Mahmood Alaghmandan, Pure Mathematics, University of Waterloo
"Amenability properties of Hypergroups"
A
hypergroup
is
a
locally
compact
Hausdorff
space
equipped
with
a
convolution
product
which
maps
any
two
points
to
a
probability
measure
with
a
compact
support.
Hypergroups
generalize
locally
compact
groups
in
which
the
above
convolution
reduces
to
a
point
mass
measure.
In
this
talk,
after
discussing
the
definition
of
hypergroups
and
introducing
algebras
constructed
on
them,
we
study
their
different
amenability
properties.
We
specifically
consider
these
notions
for
some
classes
of
hypergroups
related
to
locally
compact
groups.
Subsequently,
we
demonstrate
some
applications
to
locally
compact
groups
and
their
Banach
algebras.