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SUMMARY:Moduli spaces of bundles and Kloosterman sheaves
DTSTART:20130220T131500
DTEND:20130220T150000
DTSTAMP:20260427T200119Z
UID:035bf9c222799a1e0c62dffa8ef3665db216b66ba774b44de5bce4f8
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jochen Heinloth\, Universität Duisburg-Essen\nThe relation be
 tween analytic properties of modular forms and arithmetic results has led
  to many famous results and conjectures. In the geometric analogue of thi
 s conjectural relation - called geometric Langlands correspondence quotie
 nts of the upper half plane are replaced by moduli spaces of bundles on a
  curve (or a Riemann surface). In the first part of the talk I will try t
 o motivate this analogy.\nSince the geometry of these moduli spaces is com
 plicated in general\, very few explicit examples of such modular forms ar
 e known. In joint work with\nB.C. Ngô and Z. Yun\, which was motivated by
  work of Gross and Frenkel\, we found an explicit series of such forms wh
 ich turn out to be closely related to classical Kloosterman sums.\nThis g
 ives a rather explicit example of the (wild) geometric Langlands correspon
 dence. Recently X. Zhu managed to relate this example back to the origina
 l work of Gross and Frenkel. In particular this allows to remove the word
  "rather" from the above. If time permits we will end by giving some indi
 cation on his argument.
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STATUS:CONFIRMED
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