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SUMMARY:Ilaria Castellano (University of Milan - Bicoca)
DTSTART:20210621T080000Z
DTEND:20210621T090000Z
DTSTAMP:20260423T021448Z
UID:SiN/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/24/">The
  Euler characteristic and the zeta-functions of a totally disconnected loc
 ally compact group</a>\nby Ilaria Castellano (University of Milan - Bicoca
 ) as part of Symmetry in Newcastle\n\n\nAbstract\nThe Euler characteristic
  and the zeta-functions of a totally disconnected locally compact group\nA
 bstract: The Euler-Poincaré characteristic of a discrete group is an impo
 rtant (but also quite mysterious) invariant. It is usually just an integer
  or a rational number and reflects many quite significant properties. The 
 realm of totally disconnected locally compact groups admits an analogue of
  the Euler-Poincaré characteristic which surprisingly is no longer just a
 n integer\, or a rational number\, but a rational multiple of a Haar measu
 re. Warning: in order to gain such an invariant the group has to be unimod
 ular and satisfy some cohomological finiteness conditions. Examples of gro
 ups satisfying these additional conditions are the fundamental groups of f
 inite trees of profinite groups. What arouses our curiosity is the fact th
 at - in some cases - the Euler-Poincaré characteristic turns out to be mi
 raculously related to a zeta-function. A large part of the talk will be de
 voted to the introduction of the just-cited objects. We aim at concluding 
 the presentation by facing the concrete example of the group of F-points o
 f a split semisimple simply connected algebraic group G over F (where F de
 notes a non-archimedean locally compact field of residue characteristic p)
 .\nJoint work with Gianmarco Chinello and Thomas Weigel.\n
LOCATION:https://researchseminars.org/talk/SiN/24/
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