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SUMMARY:Automorphic Forms and Optimization in Euclidean Space
DTSTART;VALUE=DATE-TIME:20190515T080000Z
DTEND;VALUE=DATE-TIME:20190515T100000Z
DTSTAMP;VALUE=DATE-TIME:20210417T180749Z
UID:indico-event-4581@indico.math.cnrs.fr
DESCRIPTION:The goal of this lecture course is to prove the universal opti
mality of the E8 and Leech lattices.\n\nThis theorem is the main result of
a recent preprint "Universal optimality of the E8 and Leech lattices and
interpolation formulas" written in collaboration with Henry Cohn\, Abhinav
Kumar\, Stephen D. Miller and Danylo Radchenko. We prove that E8 and Leec
h lattices minimize energy of every potential function that is a completel
y monotonic function of squared distance (for example\, inverse power laws
of Gaussians).\n\nThis theorem implies recently proven optimality of E8 a
nd Leech lattices as sphere packings and broadly generalizes it to long-ra
nge interactions. The key ingredient of the proof is sharp linear programm
ing bounds. To construct the optimal auxiliary functions attaining these b
ounds\, we prove a new interpolation theorem.\n\nAt the last lecture\, we
will discuss open questions and conjectures which arose from our work.\n\n
https://indico.math.cnrs.fr/event/4581/
LOCATION:IHES Centre de confĂ©rences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/4581/
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