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SUMMARY:Special cohomology classes arising from the Weil representation - 
 Jens Funke (Durham)
DTSTART:20090226T160000Z
DTEND:20090226T170000Z
UID:TALK15759@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:The Weil representation is a well-known tool to study arithmet
 ic and cohomological aspects of orthogonal groups. \n\nWe construct certai
 n\, "special"\, cohomology classes for orthogonal groups O(p\,q) with coef
 ficients in a finite dimensional representation and discuss their automorp
 hic and geometric properties. In particular\, these classes are generaliza
 tions of previous work of Kudla and Millson and give rise to Poincare dual
  forms for certain\, "special"\, cycles with non-trivial coefficients in a
 rithmetic quotients of the associated symmetric space for the orthogonal g
 roup. \n\nFurthermore\, we determine the behavior of these classes at the 
 boundary of the Borel-Serre compactification of the associated locally sym
 metric space. As a consequence we are able to obtain new non-vanishing res
 ults for the\nspecial cycles. We also indicate how to recover the celebrat
 ed work of Hirzebruch and Zagier on cycles in a Hilbert modular surface.\n
 \nThis is joint work with John Millson.\n
LOCATION:MR13
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