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UID:20250723T174641EDT-0387gL0nIo@132.216.98.100
DTSTAMP:20250723T214641Z
DESCRIPTION:Title: A residue map and a Poisson kernel for Drinfeld cusp for
 ms of rank 3\n\nAbstract:Drinfeld modules and Drinfeld modular forms are c
 ertain function field analogs of elliptic curves and classical modular for
 ms. In the first part of this talk\, I will introduce these objects\, as w
 ell as explain analogies and highlight differences compared to the classic
 al case. A new phenomenon appearing is that Drinfeld modules can have arbi
 trary rank\, with Drinfeld modules of rank 2 being the direct analog of el
 liptic curves.\n	In analogy with the classical situation\, it is very usefu
 l to have a combinatorial description of Drinfeld modular forms akin to mo
 dular symbols. In the second part of the talk\, I will discuss recent work
  towards such a description in the next case beyond the well understood ra
 nk-2 theory. More precisely\, I will explain the construction of a residue
  map between Drinfeld cusp forms of rank 3 and of arbitrary weight\, and c
 ertain harmonic cocycles on the Bruhat-Tits building. Assuming a non-criti
 cality statement for certain automorphic forms\, I will show that this res
 idue map is in fact a Hecke-equivariant isomorphism in favorable situation
 s.\n\n \n
DTSTART:20221124T153000Z
DTEND:20221124T170000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Peter Gräf (Boston University)
URL:/mathstat/channels/event/peter-graf-boston-univers
 ity-343761
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