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DTSTART:20240331T030000
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DTSTAMP:20240304T165428Z
UID:1700491500@ist.ac.at
DTSTART:20231120T154500
DTEND:20231120T164500
DESCRIPTION:Speaker: Isao Sauzedde\nhosted by M. Beiglböck\, N. Berestycki
\, L. Erdös\, J. Maas\, F. Toninelli\, E. Schertzer\nAbstract: We will ta
lk about the determinant of a Laplacian on a continuous space of dimension
2 or 3. As a motivating example\, we will see that this determinant appea
rs naturally as the partition function of a Gaussian free field\, and that
it is necessary to define these determinants in order to pose properly so
me more complicated interacting model. We will then define rigorously thes
e determinants\, through the so-called zeta-regularization method\, and ex
plain why indeed they can be interpreted as determinants. Then\, we will d
efine the Brownian loop soup and show that the determinant we have defined
can be expressed as the expectation of a product over the Brownian loop s
oup. If the time allows it\, we will then look at a few things this formu
la allows to deduce about the determinant\, and at another application of
these determinants to the construction of a very powerful topological inva
riant (i.e. to show that "spheres and tori don't look alike"). The talk i
s based on a joint work with P. Perruchaud (University of Luxembourg).
LOCATION:Mondi 2 (I01.01.008)\, Central Building\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Isao Sauzedde: Stochastic formulas for determinants of Laplacians
URL:https://talks-calendar.ista.ac.at/events/4604
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