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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Beyond the Hoermander condition - Michela Ottobre\
, Heriot Watt University
DTSTART;TZID=Europe/London:20180319T163000
DTEND;TZID=Europe/London:20180319T173000
UID:TALK101437AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/101437
DESCRIPTION: In 1968 Hormander introduced a sufficient conditi
on to ensure hypoellipticity of second order parti
al differential operators. As is well known\, this
seminal work of Hoermander had deep repercussions
both in the analysis of PDEs and in probability t
heory. In this talk we will first review the Horma
nder condition by an analytical\, probabilistic an
d geometric perspective. We then present the UFG c
ondition\, which is weaker than the Hormander cond
ition. Such a condition was introduced by Kusuoka
and Strook in the eighties. In particular\, Kusuok
a and Strook showed that it is still possible to b
uild a solid PDE theory for diffusion semigroups e
ven in absence of the Hormander condition. We will
therefore come to explain the significance of the
UFG condition by various perspectives\, and prese
nt new results (the first of this type to the best
of our knowledge) on the geometry and long time b
ehaviour of diffusion semigroups that do not satis
fy the Hoermander condition. This is a joint work
with P. Dobson\, D. Crisan and T. Cass.\n
LOCATION:CMS\, MR13
CONTACT:Josephine Evans
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