BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mathieu Dutour (University of Alberta)
DTSTART:20221128T190000Z
DTEND:20221128T200000Z
DTSTAMP:20260423T035415Z
UID:NTC/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/4/">Thet
 a-finite pro-Hermitian vector bundles from loop groups elements</a>\nby Ma
 thieu Dutour (University of Alberta) as part of Lethbridge number theory a
 nd combinatorics seminar\n\nLecture held in University of Lethbridge\, roo
 m M1040 (Markin Hall).\n\nAbstract\nIn the finite-dimensional situation\, 
 Lie's third theorem provides a correspondence between Lie groups and Lie a
 lgebras. Going from the latter to the former is the more complicated const
 ruction\, requiring a suitable representation\, and taking exponentials of
  the endomorphisms induced by elements of the group.\n\nAs shown by Garlan
 d\, this construction can be adapted for some Kac-Moody algebras\, obtaine
 d as (central extensions of) loop algebras. The resulting group is called 
 a loop group. One also obtains a relevant infinite-rank Chevalley lattice\
 , endowed with a metric. Recent work by Bost and Charles provide a natural
  setting\, that of pro-Hermitian vector bundles and theta invariants\, in 
 which to study these objects related to loop groups. More precisely\, we w
 ill see in this talk how to define theta-finite pro-Hermitian vector bundl
 es from elements in a loop group. Similar constructions are expected\, in 
 the future\, to be useful to study loop Eisenstein series for number field
 s.\n\nThis is joint work with Manish M. Patnaik.\n
LOCATION:https://researchseminars.org/talk/NTC/4/
END:VEVENT
END:VCALENDAR