDAR