BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Buildings of type \\tilde{A}_n and the growth of the natural cocyc
 le for the Steinberg representation
DTSTART:20141127T130000
DTEND:20141127T140000
DTSTAMP:20260916T220422Z
UID:c381fba7172cbf35acba8d5ca788accef1478d11c297cdbca43cf6ac
CATEGORIES:Conferences - Seminars
DESCRIPTION:Thibaut Dumont (EPFL)\nIn this talk\, I will try to present so
 me basics about Euclidean buildings and explain the topic of my Ph.D. thes
 is. Buildings are very complicated structures\; to simplify the picture\, 
 we will keep in mind a building of type \\tilde{A}_n. Those buildings are 
 modelled on the Euclidean space \\mathbb{R}^n tessellated by equilateral n
 -tetrahedrons. I will briefly explain how one gets a building from a (B\,N
 )-pair of a group. The most famous such example is the building of Bruhat 
 and Tits associated to the group SL_{n+1}(F) where F is a non-archimedean 
 local field\, say \\mathbb{Q}_p. Such groups have a unitarisable represent
 ation "St"\, the so-called the Steinberg representation\, which is of coho
 mological interest\, and a natural cocycle "Vol". The latter is a geometri
 cally defined map that sends an n-tuple of points in the building to a vec
 tor in St. The aim of my thesis is to compute the growth of the norm of th
 ese vectors as the points get far away from each other inside the building
 . If time permits\, I will present the case n=1\, in which case the buildi
 ng is the (p+1)-regular tree T and the cocycle Vol is the Busemann cocycle
  of T. Here\, the square of the norm grows at most linearly with the dista
 nce between two points.
LOCATION:MA A 3 31 http://plan.epfl.ch/?room=MA%20A3%2031
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR