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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A bridge built using differential equations in aut
omorphic forms - Kim Klinger-Logan (Rutgers\, The
State University of New Jersey)
DTSTART;TZID=Europe/London:20220823T160000
DTEND;TZID=Europe/London:20220823T170000
UID:TALK177221AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/177221
DESCRIPTION:In this talk we will attempt to build our metaphir
cal bridge by making a connection between zeros an
d special values of L-functions and scattering amp
litudes. The connection is best seen through solut
ions to differential equations of the form $$(\\De
lta - \\lambda ) f = S$$ on $SL_2(\\mathbb{Z})\\ba
ckslash\\mathfrak{H}$ for $\\Delta=y^2(\\partial_x
^2+\\partial_y^2)$ and $S \\in H^{-infty}(SL_2(\\m
athbb{Z})\\backslash\\mathfrak{H})\\cup M$ where $
M$ is the space of moderate growth functions. Rece
ntly\, Bombieri and Garrett (following work of Has
s\, Hejhal\, and Colin de Verdiere) laid out the p
ossibly connection with eigenvalue solutions to eq
uations of this form with zeros of L-functions.&nb
sp\; On the other hand\, physicists such as Green\
, Kwan\, Russo\, Vanhove found that eigenfunction
solutions to equations of this form give coefficie
nts of the 4-graviton scattering amlitude. We will
elaborate on these connections and discuss some r
ecent work on finiding solutions for such equation
s. This work is in collaboration with Ksenia Fedos
ova\, Stephen D. Miller\, and Danylo Radchenko.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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