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SUMMARY:Beyond the Hoermander condition - Michela Ottobre\, Heriot Watt Un
 iversity
DTSTART:20180319T163000Z
DTEND:20180319T173000Z
UID:TALK101437@talks.cam.ac.uk
CONTACT:Josephine Evans
DESCRIPTION: In 1968 Hormander introduced a sufficient condition to ensure
  hypoellipticity of second order partial differential operators. As is wel
 l known\, this seminal work of Hoermander had deep repercussions both in t
 he analysis of PDEs and in probability theory. In this talk we will first 
 review the Hormander condition by an analytical\, probabilistic and geomet
 ric perspective. We then present the UFG condition\, which is weaker than 
 the Hormander condition. Such a condition was introduced by Kusuoka and St
 rook in the eighties. In particular\, Kusuoka and Strook showed that it is
  still possible to build a solid PDE theory for diffusion semigroups even 
 in absence of the Hormander condition. We will therefore come to explain t
 he significance of the UFG condition by various perspectives\, and present
  new results (the first of this type to the best of our knowledge) on the 
 geometry and long time behaviour of diffusion semigroups that do not satis
 fy the Hoermander condition. This is a joint work with P. Dobson\, D. Cris
 an and T. Cass.\n
LOCATION:CMS\, MR13
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