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:20260404T132231Z UID:NTC/4 DESCRIPTION:Title: Theta-finite pro-Hermitian vector bundles from loop groups elements \nby Mathieu Dutour (University of Alberta) as part of Lethbridge number t heory and combinatorics seminar\n\nLecture held in University of Lethbridg e\, room M1040 (Markin Hall).\n\nAbstract\nIn the finite-dimensional situa tion\, Lie's third theorem provides a correspondence between Lie groups an d Lie algebras. Going from the latter to the former is the more complicate d construction\, requiring a suitable representation\, and taking exponent ials of the endomorphisms induced by elements of the group.\n\nAs shown by Garland\, this construction can be adapted for some Kac-Moody algebras\, obtained as (central extensions of) loop algebras. The resulting group is called a loop group. One also obtains a relevant infinite-rank Chevalley l attice\, endowed with a metric. Recent work by Bost and Charles provide a natural setting\, that of pro-Hermitian vector bundles and theta invariant s\, in which to study these objects related to loop groups. More precisely \, we will see in this talk how to define theta-finite pro-Hermitian vecto r bundles from elements in a loop group. Similar constructions are expecte d\, in the future\, to be useful to study loop Eisenstein series for numbe r fields.\n\nThis is joint work with Manish M. Patnaik.\n LOCATION:https://stable.researchseminars.org/talk/NTC/4/ END:VEVENT END:VCALENDAR