Description
Mathematics Colloquium
Date & Time: 26th September 2018, 4-5pm
Venue: Ramanujan Hall
Speaker: Prof.Carlos Conca, University of Chile, Santiago.
Title: Modeling our sense of smell
Abstract
In this lecture, we are interested in the study of an inverse problem for an
integral equation arising from the biology of the human olfaction system.
The transduction of an odour into an electrical signal is accomplished by
a depolarising influx of ions through cyclic-nucleotide-gated (CNG for
short) channels on the cilium membrane. The inverse problem studied is to
determine the spatial distribution of these ion channels from measurements
of the electrical current at the ends of the cilium. The Mellin
transform will allow us to write an explicit formula for its solution, so
obtaining observability or continuity results will then amounts
to punctual estimates of the kernel of this integral equation on vertical
lines of the complex plane. These will be accomplished using arguments in
the spirit of the stationary phase method.