prof. Spera's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT


Mauro Spera
(Universita` di Verona)

The Riemann zeta function as an equivariant Dirac index

In this talk an interpretation of Riemann's zeta function is presented
in terms of an R-equivariant L^2-index of a Dirac-Ramond type operator, 
akin to the one on (mean zero) loops in flat space constructed in 
S.Wurzbacher, JFA (2003). We build on the formal similarity between
Euler's partitio numerorum function (the S^1-equivariant L^2-index
of the loop space Dirac-Ramond operator) and Riemann's zeta function.
Also, a Lefschetz-Atiyah-Bott interpretation of the result is given.
Generalisations to Lapidus' fractal membranes are also discussed.
A fermionic Bost-Connes type statistical mechanical model is presented
as well, exhibiting a "phase transition" at (inverse) temperature
beta = 1, which also holds for some "well-behaved" g-prime systems
in the sense of Hilberdink-Lapidus.



Tuesday 26 June 2012, 14:30, room 136, SISSA

-- 
Dr. Emanuele Tuillier Illingworth
Secretary of the Mathematics Area
Building A, II floor, room 214
phone (+39) 040 37 87 598
fax (+39) 040 37 87 466
SISSA
Via Bonomea 265
34136
Trieste, ITALY
emanuele.tuillier at sissa.it