BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carsten Peterson (Institut de Mathématiques de Jussieu) DTSTART:20250910T220000Z DTEND:20250910T230000Z DTSTAMP:20260423T024700Z UID:UtahRTNT/3 DESCRIPTION:Title: The multitemporal wave equation on Bruhat–Tits buildings\nby Carste n Peterson (Institut de Mathématiques de Jussieu) as part of University o f Utah Representation Theory / Number Theory Seminar\n\nLecture held in LC B 222.\n\nAbstract\nThe Satake isomorphism is an algebra isomorphism from the spherical Hecke algebra $H(G\, K)$ of a (adjoint) semisimple group ove r a non-archimedean local field to $W$-invariant elements in the group rin g of the coweight lattice $P$. The multitemporal wave equation on the Bruh at–Tits building\, first introduced in the work of Anker–Rémy–Troja n '23\, then corresponds to functions $G/K \\times P \\to \\mathbb{C}$ su ch that applying an element in $H(G\, K)$ to the “space variable” $G/K $ is equal to applying its image under the Satake isomorphism in the “ti me variable” $P$. \n\nIn this talk we shall motivate this equation\, lar gely by focusing on the rank one case\, and discuss several of its propert ies such as existence and uniqueness of solutions\, finite speed of propag ation\, conservation of energy\, scattering theory\, and the connection wi th objects of central interest in representation theory such as Schur poly nomials and Kazhdan–Lusztig polynomials. This is based on joint ongoing work with Jean–Philippe Anker\, Bertrand Rémy\, and Bartosz Trojan.\n LOCATION:https://researchseminars.org/talk/UtahRTNT/3/ END:VEVENT END:VCALENDAR